Spin-chain model of a many-body quantum battery

Thao P. Le, Jesper Levinsen, Kavan Modi, Meera M. Parish, and Felix A. Pollock

Phys. Rev. A 97, 022106 – Published 13 February 2018

Abstract

Recently, it has been shown that energy can be deposited on a collection of quantum systems at a rate that scales superextensively. Some of these schemes for quantum batteries rely on the use of global many-body interactions that take the batteries through a correlated shortcut in state space. Here we extend the notion of a quantum battery from a collection of a priori isolated systems to a many-body quantum system with intrinsic interactions. Specifically, we consider a one-dimensional spin chain with physically realistic two-body interactions. We find that the spin-spin interactions can yield an advantage in charging power over the noninteracting case and we demonstrate that this advantage can grow superextensively when the interactions are long ranged. However, we show that, unlike in previous work, this advantage is a mean-field interaction effect that does not involve correlations and that relies on the interactions being intrinsic to the battery.

Received 13 December 2017

DOI:https://doi.org/10.1103/PhysRevA.97.022106

Physics Subject Headings (PhySH)

Quantum correlations in quantum information Quantum thermodynamics

1-dimensional spin chains

Quantum spin chains Spin chains

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Thao P. Le^1,2, Jesper Levinsen^1,3, Kavan Modi¹, Meera M. Parish^1,3, and Felix A. Pollock¹

¹School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
²Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
³ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Monash University, Clayton, Victoria 3800, Australia

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Issue

Vol. 97, Iss. 2 — February 2018

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Images

Figure 1
(a) Many-body spin-chain battery with internal interactions (represented by bundles of lines), which is charged by local charging fields (light shaded regions), i.e., charging fields that in themselves do not couple the spins together. (b) In contrast, previous literature considered independent subsystems charged by a entangling field (large shaded region) that can couple the system together temporarily during the charging process.
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Figure 2
Maximum power (maximized over time) achievable by a spin chain of length $N = 4$ as a function of anisotropy parameter $α$ [see Eq. (3)]. For this illustration, we consider LR interactions with $p = 1$ , as well as NN interactions [see Eq. (4)]. The remaining parameters are chosen as $g = B$ and $ω = 4 B$ . Here $P_{ind}$ is the power achieved with isotropic interactions, $α = 1$ , corresponding to that of four independent spins.
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Figure 3
Work as a function of time for a two-spin battery in the strong-coupling regime (for this illustration we set $ω = 3 B$ , $α = 0$ , and $g = 20 B$ ). The exact result is shown as the solid blue curve. The slow oscillations [Eq. (14)], related to the effective low-energy Hamiltonian (15), are shown as a black solid line, while the sum of the slow and the fast oscillations of Eq. (13) are shown as a dotted red line.
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Figure 4
(a) Maximum achievable work and (b) power as a function of the spin-chain length. We illustrate this for isotropic (interaction-independent) spin chains ( $XXX$ ) and for anisotropic ( $α = 0$ ) NN interactions and LR interactions with $p = 1$ . We show, for comparison, (c) the average power at maximum work and (d) the work achievable at maximum power. For this illustration, we set $g = 100 B$ and $ω = 4 B$ .
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Figure 5
(a) Work and (b) power as a function of time for a battery with seven spins in the weak-coupling regime (for this illustration we set $ω = 10 B$ , $g = B$ , $α = 0$ , and $p = 1$ ). The perturbative result in Eq. (18) is shown as a dotted red curve, while the exact result corresponds to the solid blue curve.
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Figure 6
Comparison of the maximum power achievable for quantum ( $Q$ ) and classical ( $C$ ) spin chains of varying length. Here we consider isotropic (independent) spin chains ( $XXX$ ) as well as maximally anisotropic spin chains, $α = 0$ , where we have long-range interactions with $p = 1$ (LR Ising) and nearest-neighbor (NN Ising) interactions. In (b), the solid line gives the quantum spin chain results and the dotted line the classical spin chains. For this illustration, we have set $g = B$ and $ω = 4 B$ .
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