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arXiv:2112.10451 · Physical review. E

Periodically driven many-body quantum battery

Saikat Mondal, Sourav Bhattacharjee

Published Apr 18, 2022• 22 citations
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Abstract

We explore the charging of a quantum battery based on spin systems through periodic modulation of a transverse-field-like Ising Hamiltonian. In the integrable limit, we find that resonance tunneling can lead to a higher transfer of energy to the battery and better stability of the stored energy at specific drive frequencies. When the integrability is broken in the presence of an additional longitudinal field, we find that the effective Floquet Hamiltonian contains terms which may lead to a global charging of the battery. However, we do not find any quantum advantage in the charging power, thus demonstrating that global charging is only a necessary and not sufficient condition for achieving quantum advantage.

DOI
10.1103/physreve.105.044125

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We explore the charging of a quantum battery based on spin systems through periodic modulation of a transverse-field-like Ising Hamiltonian. In the integrable limit, we find that resonance tunneling can lead to a higher transfer of energy to the battery and better stability of the stored energy at specific drive frequencies. When the integrability is broken in the presence of an additional longitudinal field, we find that the effective Floquet Hamiltonian contains terms which may lead to a global charging of the battery. However, we do not find any quantum advantage in the charging power, thus demonstrating that global charging is only a necessary and not sufficient condition for achieving quantum advantage.
While quantum batteries have been widely studied under static driving, their performance under periodic driving in many-body systems has received only limited attention. In this Letter, we uncover structural principles showing that many-body structure fundamentally determines the charging performance of a collective spin-1/2 quantum battery driven by a periodic Ising charger. In particular, interaction range, boundary conditions, system size, and integrability -- capturing graph connectivity, geometry, even-odd effects, and many-body dynamics -- emerge as critical factors for enhancing stored energy and charging power. First, we analyze how connectivity scaling and boundary geometry shape battery performance. We show that long-range interacting chargers exhibit superextensive energy storage, approaching the fundamental upper bound over broad ranges of driving periods and system sizes. In contrast, nearest-neighbor chargers achieve optimal charging only under finely tuned commensurability conditions. Moreover, we find that open boundary conditions (OBC) enhance robustness compared to periodic boundary conditions (PBC). Second, we examine the role of integrability under periodic driving. We demonstrate that nonintegrability enhances energy storage by suppressing conserved quantities and promoting ergodic Floquet dynamics, thereby enabling efficient population of the many-body spectrum. Through systematic structural optimization across multiple parameters, we identify long-range nonintegrability as a central resource for fast, scalable, and robust charging of collective quantum batteries. Our results clarify how structural features of many-body systems, together with periodic driving, can be harnessed to achieve efficient collective charging dynamics.
Most quantum batteries studied so far with notable exception of Sachdev-Ye-Kitaev (SYK) batteries are based on integrable models, where superlinear scaling of charging power and hence a quantum advantage can be achieved, but at the cost of unstable stored energy due to integrability. Here, by considering the sunburst quantum Ising battery driven by periodic delta-kicks, we show that in the quantum chaotic regime a quantum advantage is achieved for number of batteries nb≤4n_b\leq 4nb​≤4, together with excellent stability of energy storage. In the integrable regime optimal energy storage and extraction are possible irrespective of the initial state of the charger. Finally, we show that the observed advantage does not originate from multipartite entanglement within the battery subsystem and is therefore classical in nature.
Recent advances in quantum information and quantum thermodynamics have reshaped the understanding of energy storage at the microscopic scale, paving the way toward protocols for storing and transferring energy in quantum devices. These systems, known as quantum batteries, offer a conceptual alternative to conventional macroscopic chemical batteries by exploiting quantum coherence, correlations, and many-body dynamics. By navigating the landscape of established spin-based quantum batteries, we review existing charging and work-extraction protocols, as well as the impact of external factors on their performance. Motivated by Floquet-engineered proposals, we further establish a connection between continuously and periodically driven spin chains as platforms for quantum energy storage. Finally, we survey experimental realizations and proposals, highlighting their implementability and scalability in current and near-term quantum technologies.
The operation of conventional batteries relies primarily on electrochemical reactions and classical physics. However, an important question is whether quantum effects, such as entanglement, can lead to a significant change in the behaviour of a battery. In addition to being a fundamental problem, this is of technological interest, since there is the prospect of exploiting quantum effects to increase charging power and energy density of a battery, and to overcome the limitations of classical batteries. In this thesis, we investigate how to charge a battery composed of quantum systems and determine which quantum effects play a part in this charging. We find that certain broken symmetries in the battery model give rise to entanglement and enhance charging relative to other batteries without entanglement. We use Heisenberg XXZ spin chains as the basic model of our quantum many-body battery. The Heisenberg spin chain is a paradigmatic model of solid-state physics; simple, yet able to describe the magnetic behaviour of more complex physical systems. The models we consider either have a nearest neighbour spin-spin coupling interaction or a long range 1/r interaction. Local identical charging fields are used to deposit work in the battery. We also investigate adding noise into the charging process, and consider the performance and stability of the spin chain battery in the presence of a heat bath. We compare the different spin chains with one another, and also compare them with several different classical models, in order to determine whether or not there is a “quantum advantage”. We find that whether or not there is a quantum advantage depends on which models and what quantity we are comparing.
We study the charging performance of a one-dimensional many-body bosonic quantum battery coupled to a harmonic-oscillator charger. In the weak-coupling regime, we show that the battery--charger dynamics can be accurately described by an effective two-level model, which predicts the resonance condition, optimal charging time, stored work, ergotropy, and charging power. We demonstrate that tuning the charger frequency to the interaction-shifted resonance enables complete energy transfer and maximum extractable work. A many-body charging advantage is observed: increasing the particle number reduces the quantum speed-limit time and enhances the charging power with a characteristic NB\sqrt{N_B}NB​​ scaling. We further introduce a decomposition of the switching cost into resonance-shifting and excitation contributions, allowing us to quantify the energetic overhead associated with the charging process. Owing to the small charging cost relative to the available charger energy, stronger battery--charger couplings can be employed to significantly boost the charging power while maintaining a low excitation cost. Our results highlight the role of resonance engineering and many-body effects in designing fast and efficient quantum batteries, and provide a promising route toward their realization in ultracold-atom platforms.
We study a quantum battery consisting of NNN qubits interacting uniformly with each other. Starting from its ground state, the battery is charged by introducing periodic kicks in the transverse direction along with adding disorder in the interaction direction. Although the battery Hamiltonian along with the initial state preserves the permutation symmetry, the dynamics in presence of disorder during the charging phase takes the system out of the permutation symmetric subspace, resulting to a larger amount of stored energy as compared to that without disorder. In the limit of large disorder, this interplay brings in a possibility of a chaotic charging phase when stored energy can be exactly calculated using random matrix theory. More importantly, we also find that the energy fluctuations decrease and become negligible in the limit of large disorder, which is also when the energy stored is maximum, a condition highly desirable for the optimum functioning of the battery. We complete the battery cycle by considering the storage phase in the presence of dephasing noise. We find that for larger disorder strengths, the ergotropy remains close to the stored energy, indicating nearly complete energy extractability with an efficiency approaching unity.