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arXiv:2312.13444 · Physical Review A

Optimal energy storage in the Tavis-Cummings quantum battery

Huiyu Yang, Hailong Shi, Qing-Kun Wan, Kun Zhang, Xiao-Hui Wang, Wen‐Li Yang

Published Jan 8, 2024• 41 citations
arXivHTMLPDF

Abstract

The Tavis-Cummings (TC) model, which serves as a natural physical realization of a quantum battery, comprises ${N}_{b}$ atoms as battery cells that collectively interact with a shared photon field, functioning as the charger, initially containing ${n}_{0}$ photons. In this paper, we introduce the invariant subspace method to effectively represent the quantum dynamics of the TC battery. Our findings indicate that in the limiting case of ${n}_{0}\ensuremath{\gg}{N}_{b}$ or ${N}_{b}\ensuremath{\gg}{n}_{0}$, a distinct SU(2) symmetry emerges in the dynamics, thereby ensuring the realization of optimal energy storage. We also establish a negative relationship between the battery-charger entanglement and the energy storage capacity. As a result, we demonstrate that asymptotically optimal energy storage can be achieved in the scenario where ${N}_{b}={n}_{0}\ensuremath{\gg}1$. Our approach not only enhances our comprehension of the algebraic structure inherent in the TC model but also contributes to the broader theoretical framework of quantum batteries. Furthermore, it provides crucial insights into the relation between energy transfer and quantum correlations.

DOI
10.1103/physreva.109.012204

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The Tavis-Cummings (TC) model, which serves as a natural physical realization of a quantum battery, comprises Nb{N}_{b}Nb​ atoms as battery cells that collectively interact with a shared photon field, functioning as the charger, initially containing n0{n}_{0}n0​ photons. In this paper, we introduce the invariant subspace method to effectively represent the quantum dynamics of the TC battery. Our findings indicate that in the limiting case of n0\ensuremath≫Nb{n}_{0}\ensuremath{\gg}{N}_{b}n0​\ensuremath≫Nb​ or Nb\ensuremath≫n0{N}_{b}\ensuremath{\gg}{n}_{0}Nb​\ensuremath≫n0​, a distinct SU(2) symmetry emerges in the dynamics, thereby ensuring the realization of optimal energy storage. We also establish a negative relationship between the battery-charger entanglement and the energy storage capacity. As a result, we demonstrate that asymptotically optimal energy storage can be achieved in the scenario where Nb=n0\ensuremath≫1{N}_{b}={n}_{0}\ensuremath{\gg}1Nb​=n0​\ensuremath≫1. Our approach not only enhances our comprehension of the algebraic structure inherent in the TC model but also contributes to the broader theoretical framework of quantum batteries. Furthermore, it provides crucial insights into the relation between energy transfer and quantum correlations.
Quantum batteries (QBs) exploit principles of quantum mechanics to accelerate the charging process and aim to achieve optimal energy storage. However, analytical results for investigating these problems remain lacking due to the challenges associated with nonequilibrium dynamics. In this work we analytically investigate a central-spin QB model in which Nb{N}_{b}Nb​ spin-12\frac{1}{2}21​ battery cells interact with Nc{N}_{c}Nc​ spin-12\frac{1}{2}21​ charger units, using mmm initially excited charger units as a resource. By employing the invariant subspace method and the shifted Holstein-Primakoff transformation, we identify four scenarios in which optimal energy storage can be achieved: (i) ${N}_{b}\ensuremath{\ll}m\ensuremath{\ll}{N}_{c}$, (ii) $m\ensuremath{\ll}{N}_{b}\ensuremath{\ll}{N}_{c}$, (iii) $m\ensuremath{\ll}{N}_{c}\ensuremath{\ll}{N}_{b}$, and (iv) ${N}_{b}\ensuremath{\ll}m=k{N}_{c} [k\ensuremath{\in}(0,1)]$. In these cases, optimal storage is ensured by the SU(2) symmetry emerging from the charging dynamics. The first three cases map the central-spin QB to different Tavis-Cummings (TC) QBs, while the fourth corresponds to the non-TC limit. We analytically determine the charging time and demonstrate that in the fully charging cases (i) and (iv), the collective charging exhibits an Nb{N}_{b}Nb​-fold enhancement in speedup compared to the parallel charging scheme. Additionally, we numerically observe a unified charging behavior when m=Ncm={N}_{c}m=Nc​, showing that asymptotically optimal energy storage is possible when Nb=m=Nc{N}_{b}=m={N}_{c}Nb​=m=Nc​. In this case, we find a collective charging enhancement scaling as Nb0.8264{N}_{b}^{0.8264}Nb0.8264​. The origin of the collective charging advantage in central-spin quantum batteries is also analyzed through the quantum speed limit and a multipartite entanglement witness. Our results highlight the crucial role of dynamically emergent SU(2) symmetry in providing an analytical understanding of nonequilibrium charging dynamics in QBs.
We study the influence of single-atom dissipation and dephasing noise on the performance of Dicke and Tavis-Cummings quantum batteries, where the electromagnetic field of the cavity hosting the system acts as a charger. For these models a genuine charging process can only occur in the transient regime. Indeed, unless the interaction with the environment is cut off, the asymptotic energy of the battery is solely determined by the environment and does not depend on the initial energy of the electromagnetic field. We numerically estimate the fundamental figures of merit for the model, including the time at which the battery reaches its maximum ergotropy, the average energy, and the energy that needs to be used to switch the battery-charger interaction on and off. Depending on the scaling of the coupling between the battery and the charger, we show that the model can still exhibit a subextensive charging time. However, for the Dicke battery, this effect comes with a higher cost when switching the battery-charger interaction on and off. We also show that as the number of battery constituents increases, both the Dicke and Tavis-Cummings models become asymptotically free, meaning the amount of energy that is not unitarily extractable becomes negligible. We obtain this result numerically and demonstrate analytically that it is a consequence of the symmetry under permutations of the model. Finally, we perform simulations for different values of the detuning, showing that the optimal regime for the Dicke battery is off-resonance, in contrast with what is observed in the Tavis-Cummings case.
Abstract Quantum battery exploits the principle of quantum mechanics to transport and store energy. We study the energy transportation of the central-spin quantum battery, which is composed of N b spins serving as the battery cells, and surrounded by N c spins serving as the charger cells. We apply the invariant subspace method to solve the dynamics of the central-spin battery with a large number of spins. We establish a universal inverse relationship between the battery capacity and the battery–charger entanglement, which persists in any size of the battery and charger cells. Moreover, we find that when N b = N c, the central-spin battery has the optimal energy transportation, corresponding to the minimal battery–charger entanglement. Surprisingly, the central-spin battery has a uniform energy transportation behaviors in certain battery–charger scales. Our results reveal a nonmonotonic relationship between the battery–charger size and the energy transportation efficiency, which may provide more insights on designing other types of quantum batteries.
Quantum batteries provide a useful setting for exploring nonequilibrium many-body effects in energy storage. Here we investigate the optimization of a quantum battery based on the central-spin model. We identify two complementary structural indicators associated with the effective charging dynamics: one yields an upper bound on the average charging power, while the other characterizes the buildup of stored energy. We show that these two indicators are jointly optimized at a distinguished initial charger excitation number, which selects a particular Dicke sector of the model. At this common optimal point, the effective charging Hamiltonian becomes exactly mirror symmetric, suggesting mirror symmetry as a useful structural indicator for optimizing the performance of quantum batteries in terms of both charging power and energy storage. We further show that the corresponding optimal dynamics can be closely approximated by product initial states, in particular by spin coherent states whose excitation-number distribution is centered at the symmetry-selected point. Our results establish a direct connection between charging performance, optimal-state structure, and emergent symmetry in the central-spin quantum battery, and suggest symmetry as a useful organizing principle for efficient charging in interacting many-body quantum systems.
In this paper, we investigate the effect of different optical field initial states on the performance of the Tavis-Cummings (TC) quantum battery. In solving the dynamical evolution of the system, we found a fast way to solve the Bethe ansatz equation. We find that the stored energy and the average charging power of the TC quantum battery are closely related to the probability distribution of the optical field initial state in the number states. We define a quantity called the number-state stored energy. With this prescribed quantity, we only need to know the probability distribution of the optical field initial state in the number states to obtain the stored energy and the average charging power of the TC quantum battery at any time. We propose an equal probability and equal expected value splitting method by which we can obtain two inequalities, and the two inequalities can be reduced to Jensen's inequalities. By this method, we found the optimal initial state of the optical field. We found that the maximum stored energy and the maximum average charging power of the TC quantum battery are proportional to the initial average photon number, and the quantum battery can be fully charged when the initial average photon number is large enough. We found two phenomena, which can be described by two empirical inequalities. These two phenomena imply the hypersensitivity of the stored energy of the TC quantum battery to the number-state cavity field. Finally, we discuss the impact of decoherence on battery performance.
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.