diff --git "a/DNFRT4oBgHgl3EQfxDge/content/tmp_files/load_file.txt" "b/DNFRT4oBgHgl3EQfxDge/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/DNFRT4oBgHgl3EQfxDge/content/tmp_files/load_file.txt" @@ -0,0 +1,671 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf,len=670 +page_content='Vacuum enhanced charging of a quantum battery Tiago F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Santos,1 Yohan Vianna de Almeida,1 and Marcelo F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Santos1, ∗ 1Instituto de F´ısica, Universidade Federal do Rio de Janeiro, CP68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil (Dated: February 1, 2023) Quantum batteries are quantum systems that store energy which can then be used for quantum tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' One relevant question about such systems concerns the differences and eventual advantages over their classical counterparts, whether in the efficiency of the energy transference, input power, total stored energy or other relevant physical quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Here, we show how a purely quantum effect related to the vacuum of the electromagnetic field can enhance the charging of a quantum battery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In particular, we demonstrate how an anti-Jaynes Cummings interaction derived from an off-resonant Raman configuration can be used to increase the stored energy of an effective two-level atom when compared to its classically driven counterpart, eventually achieving full charging of the battery with zero entropic cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The quest for advanced quantum technologies or the ir- reversible role of measurements in quantum dynamics are examples of subjects that have stimulated the study of thermodynamics in the microscopic world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' An important recent topic of investigation involves the role played by quantum resources in the storage and use of energy by quantized systems [1–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' For example, coherence and entanglement have been proven useful to speed up or to super-extend the charging of quantum batteries [20– 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Experimental results have also shown advances to- wards the production of microscopic quantum thermal machines and quantum batteries [28–33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Most results re- garding quantum properties influencing the performance of quantum batteries, however, focus on increasing the power of the process rather than enhancing the charg- ing capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' That is because the latter usually requires entropy producing mechanisms [7–12, 18] that have dele- terious effects in properties such as coherence and entan- glement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In this work we investigate how the quantized nature of part of an entropy preserving charging circuit can in- fluence the charging of a quantum battery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The circuit comprises a classical power source (p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=') and an auxiliary frequency changer (f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' We compare the variation of the internal energy stored in the battery and the efficiency of the work extraction from the p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=', both for a classical and quantum version of the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In both cases, the overall dynamics is unitary and, therefore, comes at zero entropic cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In the classical scenario, both p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' and f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' are connected to the battery for a fixed amount of time, τc (“c” for classical), unitarily charging its ini- tially thermal state: ρB(τc) = Uc(τc)ρT BU −1 c (τc), where Uc(τc) is derived from the coupling Hamiltonian Hc = HB0 + Vp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (t) + Vf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (t), Vj(t) is the potential created by the circuit component j and HB0 is the free Hamilto- nian of the battery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Thermal states are free resources in thermodynamics [34–36] and, therefore, ideal to establish the classical benchmark to be challenged by the quantum version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The charging is measured by the variation ∆U of internal energy of the battery, where U = Tr[ρBHB0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In the quantized version, Vf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (t) is replaced by the inter- action Hamiltonian HB−f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (t) and the initial state must include the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' system which is also in a thermal state: ρ(0) = ρT B ⊗ ρT f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='. The variation of energy of the bat- tery is now given by ∆U = Tr{[ρB(τq) − ρT B]HB0} ( “q” for quantum) where ρB(τq) = Trf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='Uq(τq)ρ(0)U −1(τq) and Uq is the time evolution operator obtained from Hq = HB0 + Hf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0 + HB−f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c(t) + Vp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Note that, in both cases we assume isolation from the environment and the charging does not produce any entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' For com- pleteness, we later add dissipative non-unitary terms to the dynamics to verify how our results are affected by the heat exchanged with surrounding reservoirs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' We investigate the classical protocol in a particular setup where the battery is an oscillating two-level sys- tem of frequency ωeg, the p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' generates an oscillat- ing potential of frequency ωL > ωeg and the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='. gen- erates another potential of frequency ωq = ωL − ωeg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This situation is commonly found in many different quantum optical experiments [37–43], where the battery consists of two non-degenerate ground states {|g⟩, |e⟩} (ωeg ≡ ωe − ωg > 0) of a real or artificial atom and two modes of the electromagnetic field play the role of power supply and f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='. The couplings are intermedi- ated by a third atomic level |m⟩ working as an ancilla as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (1a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Level |m⟩ should only con- tribute virtually to the transference of energy and has to be adiabatically eliminated from the dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This is achieved when each of p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' and f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' couples off- resonantly one of the lower levels of the battery to |m⟩ in a Raman configuration, where HB0 = ℏ � j=g,e,m ωjσjj (σjk ≡ |j⟩⟨k|), Vf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (t) = ℏΩq(σemeiωqt + σmee−iωqt) and Vp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (t) = ℏΩL(σgmeiωLt + σmge−iωLt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' If ∆ = ωmg − ωL = ωme − ωq ≫ ΩL, Ωq, the corresponding time evolution Uc(t) induces Rabi oscillations between levels |g⟩ and |e⟩ that are equivalent to directly cou- pling them through one effective classical field of cou- pling strength ¯Ω = ΩLΩq ∆ [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The optimal charg- ing of the battery is then obtained for a full Rabi flip that swaps the populations pT g,e in the original ther- arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='13640v1 [quant-ph] 31 Jan 2023 2 mal state ρT B = � j=g,e pT j σjj, where pT j = e ℏωj KBT ZB and ZB = � j e ℏωj KBT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In this case, ∆Uc = ℏωeg[pT g − pT e ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Note that this is the most that a unitary transforma- tion can charge an initially thermalized two-level bat- tery and corresponds to the ergotropy Ec of the resulting state, ρB(τc) = pT e σgg + pT g σee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Ergotropy is defined as Eρ(τ) = � k,j rkEj(|⟨rk|Ej⟩|2 − δkj), where Ej are the eigenenergies of H0 in increasing magnitude, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=', Ei ≥ Ej for i > j, and rk are the eigenvalues of ρ(τ) in decreasing order, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=', ri ≤ rj for i > j [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' |m〉 |e〉 |g〉 Δ 𝛀L gq, 𝛀q 𝚪mg 𝚪gm 𝚪em 𝚪me |e〉 |g〉 N = 1 |e, 0〉 |e, 1〉 |g, 0〉 N = 2 N = k |e, 2〉 |e, k〉 |g, 1〉 |g, k-1〉 N = 1 N = 2 N = k (a) (b) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (a) off-resonant Raman configuration: the battery is a two-level atom ({|g⟩, |e⟩});' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' the p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' is a laser of frequency ωL (coupling ΩL), the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' is another harmonic oscillator of frequency ωq and couplings Ωq (classical) and gq (quantum).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Level |m⟩ is an ancilla that intermediates both couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Each channel can also exchange heat with the surrounding reservoirs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='the battery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (b) Selective scheme to charge the bat- tery: in each step N, a selective Rabi flip transfers energy from |g, N − 1⟩ to |e, N⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' If, now, the classical f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' is replaced by a quantized field, we need to add its free energy Hf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0 = ℏωqˆb†ˆb to the Hamiltonian, where ˆb† creates an excitation, and replace Vf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (t) by the interaction term HB−f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' = ℏgq(σemˆb†+σmeˆb).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Once again, for ∆ ≫ ΩL, gq, we elim- inate level |m⟩ and, as shown in [46–48], the dynamics of the Battery-f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' system becomes approximately given by the effective Hamiltonian (ℏ = 1) Heff = −g2 qN ∆ σgg − g2 qˆb†ˆb ∆ σee + ΩLgq ∆ (σgeˆb + σegˆb†), (1) Note that Heff also includes a small correction to the energy difference between levels |g⟩ and |e⟩, given by ℏ∆N eg = ℏ Ω2 L−g2 qN ∆ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This term, of the same order of Heff, does not affect the conditions for eliminating |m⟩ and can be physically implemented by applying a d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Stark shift to the atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' There are a few aspects of Heff useful for us: first, the a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Stark shift correction to level |e⟩ depends on the number of excitations of the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' and |e, 0⟩ is an eigen- state of Heff with eigenvalue 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' second, the Rabi oscil- lations occur in the joint Hilbert space of atom and f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=', splitting it into doublets {|g, n⟩, |e, n + 1⟩}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This corre- sponds to the anti-Jaynes-Cummings (anti-JC) configu- ration where the p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' excites both the battery and the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Third, each doublet oscillates at its own Rabi frequency given by Ωn = � ∆2n/4 + G2n, where ∆n = r2Ω2 L(n+1−N) ∆ , Gn = rΩ2 L √n+1 ∆ and r ≡ gq ΩL , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' each doublet is detuned from resonance by an amount ∆n proportional to the number of excitations of the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='. Such Hamiltonians were predicted and implemented in trapped ions, cavity QED and superconducting cir- cuits, and for r ≫ 1, they operate in a selective regime where ∆n ≫ Gn and the Rabi oscillation in all the dou- blets is highly detuned except if n = N − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In this case, {|g, N −1⟩, |e, N⟩} oscillates resonantly (∆N−1 = 0, ΩN−1 = rΩ2 L √ N ∆ ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Therefore, by properly choosing ∆N eg the battery population exchange is conditioned on the number of excitations of the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' field as shown in [46, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' For example, for N = 1, after an interaction time τq = π∆ 2rΩ2 L , the population in the {|g, 0⟩, |e, 1⟩} subspace swaps while all other states only gain number dependent phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' That takes the initial state ρ(0) = ρT B ⊗ ρT f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' to ρ(τq) = pT e pT 0 |e, 0⟩⟨e, 0| + pT g pT 0 |e, 1⟩⟨e, 1| + pT e pT 1 |g, 0⟩⟨g, 0| + pT g pT 1 |g, 1⟩⟨g, 1| + ( � n>1 pT n|n⟩⟨n|) ⊗ ρT B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (2) Here, ρT f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' = � n pT nσnn, pT n = e− nℏωq KBT (1 − e− ℏωq KBT ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' A simple algebraic manipulation shows that this swap in- creases the charge of the battery by ∆Uq = (pT 0 pT g − pT e pT 1 )ℏωeg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In this case, there is an advantage over ∆Uc if pT e pT g > 1−pT 0 1−pT 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' We can better understand this condition at low temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' When KBT ≪ ℏωq, ℏωm, the prob- abilities pT n are negligible for n > 1 and so is pT m and we can approximate 1 − pT 1 ≈ pT 0 and pT e ≈ 1 − pT g , mean- ing that ∆Uq > ∆Uc if pT e pT 0 pT g pT 1 ≈ e ℏωeg(ξ−1) KBT > 1, where ξ = ωq ωeg .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This happens whenever ξ > 1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' whenever the battery’s gap is smaller than one excitation of field ˆb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In principle, the larger the value of ξ, the more accentu- ated the enhancement due to the vacuum of field ˆb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This is a purely quantum effect due solely to the vacuum of the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Note, however, that the quantum protocol allows for the relaxation of the ξ > 1 condition and an even more enhanced charging, which is a much more powerful result, due to the selectivity of Heff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In fact, similar Rabi flips can be sequentially applied, each one tuned to resonance by adjusting ∆N eg in consecutive subspaces (N = 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=') as pictorially shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (1b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In principle, this se- quence must be infinite to maximize the charging of the battery but, in practice, pT n tends rapidly to zero unless T is very high, and only a few cycles are required to ap- proach maximum charging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' After the sequence, the final 3 state reads ρ(� j τqj) ≈ [pT e (1 − pT 0 )σgg + (pT g + pT e pT 0 )σee and the variation of internal energy is ∆Uq = ∆Uc + pT e pT 0 ℏωeg ≥ ∆Uc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This shows an advantage for any pos- itive temperature and independent of ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' More than that, in the limit of ℏωq ≫ KBT, pT 0 → 1 and the quantized protocol fully charges the battery, independent of its ini- tial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This is a purely quantum effect due to the vacuum of the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' and consists in the main result of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Not that similar charging can be obtained with open system entropy producing dynamics, such as opti- cal pumping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Here, we match it in an entropy preserving protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This sequence of cycles, however, can be cumbersome and, in practice, escape from the isentropic condition of no heat exchanged with external reservoirs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Furthermore, the classical protocol is much faster, only requiring one Rabi flip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' One may wonder, then, if the quantized ad- vantage still holds under equivalent restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' To an- alyze this, we compute, from now on, single shot scenar- ios designed with a sole detuning adjustment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The en- ergy variation is obtained by solving the Von-Neumann equation with Heff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The separation of Heff in doublets makes it easy to derive the time evolution of the eigen- states of HB0 + Hf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The anti-JC dynamics is similar to the JC and it is simple to show that an initial state |Ψ(0)⟩ = |g, n⟩ evolves to |Ψ(t)⟩ = e−i∆nt/2[(cos Ωnt + i∆n 2Ωn sin Ωnt)|g, n⟩ − iGn Ωn sin Ωnt|e, n + 1⟩].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' A similar ex- pression can be found for the initial state |e, n+1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' There- fore, after evolving for τq, the state of the battery changes to ρB(τq) = Trf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [e−iHeff τq/ℏ(ρT B ⊗ ρT f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' )eiHeff τq/ℏ] = � pjσjj where pg = pT g − S(τq), pe = pT e + S(τq) and pm = pT m (due to the elimination of level |m⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Here, S(τq) = �∞ n=0 An[pT g pT n(0) − pT e pT n+1] sin2 � Ωnτq 2 � , An = 1 1+ r2(n+1−N0)2 4(n+1) and r = gq ΩL (see Sup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' for full deriva- tion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In this case, ∆Uq = ℏωegS(τq) and the battery’s ergotropy reads Eq = ℏωeg[pT e −pT g +2S(τq)] = 2∆Uq−Ec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The quantized version will be advantageous whenever ∆Uq > Ec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' A quick inspection of S(τq) shows that, for single shots (ss), it is the non-selective regime of r ≪ 1 that optimizes the charging of the atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In this case, all the doublets evolve almost resonantly, each of them contributing to enhance the charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Because they oscillate at different Rabi frequencies, it is impossible to choose a τq,ss that simultaneously maximizes the energy transfer in all of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The optimal interaction time, which depends on T, has to be numerically extracted by maximizing S(t) and, because higher excited states oscillate faster, it gets shorter for higher temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (2) we plot the relative gain Kq ≡ ∆Uq ss−∆Uc ∆Uc = ∆Uq ss ∆Uc − 1 induced by the single shot quantized protocol as a function of ξ and for two temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Note that, similar to the single shot selective case, Kq increases with T and requires ξ > 1 to represent positive gain over the classical counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' We also plot in the same figure the efficiency of the work extraction, defined as η ≡ Eq WL , where WL is the work injected by the power supply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The first law of thermodynamics says that WL = ∆Uq + ∆Ufc where ∆Ufc = ℏωqS(τq) is the energy variation of the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='. Therefore, the efficiency assumes the very simple formula η = 1 1+ξ 1+2Kq 1+Kq .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' For a fixed value of ξ, the best efficiency, η = 2 1+ξ, is achieved when Kq ≫ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' On the other hand, because ξ > 1 is a necessary condition for the advan- tage of the single shot quantum protocol and because Kq increases for larger values of ξ, it is clear that the best gains are achieved at lower efficiencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This should be expected since ξ ≫ 1 means that most of the energy in- jected by the power supply is actually going to the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='. Note that for each temperature, there is an ideal value of ξ if one wishes for the best gain at a given efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Relative gain Kq = ∆Uq−∆Uc ∆Uc (blue, straight) and efficiency η = Eq WL (red, curved) as a function of parameter ξ = ωq ωeg for different values of the adimensional temperature ¯T = KBT ℏωm (≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='1 for solid and ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='4 for dashed lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' ∆ 2π = 1 MHz, gq = ∆ 600, ΩL = ∆ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' So far, we have considered the isentropic injection of energy by the external source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' However, neither the battery nor the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' are ever fully isolated from their environment and there will always be heat exchanged with the external reservoir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' From the battery’s perspec- tive, if both |g⟩ → |m⟩ and |e⟩ → |m⟩ transitions are dipole coupled, levels |g⟩ and |e⟩ must be of the same parity and, therefore, cannot be dipole coupled them- selves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' That means that the time scale for direct energy exchange between them is usually much slower than any other time scale of the problem and, in general, the cor- responding heat channel can be ignored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Considering the standard weak coupling to thermal reservoirs, the overall dynamics of the system is, then, governed by a master equation of the form ˙ρ = − i ℏ[Hq, ρ] + L(ρ) [49], where L(ρ) = � s Γs[2LsρL† s − {L† sLs, ρ}], with s = gm, mg, em, me, +, −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The rates of the non-unitary parts are given by Γjm = γ0j(¯nj + 1), Γmj = γ0j¯nj, Γ− = 0 20 40 60 80 100 35 6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='6 Kq n 30 E 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='5 25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='4 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='3 15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='2 10 E 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0 0 20 40 60 80 100 54 γ0q(¯nq + 1), and Γ+ = γ0q¯nq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Here, the γ0’s indicate the spontaneous decay rates and ¯n’s the average number of photons of the thermal reservoir at frequencies ωmj and ωq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The respective jump operators are Ljk = σjk, L− = ˆb and L+ = ˆb†.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0 T 0 10 20 30 40 50 60 Kq 0 = 0 0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='01 gq L 0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='1 gq L 0 = gq L 0 = 10 gq L FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Relative gain as a function of the adimensional tem- perature ¯T ≡ kBT ℏωm for different values of spontaneous decay rates γ0 and for ξ = 99, ∆ 2π = 1 MHz, gq = ∆ 600, ΩL = ∆ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The solid curve is obtained from the unitary evolution with Heff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The dotted curves are numerical solutions of the open system dynamics (master equation) with full Hamiltonian Hq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The couplings to the thermal reservoirs establish at least four typical regimes to the problem, depending on their strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The first one, already addressed, corre- sponds to γ0’s much smaller than the effective coupling gqΩL ∆ and kBT ≪ ℏωeg, ℏωq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This is well approximated by the isentropic dynamics considered so far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' However, we saw that the higher the temperature, the more advan- tageous the quantum protocol is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This may not hold true when we take into consideration the heat exchanges with the reservoir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' As the spontaneous decay rates increase, a combination of effects begin to affect the charging of the battery and may even create optimal temperatures for better quantum gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (3) we present Kq as a function of the adimen- sional temperature ¯T ≡ kBT ℏωm for different values of γ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' ¯T is relevant to the problem because it regulates the pop- ulation of level |m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Although each reservoir has its own spontaneous decay rate, they all produce similar effects on both Kq and η, therefore we have considered a single γ0 for all of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The result was obtained by solving the full dynamics of the open quantum system and choos- ing the best τq,ss for each temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In these plots, ωm 2π = 1012Hz, ∆ = 2πMHz = 600g = 20ΩL, ξ = 99, r = 1/30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' As previously discussed, for γ0 ≪ gqΩL ∆ we reach the unitary regime calculated with Hamiltonian (1) (solid curve), except for very high temperatures ( ¯T ∼ 2) when the population of level |m⟩ becomes too significant and start to affect the protocol as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' As we in- crease γ0, effects such as decoherence of the f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' field and the augmented relaxation rates Γj begin to limit the quantum advantage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' These effects become particularly relevant when Γ’s rates approach the effective battery- f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' coupling gqΩL/∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Note, however, that even for such values of dissipation, the quantum protocol can still pro- duce gains 30 times larger than its classical counterparts for ξ = 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Finally, a fourth effect takes place for higher values of γ0 and at much higher temperatures: when Γ’s become of the order of ∆ the heat exchange eventually brings the transitions back into resonance in which case level |m⟩ cannot be adiabatically eliminated anymore and the charging scheme breaks down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='00 T 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0050 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0075 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0125 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0175 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='0200 0 = 0 0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='01 gq L 0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='1 gq L 0 = gq L 0 = 10 gq L FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Efficiency as a function of the adimensional tempera- ture ¯T ≡ kBT ℏωm for different values of spontaneous decay rates γ0 and for ξ = 99, ∆ 2π = 1 MHz, gq = ∆ 600, ΩL = ∆ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The solid curve is obtained from the unitary evolution with Heff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The dotted curves are numerical solutions of the open system dynamics (master equation) with full Hamiltonian Hq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' (4) we repeat the numerical calculations of the open system dynamics (same parameters), this time for the efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Again, we see that very low γ0’s are consistent with the isentropic hypothesis, whereas higher values of the spontaneous decay rates severely affect the efficiency, specially for higher values of ¯T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Note that for some parameters, the plotted efficiency is corrected to η = Eq WL+Qem to adjust for the fact that the |e⟩ → |m⟩ reservoir may also inject energy in the system in the form of heat Qem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' The correction takes place whenever we obtain Qem > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' To conclude, we have shown that the quantized nature of a component of a charging circuit can significantly enhance the isentropic charging of a quantum battery when benchmarked against its classical counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This is a purely quantum effect due to the vacuum state of the quantized component and the ability to selectively manipulate quantum states in the Hilbert space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' We have also shown that our protocol can achieve the same full charging capacity of open system entropy producing equivalent schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' We have demonstrated the effect in 5 a typical setup of off-resonant Raman population transfer in three-level λ−configuration where the power supply is an external laser field and the quantized component is a harmonic oscillator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This example is particularly useful due to its broad presence in a variety of quantum opti- cal setups such as trapped ions and atoms, cavity QED, superconducting qubits, quantum dots and many other equivalent experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' This work was supported by CNPq Projects 302872/2019-1, INCT-IQ 465469/2014-0, and FAPERJ project E-26/202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='576/2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' TFFS and YVA thank Capes for financial support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' ∗ Corresponding author: mfsantos@if.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='ufrj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='br [1] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Hovhannisyan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Perarnau-Llobet, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='s Huber, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Ac´ın, Entanglement Generation is Not Neces- sary for Optimal Work Extraction, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 111, 240401 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [2] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Binder, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Vinjanampathy, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Modi & J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Goold, Quantacell: power charging of quantum batteries, New Journal of Physics 17, 075015 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [3] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Ferraro, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Campisi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Andolina, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Pellegrini & M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Polini, High-power collective charging of a solid-state quantum battery, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 120, 117702 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [4] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Andolina, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Keck, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Campisi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Gio- vannetti and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Polini, Extractable Work, the Role of Correlations, and Asymptotic Freedom in Quantum Bat- teries, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 122, 047702 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [5] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Andolina, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Farina, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mari, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Pellegrini, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Giovannetti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Polini, Charger-mediated energy trans- fer in exactly solvable models for quantum batteries, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' B 98, 205423 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [6] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Farina, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Andolina, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Polini and Vittorio Giovannetti, Charger-mediated energy transfer for quantum batteries: An open-system approach, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' B 99, 035421 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [7] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Barra, Dissipative Charging of a Quantum Battery, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 122, 210601 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Santos, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' C¸akmak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Campbell and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Zinner, Stable adiabatic quantum batteries, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' E 100, 032107 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Crescente, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Carrega, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Sassetti and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Ferraro, Charging and energy fluctuations of a driven quantum battery, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 22 063057 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [10] Sergi Julia-F`arr´e, Tymoteusz Salamon, Arnau Riera, Manabendra N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Bera, and Maciej Lewenstein, Bounds on the capacity and power of quantum batteries, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Research 2, 023113 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [11] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Tacchino, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Santos, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Gerace, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Campisi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Santos, Charging a quantum battery via nonequi- librium heat current, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' E 102, 062133 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Carrega, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Crescente, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Ferraro and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Sassetti, Dissipative dynamics of an open quantum battery, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 22 083085 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [13] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Kamin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Tabesh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Salimi, and Alan C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' San- tos, Entanglement, coherence, and charging process of quantum batteries, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' E 102, 052109 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [14] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Santos, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Tacchino, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Gerace, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Campisi and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Santos, Maximally efficient quantum thermal machines fueled by nonequilibrium steady states, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' A 103, 062225 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [15] Thiago R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' de Oliveira and Daniel Jonathan, Efficiency gain and bidirectional operation of quantum engines with decoupled internal levels, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' E 104, 044133 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [16] Javier Carrasco, Jer´onimo R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Maze, Carla Hermann- Avigliano, and Felipe Barra, Collective enhancement in dissipative quantum batteries, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' E 105, 064119 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [17] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Maillette de Buy Wenniger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Thomas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Maffei, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Wein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Pont, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Harouri, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lemaˆıtre, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Sagnes, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Somaschi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Auff`eves, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Senellart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Coherence- powered work exchanges between a solid-state qubit and light fields, arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='01109 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [18] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Santos and Marcelo F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Santos, Efficiency of opti- cally pumping a quantum battery and a two-stroke heat engine, arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='02373 (2022), accepted in Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [19] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Ahmadi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mazurek, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rodr´ıguez, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Barzan- jeh, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Alicki, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Horodecki, Catalysis in Charging Quantum Batteries, arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='05018 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [20] Francesco Campaioli, Felix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Pollock, Felix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Binder, Lucas C´eleri, John Goold, Sai Vinjanampathy, and Ka- van Modi, Enhancing the Charging Power of Quantum Batteries, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 118, 150601 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [21] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Le, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Levinsen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Modi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Parish, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Pollock, Spin-chain model of a many-body quantum battery, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' A 97, 022106 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [22] YY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Zhang, TR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Fu and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Wang, Powerful harmonic charging in a quantum battery, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' E 99, 052106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [23] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Zakavati, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Tabesh, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Salimi, Bounds on charging power of open quantum batteries, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' E 104, 054117 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Ghosh, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Chanda, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mal, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Sen, Fast charging of a quantum battery assisted by noise, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' A 104, 032207 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [25] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='Seah, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Perarnau-Llobet, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Haack, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Brunner, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Nimmrichter, Quantum Speed-Up in Collisional Bat- tery Charging, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 127, 100601 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [26] James Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Quach, and William J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Munro, Using Dark States to Charge and Stabilize Open Quantum Batteries, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Applied, 14, 024092 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [27] JX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Liu, HL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Shi, YH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Shi, XH Wang, and WL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Yang, En- tanglement and work extraction in the central-spin quan- tum battery, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' B 104, 245418 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Roßnagel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Dawkins, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Tolazzi, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Abah, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lutz, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Schmidt-Kaler, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Singer, A single-atom heat engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Science 352, 325–329 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [29] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' von Lindenfels, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Gr¨ab, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Schmiegelow, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Kaushal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Schulz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mitchison, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Goold, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Schmidt-Kaler, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Poschinger, Spin heat engine coupled to a harmonic oscillator flywheel, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 123, 080602 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Klatzow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Becker, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Ledingham, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Weinzetl, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Kaczmarek, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Saunders, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Nunn, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Walms- ley, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Uzdin, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Poem, Experimental demonstration of quantum effects in the operation of microscopic heat engines, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 122, 110601 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [31] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Van Horne, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Yum, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Dutta, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' H¨anggi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Gong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Poletti, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mukherjee, Single-atom energy- conversion device with a quantum load, npj Quantum Information 6, 37 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 6 [32] James Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Quach, Kirsty E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' McGhee, Lucia Ganzer, Do- minic M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rouse, Brendon W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lovett, Erik M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Gauger, Jonathan Keeling, Giulio Cerullo, David G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lidzey, and Tersilla Virgili.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Superabsorption in an organic micro- cavity: Toward a quantum battery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Science advances, 8(2):eabk3160, (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [33] Chang-Kang Hu et al, Optimal charging of a super- conducting quantum battery, Quantum Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 7 045018 (2022) [34] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Goold, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Huber, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Riera, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' del Rio and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Skrzypczyk, The role of quantum information in thermo- dynamics—a topical review, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' A: Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 49 143001 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [35] Matteo Lostaglio, An introductory review of the resource theory approach to thermodynamics, Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys 82 114001 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [36] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Narasimhachar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Assad, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Binder, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Thomp- son, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Yadin, and Mile Gu, Thermodynamic resources in continuous-variable quantum systems, npj Quantum Inf 7, 9 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [37] Michael Fleischhauer, Atac Imamoglu, and Jonathan P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Marangos, Electromagnetically induced transparency: Optics in coherent media, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 77, 633 (2005) [38] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Bergmann, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Theuer, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Shore, Coherent population transfer among quantum states of atoms and molecules, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 70, 1003 (1998) [39] Petr Kr´al, Ioannis Thanopulos, and Moshe Shapiro, Col- loquium: Coherently controlled adiabatic passage, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 79, 53 (2007) [40] Nikolay V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Vitanov, Andon A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rangelov, Bruce W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Shore, and Klaas Bergmann, Stimulated Raman adia- batic passage in physics, chemistry, and beyond, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 89, 015006 (2017) [41] Carl E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Wieman, David E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Pritchard, and David J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Wineland, Atom cooling, trapping, and quantum manip- ulation, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 71, S253 (1999) [42] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Leibfried, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Blatt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Monroe, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Wineland, Quantum dynamics of single trapped ions, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 75, 281 (2003) [43] Klemens Hammerer, Anders S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Sørensen, and Eugene S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Polzik, Quantum interface between light and atomic en- sembles, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 82, 1041 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [44] E Brion, L H Pedersen1 and K Mølmer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' A: Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 40, 1033 (2007) [45] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Allahverdyan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Balian, and Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Nieuwen- huizen, Maximal work extraction from finite quantum systems, Europhys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 67, 565 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [46] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Santos, E Solano, RL de Matos Filho, Conditional large Fock state preparation and field state reconstruc- tion in Cavity QED, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 87, 93601 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [47] MF Santos, Universal and deterministic manipulation of the quantum state of harmonic oscillators: a route to unitary gates for Fock State qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' 95, 010504 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' [48] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Zagury, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Arag˜ao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Casanova, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Solano, Uni- tary expansion of the time evolution operator, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' A, 82, 042110 (2010) [49] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Breuer and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'} +page_content=' Petruccione, The theory of open quantum systems (Oxford University Press, 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/DNFRT4oBgHgl3EQfxDge/content/2301.13640v1.pdf'}