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arXiv:2003.09814 · Physical review. E

Bounds on charging power of open quantum batteries

Shadab Zakavati, F. T. Tabesh, S. Salimi

Published Nov 17, 2021• 76 citations
arXivHTMLPDF

Abstract

In general, quantum systems most likely undergo open-system dynamics due to their smallness and sensitivity. Energy storage devices, so-called quantum batteries, are not excluded from this phenomenon. Here, we study fundamental bounds on the power of open quantum batteries from the geometric point of view. By defining an activity operator, a tight upper bound on the charging power is derived for the open quantum batteries in terms of the fluctuations of the activity operator and the quantum Fisher information. The variance of the activity operator may be interpreted as a generalized thermodynamic force, while the quantum Fisher information describes the speed of evolution in the state space of the battery. The thermodynamic interpretation of the upper bound is discussed in detail. As an example, a model for the battery, taking into account the environmental effects, is proposed, and the effect of dissipation and decoherence during the charging process on both the stored work and the charging power is investigated. Our results show that the upper bound is saturated in some time intervals. Also, the maximum value of both the stored work and the corresponding power is achieved in the non-Markovian underdamped regime.

DOI
10.1103/physreve.104.054117

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In general, quantum systems most likely undergo open-system dynamics due to their smallness and sensitivity. Energy storage devices, so-called quantum batteries, are not excluded from this phenomenon. Here, we study fundamental bounds on the power of open quantum batteries from the geometric point of view. By defining an activity operator, a tight upper bound on the charging power is derived for the open quantum batteries in terms of the fluctuations of the activity operator and the quantum Fisher information. The variance of the activity operator may be interpreted as a generalized thermodynamic force, while the quantum Fisher information describes the speed of evolution in the state space of the battery. The thermodynamic interpretation of the upper bound is discussed in detail. As an example, a model for the battery, taking into account the environmental effects, is proposed, and the effect of dissipation and decoherence during the charging process on both the stored work and the charging power is investigated. Our results show that the upper bound is saturated in some time intervals. Also, the maximum value of both the stored work and the corresponding power is achieved in the non-Markovian underdamped regime.
We studied the dynamics of entropic uncertainty in Markovian and non-Markovian systems during the charging of open quantum batteries (QBs) mediated by a common dissipation environment. In the non-Markovian regime, the battery is almost fully charged efficiently, and the strong non-Markovian property is beneficial for improving the charging power. In addition, the results show that the energy storage is closely related to the couplings of the charger-reservoir and battery-reservoir; that is, the stronger coupling of a charger reservoir improves energy storage. In particular, entanglement is required to obtain the most stored energy and is accompanied by the least tight entropic bound. Interestingly, it was found that the tightness of the entropic bound can be considered as a good indicator of the energy transfer in different charging processes, and the complete energy transfer always corresponds to the tightest entropic bound. Our results provide insight into the optimal charging efficiency of QBs during practical charging.
In an article by García-Pintos et al. [Rev. Lett. 125, 040601 (2020)] the connection between the charging power of a quantum battery and the fluctuations of a "free energy operator" whose expectation value characterizes the maximum extractable work of the battery is studied. The result of the closed-system analysis shows that for a general charging process the battery will have a nonzero charging power if and only if the state of the battery is not an eigenstate of the free energy operator. In this Comment, we point out a few mistakes in the analysis and obtain the correct bound on the charging power. Consequently, the result for closed-system dynamics is in general not correct.
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.
Can collective quantum effects make a difference in a meaningful thermodynamic operation? Focusing on energy storage and batteries, we demonstrate that quantum mechanics can lead to an enhancement in the amount of work deposited per unit time, i.e., the charging power, when N batteries are charged collectively. We first derive analytic upper bounds for the collective quantum advantage in charging power for two choices of constraints on the charging Hamiltonian. We then demonstrate that even in the absence of quantum entanglement this advantage can be extensive. For our main result, we provide an upper bound to the achievable quantum advantage when the interaction order is restricted; i.e., at most k batteries are interacting. This constitutes a fundamental limit on the advantage offered by quantum technologies over their classical counterparts.
We study the connection between the charging power of quantum batteries and the fluctuations of the extractable work. We prove that in order to have a nonzero rate of change of the extractable work, the state ${\ensuremath{\rho}}_{\mathcal{W}}$ of the battery cannot be an eigenstate of a ``free energy operator,'' defined by $\mathcal{F}\ensuremath{\equiv}{H}_{\mathcal{W}}+{\ensuremath{\beta}}^{\ensuremath{-}1}\mathrm{log}({\ensuremath{\rho}}_{\mathcal{W}})$, where HW{H}_{\mathcal{W}}HW​ is the Hamiltonian of the battery and $\ensuremath{\beta}$ is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the free energy operator upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine.
Abstract The performance of quantum technologies that use entanglement and coherence as a resource is highly limited by the effects of decoherence due to their interaction with some environment. In particular, it is important to take into account situations where such devices unavoidably interact with surrounding. Here, we study memory effects on energy and ergotropy of quantum batteries in the framework of open system dynamics, where the battery and charger are individually allowed to access a bosonic environment. Our investigation shows that the battery can be fully charged as well as its energy can be preserved for long times in non-Markovian dynamics compared with Markovian dynamics. Moreover, the non-Markovianity increase makes it possible to extract the total stored energy as work and the discharge time becomes longer. Our results indicate that memory effects can play a significant role in improving the performance of quantum batteries.