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arXiv:2502.12839 · Physical Review A

Reservoir-assisted quantum battery charging at finite temperatures

Y. Yao, X. Q. Shao

Published May 28, 2025• 17 citations
arXivHTMLPDF

Abstract

Quantum batteries, as highly efficient energy storage devices, have garnered significant research interest. A key challenge in their development is to maximize the extractable energy (ergotropy) when operating within a finite-temperature reservoir. To address this, we applied quantum feedback control to the charger and investigated the effects of fermionic and bosonic thermal reservoirs on the performance of quantum batteries, including stored energy, ergotropy, and charging efficiency, in an open environment. Our findings reveal that, regardless of the type of thermal reservoir, the system exhibits optimal charging parameters. In particular, in a fermionic thermal reservoir, increasing the environmental temperature enhances battery performance, enabling stable and efficient charging. In contrast, within a bosonic thermal reservoir, higher temperatures hinder energy storage and extraction, significantly reducing charging efficiency. Additionally, we explored the impact of battery size and found that, under a fermionic reservoir, increasing the battery size appropriately can further improve performance.

DOI
10.1103/vqnk-kzqg

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Quantum batteries, as highly efficient energy storage devices, have garnered significant research interest. A key challenge in their development is to maximize the extractable energy (ergotropy) when operating within a finite-temperature reservoir. To address this, we applied quantum feedback control to the charger and investigated the effects of fermionic and bosonic thermal reservoirs on the performance of quantum batteries, including stored energy, ergotropy, and charging efficiency, in an open environment. Our findings reveal that, regardless of the type of thermal reservoir, the system exhibits optimal charging parameters. In particular, in a fermionic thermal reservoir, increasing the environmental temperature enhances battery performance, enabling stable and efficient charging. In contrast, within a bosonic thermal reservoir, higher temperatures hinder energy storage and extraction, significantly reducing charging efficiency. Additionally, we explored the impact of battery size and found that, under a fermionic reservoir, increasing the battery size appropriately can further improve performance.
We explore the wireless charging of a quantum battery (QB) via nnn charging units, whose coupling is mediated by a common bosonic reservoir. We consider the general scenarios in which the charger energy is not maximal and the QB has residual ergotropy initially. It is found that the charging performance improves with the increase of the coupling strength. In the strong coupling regime, the charging time is insensitive to the charger energy, the number of charging units, and the residual ergotropy in the QB, while the ergotropy charged on the QB strongly depends on the charger energy and ergotropy, and the residual ergotropy in the QB does not help to enhance its performance. Moreover, the multiple charging units help to enhance the charging performance in the weak and moderate coupling regimes, while they are less efficient in the strong coupling regime.
Using the ground states of the Bose- and Fermi-Hubbard model as the battery's initial state, we demonstrate that using the Wannier-Stark (WS) field for charging in addition to onsite interactions can increase the maximum power of the battery. Although the benefit is not ubiquitous, bosonic batteries are more affected by the WS field than fermionic ones. In particular, there exists a critical WS field strength above which the power gets increased in the battery. Further, we determine a closed form expression of the stored work when the battery is in the ground state of the Bose- and Fermi-Hubbard model with only hopping term and the charging is carried out with onsite interactions and WS field irrespective of lattice-size of the battery. Moreover, we exhibit that it is possible to extract work in the fermionic batteries even without charging when the edge sites are attached to two local thermal baths having high temperatures -- this process we refer to as {\it environment-assisted ergotropy}. Note, however, that the bosonic batteries are able to exhibit such an environmental benefit in the transient regime when the lattice-size is increased and when Wannier-Stark field is present. Nonetheless, if the onsite interaction or WS potential with a critical strength is utilized as a charger, energy can be stored and extracted from both bosonic and fermionic batteries in the presence of the thermal baths.
This study investigates the thermodynamic behavior of a two-qubit quantum system, where each qubit is coupled to an independent thermal reservoir, either bosonic or fermionic. Using a master equation approach, we analyze both steady-state and time-dependent ergotropy to understand how different reservoir statistics affect work extraction. In bosonic environments, ergotropy consistently declines with increasing temperature due to thermal noise. In contrast, fermionic reservoirs exhibit more complex behavior, with ergotropy enhanced by particle transport under non-equilibrium conditions. Our results reveal a threshold-like sensitivity to the chemical potential configuration, leading to qualitatively distinct regimes of energy storage performance. Time-resolved analyses show that the system's approach to steady state varies depending on the type of reservoir and the coupling strength between qubits. These insights highlight how carefully engineered reservoir properties and non-equilibrium driving can be leveraged to optimize quantum battery performance.
In this work, we investigate the autonomous charging process of a quantum battery coupled to a structured reservoir composed of two qubits, each locally coupled to its own bosonic thermal bath. Moreover, the reservoir interacts with a charger-battery architecture through three configurations: (I) direct coupling between reservoir qubits and battery; (II) collective coupling among the reservoir qubits, charger, and battery; and (III) a collective coupling between the reservoir qubits and charger together with a local charger-battery interaction. However, by using incoherent and coherent initial states, we analyze the stored energy, ergotropy, and charging power of the battery, and derive upper and lower bounds on the extractable work in terms of the free energy of coherence and the correlations exchanged between subsystems. Our results show that global and local coherences, as well as total correlations, act as quantum resources that enhance autonomous charging. Additionally, we demonstrate that the free energy stored in the quantum battery splits into contributions from coherence and correlations, providing numerical evidence that supports the derived ergotropy bounds. Importantly, this work highlights how structured reservoirs enable autonomous and resource-enhanced quantum battery operation.
Abstract Quantum batteries harness quantum coherence and entanglement to achieve efficient energy storage beyond classical limits. This study presents a comparative analysis of series and parallel charging protocols, evaluating their impact on charging efficiency, stability, and dissipation. Using the Lindblad master equation, we investigate the effects of multi-photon interactions, cavity decay, atomic relaxation, and thermal fluctuations on the evolution of key physical quantities, including stored energy, ergotropy, and entropy of the charger. Our findings reveal that parallel charging exhibits superior stability, reduced entropy fluctuations, and higher ergotropy, while series charging suffers from increased dissipation and oscillatory instabilities. These insights contribute to the development of high-performance quantum energy storage systems for advanced quantum technologies.
This study examines the steady state characteristics of work extraction in a two cell and three cell quantum battery interacting with multiple thermal reservoirs. Employing the quantum master equation framework within the Born-Markov approximation, we explore the non equilibrium dynamics governing energy storage and extraction in the system. Our analysis focuses on the influence of thermal gradients across the reservoirs and the impact of inter cell coupling strength on the battery performance. The findings demonstrate that an increase in the middle reservoir temperature substantially enhances the extractable work, underscoring the pivotal role of thermal bath amplification in optimizing energy storage efficiency. Furthermore, we uncover a non trivial relationship between ergotropy and the coupling strength among the quantum cells, revealing the existence of an optimal coupling regime that maximizes energy extraction. Beyond this threshold, excessive coupling induces energy localization, thereby diminishing the system efficiency. These insights provide a theoretical foundation for the strategic design of high performance quantum batteries by harnessing thermal gradients and interaction driven control mechanisms.