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arXiv:2310.17174 · Physical Review A

Steady-state charging of quantum batteries via dissipative ancillas

F. H. Kamin, S. Salimi, Mohammad B. Arjmandi

Published Feb 20, 2024• 24 citations
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Abstract

We investigate the steady-state charging process of a single-cell quantum battery embedded in an $N$-cell star network of qubits, each interacting with a fermion reservoir, collectively and individually in equilibrium and nonequilibrium scenarios, respectively. We find an optimal steady-state charging in both scenarios, which grows monotonically with the reservoirs' chemical potential and chemical potential difference, where the high base temperature of the reservoirs has a destructive role in all parameter regimes. We indicate that regardless of the strength of the nonequilibrium condition, the high base chemical potential of the battery's corresponding reservoir can significantly enhance the charging process. On the other hand, a weak-coupling strength can strongly suppress the charging. Consequently, our results could counteract the detrimental effects of self-discharging and provide valuable guidelines for enhancing the stable charging of open quantum batteries in the absence of an external charging field.

DOI
10.1103/physreva.109.022226

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We investigate the steady-state charging process of a single-cell quantum battery embedded in an NNN-cell star network of qubits, each interacting with a fermion reservoir, collectively and individually in equilibrium and nonequilibrium scenarios, respectively. We find an optimal steady-state charging in both scenarios, which grows monotonically with the reservoirs' chemical potential and chemical potential difference, where the high base temperature of the reservoirs has a destructive role in all parameter regimes. We indicate that regardless of the strength of the nonequilibrium condition, the high base chemical potential of the battery's corresponding reservoir can significantly enhance the charging process. On the other hand, a weak-coupling strength can strongly suppress the charging. Consequently, our results could counteract the detrimental effects of self-discharging and provide valuable guidelines for enhancing the stable charging of open quantum batteries in the absence of an external charging field.
We study the charging process of open quantum batteries mediated by a common dissipative environment in two different scenarios. In the first case, we consider a quantum charger-battery model in the presence of a non-Markovian environment, where the battery can be properly charged in a strong coupling regime, without any external power and any direct interaction with the charger, i.e., a wireless-like charging happens. The environment plays a major role in the charging of the battery, while this does not happen in a weak coupling regime. In the second scenario, we show the effect of individual and collective spontaneous emission rates on the charging process of quantum batteries by considering a two-qubit system in the presence of Markovian dynamics. Our results demonstrate that open batteries can be satisfactorily charged in Markovian dynamics by employing an underdamped regime and/or strong external fields. We also present a robust battery by taking into account subradiant states and an intermediate regime. Moreover, we propose an experimental setup to explore the ergotropy in the first scenario.
Abstract Quality of charging and discharging of energy in quantum batteries are mostly affected by environmental dissipations, so the advantages of using such devices depend on the protection of them from the dissipations. In this work, we show that under a certain engineering of coupling strengths of each reservoir modes with elements of charging process (charger and battery), the extension of dissipative reservoir leads to a robust charging against the arisen dissipation. The extension of reservoir is provided by auxiliary systems each of which is similar to the coupled charger–battery system and has the same interactions with the reservoir modes as of the charger and battery constituents. It is demonstrated that the robustness of charging process is well controlled by the number of involved auxiliary systems. Furthermore, a method for stable charging is proposed which provides storing energy in a loss-free dark state of the battery. Also, we observe that the robustness of charging process is related to formation of bound state for the total system (charger–battery-extended reservoir) which in turns can be manipulated by the number of involved auxiliary systems.
To take quantum advantage of collective effects in many-body system, we design an elementary block for building a quantum battery with the optimal number of atoms in a common thermal bath, which is charged collectively by a harmonic driving. Free energy is a novel tool to quantify usable energy in an open system, which includes non-preserved entropy impacts on the stored energy besides the internal energy. The interesting finding is that the free energy variation in the steady state increases non-monotonically, and reaches the maximal value at the optimal number of atoms. It ascribes to the decreasing of the internal energy and the entropy per atom with the increasing of the atoms. In particular, the elementary block with the optimal number of atoms can relax to the optimal steady state with the weak damping of the internal energy due to the strong collective driving. By comparing to each atom parallel charging independently, the optimal battery cell produces lower heat flow to the thermal bath induced by the entropy, which can not be neglected in the dissipative system. The existence of the optimal battery cell provide a guideline for designing a realizable charging scheme.
The collective charge of NNN two-level atoms interacting in an open system is investigated. In contrast to a no atomic dissipation quantum battery, the battery remains at a steady state after reaching the moment of full charge. Considering the interactions between atoms, we find that the energy storage of quantum batteries will be significantly enhanced with the increase of atomic repulsion, and the attraction between atoms will exacerbate the dissipation of batteries in the environment. We extend this conclusion to two-level batteries in the drive field and three-level atom quantum batteries. In addition, we also investigate the dissipative charging process of multiatom quantum batteries and find that the number of atoms during the charging process can to some extent affect the energy conversion efficiency during the charging process. Under extreme conditions, the inverse temperature $\ensuremath{\beta}$ can disrupt the energy storage of the battery.
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.
Quantum batteries, which use quantum systems to store and deliver energy, are promising for next-generation energy storage. However, optimizing charging strategies and understanding the interplay between dissipation and quantum coherence remain open challenges. Here, we investigate steady-state charging in an open quantum battery and demonstrate that the charging timescale depends on the spectral gap of the Liouvillian operator governing dissipative dynamics. As a minimal example, we examine a three-level quantum battery realized in a single trapped 40Ca+{}^{40}\mathrm{Ca}^{+}40Ca+ ion, where energy from an engineered thermal photon reservoir is coherently transferred to a long-lived metastable storage state. We find that long-term dynamics are confined to a low-dimensional manifold of slow Liouvillian modes, with their spectral structure determining the relaxation rate to the charged steady state. By adjusting experimentally accessible parameters, such as reservoir occupation and coherent coupling strength, the non-Hermitian Liouvillian spectrum can approach an exceptional point. This increases the spectral gap and accelerates the approach to steady state. As a result, this mechanism significantly enhances asymptotic charging power without relying on many-body collectivity or steady coherence. Our findings offer fundamental insights into open quantum thermodynamics and provide a path to efficient energy storage and fast-charging solutions in emerging quantum technologies.