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Lamb-shift-induced switching of energy transfer in open quantum batteries

Liang Luo, Shun-Cai Zhao

Abstract

Open quantum batteries (QBs) operate under unavoidable system-environment interactions, where both dissipation and coherent renormalization influence their performance. While most previous studies focus on dissipative effects, the role of environment-induced frequency renormalization, such as the Lamb shift, remains insufficiently explored.In this work, we investigate an externally driven QB composed of two coherently coupled quantum harmonic oscillators, representing the charger and the battery. By incorporating both dissipation and Lamb-shift corrections within a Lindblad master equation, we show that the Lamb shift effectively renormalizes the system eigenfrequencies and thereby modifies the resonance condition with the external drive. We demonstrate that tuning the driving frequency relative to the renormalized eigenmodes leads to a mode-selective energy transfer process, resulting in a controllable redistribution of energy between the charger and the battery. This behavior manifests as a switching of the dominant energy storage channel and can be quantitatively understood through a supermode decomposition of the coupled system. Our results clarify the dynamical role of environment-induced frequency shifts in open quantum batteries and provide a physically transparent framework for optimizing work extraction under realistic operating conditions.

Lamb-shift-induced switching of energy transfer in open quantum batteries

Abstract

Open quantum batteries (QBs) operate under unavoidable system-environment interactions, where both dissipation and coherent renormalization influence their performance. While most previous studies focus on dissipative effects, the role of environment-induced frequency renormalization, such as the Lamb shift, remains insufficiently explored.In this work, we investigate an externally driven QB composed of two coherently coupled quantum harmonic oscillators, representing the charger and the battery. By incorporating both dissipation and Lamb-shift corrections within a Lindblad master equation, we show that the Lamb shift effectively renormalizes the system eigenfrequencies and thereby modifies the resonance condition with the external drive. We demonstrate that tuning the driving frequency relative to the renormalized eigenmodes leads to a mode-selective energy transfer process, resulting in a controllable redistribution of energy between the charger and the battery. This behavior manifests as a switching of the dominant energy storage channel and can be quantitatively understood through a supermode decomposition of the coupled system. Our results clarify the dynamical role of environment-induced frequency shifts in open quantum batteries and provide a physically transparent framework for optimizing work extraction under realistic operating conditions.
Paper Structure (7 sections, 13 equations, 4 figures)

This paper contains 7 sections, 13 equations, 4 figures.

Table of Contents

  1. INTRODUCTION
  2. Model and Theoretical Framework
  3. Results and Discussions
  4. Impact of Lamb shift on energy distribution
  5. Physics analysis and interpretation
  6. Experimental Feasibility
  7. Conclusion

Figures (4)

  • Figure 1: Schematic of the quantum battery(QB) system. The charger (middle) and battery (right) are quantum harmonic oscillators coupled with strength $g$ (green arrow). The external driving field (left) initiates the charging process (red arrow), while interaction with the environment $E$ leads to both dissipation and an interference-induced shift (blue bidirectionalarrow) between the charger and the thermal reservoir.
  • Figure 2: Evolution of output energy (the charger energy $W_A$, the battery ergotropy$W_B$) under weak resonant coupling between charger and quantum battery. Here, $\omega_f = \lambda_{-}$ for (a) and (b), $\omega_f = \lambda_{+}$ for (c) and (d), $g= 0.16\omega$, $F = 0.1\omega$, $\gamma_a = 0.05\omega$, and $N(T)$ = 0, $\omega$ is the scaling unit.
  • Figure 3: Evolution of output energy (the charger energy $W_A$, the battery ergotropy$W_B$ under strong resonant coupling between charger and quantum battery. Here, $\omega_f =\lambda_{-}$ for (a) and (b), $\omega_f = \lambda_{+}$ for (c) and (d), $g= 1.6\omega$, other parameters are the same to Fig.\ref{['fig1']} .
  • Figure 4: Evolution of output energy (the charger energy $W_A$, the battery ergotropy$W_B$ under nonresonant strong coupling between charger and quantum battery. Here, $\omega_f =\lambda_{-}$ for (a) and (b), $\omega_f = \lambda_{+}$ for (c) and (d), $\omega_a =\frac{2}{3}\omega_b$, other parameters are the same to Fig.\ref{['fig2']}.