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Physical Review A

Better performance of quantum batteries in different environments compared to closed batteries

Shu-Qian Liu, Lu Wang, Hao Fan, Feng-Lin Wu, S.Y. Liu

Published Apr 11, 2024• 20 citations
Publisher

Abstract

We construct a central-spin battery model affected by noise or thermal bath and consider the impact of environment on battery performance. In a noisy environment, we show that the steady-state energy and ergotropy are related to the number of spins exposed to the noisy channel. In addition, we reveal the relationship between the steady-state energy and ergotropy with the quantum information lost in the battery. In a thermal bath, we find that the higher the mean occupation number of the thermal bath, the greater the steady-state energy. In particular, we find that, in two different environments, the steady-state energy and ergotropy are related to the effective magnetic-field strength of battery $B$, but not charger $h$. It is worth noting that, in the central-spin model, when $B$ is a constant and $|h/B\ensuremath{-}1|$ reaches a certain value, the steady-state energy and ergotropy with noise or thermal bath are always greater than or equal to the maximum energy and ergotropy of the corresponding closed battery. At the same time, we generalize the conclusions to the two-qubit, two-harmonic-oscillator, and harmonic-oscillator-qubit models.

DOI
10.1103/physreva.109.042411

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We construct a central-spin battery model affected by noise or thermal bath and consider the impact of environment on battery performance. In a noisy environment, we show that the steady-state energy and ergotropy are related to the number of spins exposed to the noisy channel. In addition, we reveal the relationship between the steady-state energy and ergotropy with the quantum information lost in the battery. In a thermal bath, we find that the higher the mean occupation number of the thermal bath, the greater the steady-state energy. In particular, we find that, in two different environments, the steady-state energy and ergotropy are related to the effective magnetic-field strength of battery BBB, but not charger hhh. It is worth noting that, in the central-spin model, when BBB is a constant and ∣h/B\ensuremath−1∣|h/B\ensuremath{-}1|∣h/B\ensuremath−1∣ reaches a certain value, the steady-state energy and ergotropy with noise or thermal bath are always greater than or equal to the maximum energy and ergotropy of the corresponding closed battery. At the same time, we generalize the conclusions to the two-qubit, two-harmonic-oscillator, and harmonic-oscillator-qubit models.
ABSTRACT This study investigates the charging performance of single‐qubit and multi‐qubit quantum batteries in both Markovian and non‐Markovian environments. Using the collision model to simulate a bosonic bath, we provide a detailed study of the impact of temperature on battery performance through both analytical and numerical solutions in a prepared thermal bath, demonstrating that high temperature generally suppresses steady‐state ergotropy of quantum batteries, while also accelerating the convergence to the steady state. By applying the Luo‐Fu‐Song measure of non‐Markovianity, it is found that the information backflow generated in a non‐Markovian environment further enhances the battery's ergotropy and speeds up the approach to the steady state. Additionally, when studying multi‐qubit quantum battery, we consider each individual spin as an independent battery unit. The results show that non‐Markovian memory effects allow spins directly coupled to the bath to store more energy. Notably, with elevated temperature even enhancing their steady‐state ergotropy due to information backflow. Finally, we find that the battery's mixedness is always positively correlated with the unavailable energy. This provides theoretical support for distributed energy extraction in quantum batteries.
We investigate the performance of a quantum battery exposed to local Markovian and non-Markovian dephasing noises. The battery is initially prepared as the ground state of a one-dimensional transverse XYXYXY model with open boundary condition and is charged (discharged) via interactions with local bosonic reservoirs. We show that in the transient regime, the quantum battery (QB) can store energy faster and has a higher maximum extractable work, quantified via ergotropy, when it is affected by local phase-flip or bit-flip Markovian noise compared to the case when there is no noise in the system. In both the charging and discharging processes, we report the enhancement in work output as well as in ergotropy when all the spins are affected by a non-Markovian Ohmic bath in both the transient and the steady-state regimes, thereby showing a counterintuitive advantage of decoherence in the QB. In both Markovian and non-Markovian cases, we identify the system parameters and the corresponding noise models which lead to maximum enhancement of work output and ergotropy. Moreover, we show that the benefit due to noise persists even with the initial state being prepared at a moderate temperature.
Abstract A model of the Heisenberg spin chain quantum battery that is charged by noise is built, and the energy can be extracted. In a phase‐flip noisy environment, it is found that there are sudden changes in steady‐state energy and ergotropy with the variation of the nearest neighbor interaction strength on the plane. These sudden changes are associated with quantum phase transition (QPT), which has been shown through the crossover of the ground state energy level and the first excited state energy level, as well as the order parameters. In a thermal bath, the changes are investigated in steady‐state energy and ergotropy with the variation of the nearest neighbor interaction strength on the plane. The components of Hamiltonian of the battery in the , , and directions are used to explain the steady‐state energy continuity at the QPT points. In addition, the effect of mean occupation number of the thermal bath on the steady‐state energy and ergotropy is also considered. For the general Heisenberg spin chain and ‐qubit batteries, it is proved that the noise can also be used to charge the battery, and the ergotropy is non‐zero.
Quantum batteries have emerged as promising platforms for exploring energy storage and transfer processes governed by quantum mechanical laws. In this work, we study three models of two-qubit open quantum systems. The first model comprises two central spins immersed in spin baths, and both central spins are collectively considered as quantum batteries. The impact of inter-qubit interactions on the performance of the quantum battery is investigated. In the second model, a two-qubit model interacting with a squeezed thermal bath serves as a collective quantum battery, where the impact of inter-atomic distance and the bath temperature on the battery's performance is explored. Furthermore, a two-qubit model is used, where one qubit is modeled as a battery and the other as a charger. The charger in this model interacts with an anisotropic spin-chain bath, which is conducive to quantum criticality. It is demonstrated that this criticality has a substantial impact on the quantum battery's storage capacity.
We investigate the global and local performances of a quantum battery exposed to the depolarizing and bit-flip channels, respectively, using the correlation matrix method. The battery is initially prepared as the highest-energy state of a two-qubit Ising model with open boundary conditions and is discharged via interaction with local noise channels. We show that compared to the independent noise channels, the correlated noise channels provide varying degrees of protection for the global and local performances of the Ising battery. The correlated depolarizing channel not only protects the global energy, ergotropy, and capacity of the Ising battery, but also protects the local ergotropy and capacity, whereas the correlated bit-flip channel provides protection only for the global ergotropy and capacity of the Ising battery. In both the correlated depolarizing and bit-flip channels, the greater the correlation strength, the greater the protective effect. Furthermore, we also use the same method to investigate the protective effect of correlated channels on the performances of the multiqubit battery and general Heisenberg battery in noise channels.
The study of quantum thermodynamics has led to the development of quantum batteries. These devices use quantum advantages to store and extract useful energy from physical systems. Ergotropy is the maximum work that can be extracted from a quantum system by cyclic unitary operations. When external thermal baths couple with the quantum battery, there is energy loss due to thermal effects on the system. In some cases, a part of the total energy available in the system cannot be stored as ergotropy. Therefore, it is important to consider the amount of residual energy that cannot be extracted as useful work from quantum batteries by unitary processes. To better understand the amount of energy lost during work extraction, it is necessary to examine the constraint of unitary processes. The system exergy represents the maximum amount of work that can be extracted from the system while bringing it into equilibrium with a thermal bath. It can be separated into two parts: ergotropy and residual energy. Thus, the present chapter describes the relationship between exergy and its potential benefits and effects on the performance of quantum batteries.