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arXiv:2402.09169 · Physical Review Letters

Controlling Energy Storage Crossing Quantum Phase Transitions in an Integrable Spin Quantum Battery

Riccardo Grazi, Daniel Sacco Shaikh, Maura Sassetti, Niccolò Traverso Ziani, Dario Ferraro

Published Nov 7, 2024• 64 citations
arXivHTMLPDF

Abstract

We investigate the performance of a one-dimensional dimerized XY chain as a spin quantum battery. Such integrable model shows a rich quantum phase diagram that emerges through a mapping of the spins onto auxiliary fermionic degrees of freedom. We consider a charging protocol relying on the double quench of an internal parameter, namely the strength of the dimerization, and address the energy stored in the systems. We observe three distinct regimes, depending on the timescale characterizing the duration of the charging: a short-time regime related to the dynamics of the single dimers, a long-time regime related to the recurrence time of the system at finite size, and a thermodynamic limit time regime. In the latter, the energy stored is almost unaffected by the charging time and the precise values of the charging parameters, provided the quench crosses a quantum phase transition. Finally, we analytically prove that the three-timescale behavior and the strong dependence of the energy stored on the quantum phase diagram also hold in the quantum Ising chain in a transverse field. Our results can play a relevant role in the design of stable solid-state quantum batteries.

DOI
10.1103/physrevlett.133.197001

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We investigate the performance of a one-dimensional dimerized XY chain as a spin quantum battery. Such integrable model shows a rich quantum phase diagram that emerges through a mapping of the spins onto auxiliary fermionic degrees of freedom. We consider a charging protocol relying on the double quench of an internal parameter, namely the strength of the dimerization, and address the energy stored in the systems. We observe three distinct regimes, depending on the timescale characterizing the duration of the charging: a short-time regime related to the dynamics of the single dimers, a long-time regime related to the recurrence time of the system at finite size, and a thermodynamic limit time regime. In the latter, the energy stored is almost unaffected by the charging time and the precise values of the charging parameters, provided the quench crosses a quantum phase transition. Finally, we analytically prove that the three-timescale behavior and the strong dependence of the energy stored on the quantum phase diagram also hold in the quantum Ising chain in a transverse field. Our results can play a relevant role in the design of stable solid-state quantum batteries.
Quantum batteries are quantum systems designed to store energy and release it on demand. The optimization of their performance is an intensively studied topic within the realm of quantum technologies. Such optimization forces the question: how do quantum many-body systems work as quantum batteries? To address this issue, we rely on symmetry and symmetry breaking via quantum phase transitions. Specifically, we analyze a dimerized quantum XY chain in a transverse field as a prototype of an energy storage device. This model, which is characterized by ground states with different symmetries depending on the Hamiltonian parameters, can be mapped onto a spinless fermionic chain with superconducting correlations, displaying a rich quantum phase diagram. We show that the stored energy strongly depends on the quantum phase diagram of the model when large charging times are considered.
We investigate the charging dynamics and energy storage performance of a quantum battery defined by an anisotropic spin-1/2 XY chain, extended by the inclusion of anisotropic three-spin interactions. This system possesses a rich ground-state phase diagram featuring non-trivial gapped topological phases separated by quantum critical lines. Utilizing the fermionization technique, we exactly diagonalize the Hamiltonian and analyze the charging process through a quantum quench from an initial state to a final Hamiltonian configuration. We derive an analytical expression for the upper bound of the stored energy. Significantly, we find that the steady-state stored energy is consistently equal to one-half of the corresponding theoretical maximum throughout the parameter regime investigated. Furthermore, we provide analytical approximations for the charging peak and demonstrate that the underlying topological phase transitions leave distinct and detectable signatures in the charging landscape. These results establish a framework for understanding the interplay between ground-state topology, quantum criticality, and nonequilibrium energy-storage dynamics in quantum spin-chain batteries.
Quantum batteries are quantum mechanical systems able to store and release energy in a controlled fashion. Among them, a special role is played by quantum structures defined as networks of two-level systems. In this context, it has recently been shown that the energy stored in free fermion quantum batteries is sensitive to the quantum phase diagram of the battery itself. This sensitivity is relevant for stabilizing the stored energy and designing optimal charging protocols. In this article, we explore universal charging behaviors of free fermion quantum batteries across quantum phase transitions. We first analyze a Dirac cone-like model to extract general features. Then, we verify our findings by means of two relevant lattice models, namely the Ising chain in a transverse field and the Haldane model.
Quantum batteries, miniaturized devices able to store and release energy on demand, are promising both because their intrinsic energy and time scales can match those of other quantum technologies and due to the intriguing possibility of achieving super-extensive charging power. While this enhanced scaling is known to appear in several settings, it is generally believed to be forbidden in Jordan-Wigner integrable spin chains charged via quantum-quench protocols. Here, we show that an extended cluster-Ising model, despite belonging to the above category, exhibits super-extensive charging power over wide ranges of system sizes, reaching up to a thousand spins, in proper parameter regimes. This remarkable anomalous scaling is due to a corresponding super-extensive growth of the stored energy, implying that it is limited to a large but finite size of the system and cannot persist in the thermodynamic limit. This phenomenon appears robust against finite-temperature effects.
Reliable charging protocols are crucial for advancing quantum batteries toward practical use. We investigate a transverse-field Ising chain as a quantum battery, focusing on the combined role of qubit interactions in the battery model and finite charging time. This interplay yields smoother and more controllable charging compared to sudden protocols or non-interacting batteries. Introducing stochastic noise reveals a strong dependence on the charging trajectory. Protocols that weakly excite the system gain energy under noise but lose extractable work. In contrast, protocols that strongly excite many modes show the opposite trend: noise reduces stored energy yet improves efficiency, defined as the ratio of ergotropy to stored energy. These findings demonstrate that finite-time ramps stabilize charging and highlight that noise can either hinder or enhance quantum-battery performance depending on the protocol.
Abstract We consider a quantum battery (QB) composed of a pair of qubits coupled with an Ising interaction in the usual NMR framework, where the longitudinal applied field is constant and the time-dependent variables controlling the system are the amplitude and phase of the transverse field, and use optimal control to derive fast charging protocols. We study both the cases where the Ising coupling is weaker and stronger than the longitudinal field. In the first case, where the lowest-energy state of the system is the spin-down state, the optimal charging protocol stipulates the transverse field amplitude to be constant and equal to its maximum allowed value, while the minimum time for full charging of the battery tends to zero as this maximum bound increases. In the second case, where the lowest-energy state is a maximally entangled Bell state, the optimal charging protocol includes a time interval where the transverse field amplitude is zero and its phase is immaterial, corresponding to singular control. In this case, the QB can be charged with higher levels of stored energy, while the minimum time for full charging tends to a nonzero limit proportional to the inverse Ising interaction, as the maximum bound of the control amplitude increases. We analyze intuitively and quantitatively the distinct behavior of the two cases and additionally use the dynamical Lie algebra of the system to elucidate the presence of a singular arc in the optimal pulse-sequence in the second case. The discovered interplay between the QB parameters, the stored energy and the minimum time for full charging, provides great flexibility for optimizing the performance of the device according to the operating constraints. The valuable insights gained regarding the design of QBs is expected to find immediate applications in modern quantum science and technology, while we aim to extend the proposed methods to larger spin chains.