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.
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.
Abstract Quantum batteries are designed to outperform classical batteries by utilizing quantum effects, particularly in charging speed and energy storage efficiency. Quantum batteries based on chargers that interact periodically with an external energy source are analyzed within an open quantum system framework, with battery performance parameters such as charging time and total energy utilized for evaluation. In this paper, the charger and quantum battery are modeled as a quantum harmonic oscillator, and their interaction is governed by the Lindblad master equation. The energy function of the quantum battery is determined by the first momenta obtained by solving a system of coupled first-order linear differential equations formed from the master equation. Based on these results, we investigate the effect of periodic driving on energy charging, energy stability, and decoherence effects in the quantum battery.
We analyze the performance of a quantum battery in terms of energy storage and energy extraction, assisted by nonlinearities in a charger-battery system utilizing an open-system approach. In particular, we consider two types of nonlinearities in the system, viz. nonlinearity in the coupling between battery and charger, and the charger itself comprising an anharmonic oscillator. In both these scenarios, the charger is connected to an environment, and is driven by an external laser source. We derive the Markovian master equation for the dynamics of the combined charger-battery system in presence of the environment. When the charger is non-linearly coupled to a battery, we find an enhancement in the steady state ergotropy over the linearly-coupled case. We further see that the times at which steady state and maximum ergotopies are attained get decreased in presence of non-linear coupling. We also identify instances where no ergotropy is obtained in the linear case, but can be obtained in presence of any non-zero value of nonlinearity. We additionally find a complementarity between the non-linear interaction strength and the coherent-drive strength in the steady-state ergotropy values, i.e. the same ergotropy as that obtained using weak nonlinearity and strong coherent drive can be obtained utilizing an opposite order of their values. In case when the charger is modeled as a multi-level transmon with an inherent anharmonicity, we find an advantage in maximum ergotropy values over the harmonic instance. Unlike the non-linearly coupled batteries, the ones mediated by an anharmonic charger prove to be useful in the transient regime. We also determine values of the coherent drive for which the anharmonic battery is beneficial over the harmonic one at all timescales. Further, we observe a distinct region of the anharmonic strength and coherent drive where ergotropy values reach their maxima.
Abstract Coupling with an external environment inevitably affects the dynamics of a quantum system. Here, we consider how charging performances of a quantum battery, modelled as a two level system, are influenced by the presence of an Ohmic thermal reservoir. The latter is coupled to both longitudinal and transverse spin components of the quantum battery including decoherence and pure dephasing mechanisms. Charging and discharging dynamics of the quantum battery, subjected to a static driving, are obtained exploiting a proper mapping into the so-called spin-boson model. Analytic expressions for the time evolution of the energy stored in the weak coupling regime are presented relying on a systematic weak damping expansion. Here, decoherence and pure dephasing dissipative coupling are discussed in details. We argue that the former results in better charging performances, showing also interesting features reminiscent of the Lamb shift level splitting renormalization induced by the presence of the reservoir. Charging stability is also addressed, by monitoring the energy behaviour after the charging protocol has been switched off. This study presents a general framework to investigate relaxation effects, able to include also non Markovian effects, and it reveals the importance of controlling and, possibly, engineering system-bath coupling in the realization of quantum batteries.
Fast charging of quantum batteries requires amplification of the energy transferred to a storage mode without uncontrolled gain or phenomenological non-Hermitian dynamics. Inspired by broken/unbroken dynamical regimes, we introduce a reservoir-engineered quantum battery in which a two-photon-driven charger and a battery mode are coupled through a lossy dissipative mediator. Eliminating the fast mediator yields a reduced two-mode Lindblad model with a complex dissipative coupling and renormalized damping rates. Its drift matrix has a pump-induced stability threshold: below threshold the seeded response is bounded, whereas above threshold a weak seed excites a growing mode and the battery occupation increases exponentially. Compared with a coherent beam-splitter charger--battery benchmark at equal effective coupling, the dissipative architecture reaches this broken regime at a lower pump amplitude. For the parameters studied here, this corresponds to about 61% less critical pump power and opens a pump-power window in which dissipative charging is exponential while the coherent benchmark remains below threshold. In the broken dissipative regime, the growth is dominated by a seed-selected coherent battery displacement rather than incoherent fluctuation buildup, so a large fraction of the stored energy is directly extractable by a displacement operation. The broken-regime boundary is a dynamical stability threshold, not generally an exceptional point, and the full three-mode Lindblad model confirms the reduced description in the fast-mediator regime. Our results give a completely positive route to pump-efficient, low-threshold, and coherently addressable quantum energy storage using engineered reservoirs.
Abstract This study investigates the dynamics of quantum batteries (QBs), focusing on the pivotal role of quantum entanglement in mediating inter-cellular energy transfer within a two-cell configuration (two-qubit), wherein one cell is directly coupled to the charging source. Employing the Lindblad master equation to model the system’s evolution, the influence of coherent state amplitudes, detuning, inter-cellular coupling strength, and dissipation rates on stored energy, ergotropy, energy fluctuations, concurrence-quantified entanglement, and their parametric interrelations is scrutinized. Our results indicate a direct correlation between the entanglement qubits and the efficiency of energy transfer. In particular, stronger entanglement between the primary cell, which is connected to the charger, and the secondary cell leads to more energy transfer. Consequently, entanglement significantly improves energy transfer between the two qubits.
Environmental dissipation and thermal fluctuations fundamentally constrain the extractable work and long-time stability of open quantum batteries. To mitigate dissipation-induced energy degradation without external driving protocols, we propose a cavity-mediated hybrid quantum battery coupled to an auxiliary coherent qubit. Using the Lindblad master equation and ergotropy analysis, we show that coherent interference between different interaction channels generates a decoherence-free-like invariant subspace that suppresses relaxation-induced energy leakage and stabilizes the steady-state ergotropy. The resulting protection mechanism remains effective under strong dissipation and finite-temperature conditions, indicating that interference-assisted coherent control may provide a feasible strategy for robust quantum energy storage in nonequilibrium open systems.