Quantum battery at the verge of a phase transition*

When the equilibrium state of a system coupled to a bath is an athermal state, i.e., not of the Gibbs form ∽exp(- βH), energy can be extracted from it in a unitary cyclic process. Starting from that observation, we introduce and study a battery--charger quantum device. The device operates in a cycle with four stages: the equilibrium storage stage is interrupted by disconnecting the battery from the charger, then work is extracted from the battery, and then the battery is reconnected with the charger; finally, the system is brought back to equilibrium.

One can engineer thermodynamic processes with an athermal equilibrium state [1]. A more straightforward possibility is to consider a system strongly coupled to a bath [2]. Here we dwell with the second option and study the case where the battery and charger comprise a spin-1/2 Ising chain [3]. We show that the figures of merit---the extracted energy and the thermodynamic efficiency---can be enhanced by operating the cycle close to the quantum phase transition point. When the battery is a single spin, we find that the output work and efficiency show a scaling behavior at criticality and derive the corresponding critical exponents. We found equivalent operations from the perspective of the battery, with different energetic costs for the cycle, and we use this purely quantum leverage to optimize the device's performance [4].

[1] F. Barra, Dissipative charging of a quantum battery, Phys. Rev. Lett. 122 210601 (2019).

[2] K. V. Hovhannisyan, F. Barra and A. Imparato, Charging assisted by thermalization, Phys. Rev. Research 2 033413 (2020).

[3] E. Barouch, B. M. McCoy and M. Dresden, Statistical mechanics of the XY model. i, Phys. Rev. A 2 1075–1092 (1970).

[4] F. Barra, K. V. Hovhannisyan and A. Imparato, Quantum batteries at the verge of a phase transition, http://arxiv.org/abs/2110.10600