Optimal Control Methods for Quantum Batteries

Abstract

We investigate the optimal charging processes for several models of quantum batteries, finding how to maximize the energy stored in a given battery with a finite-time modulation of a set of external fields. We approach the problem using advanced tools of optimal control theory, highlighting the universality of some features of the optimal solutions, for instance the emergence of the well-known Bang-Bang behavior of the time-dependent external fields. The technique presented here is general, and we apply it to specific cases in which the energy is both pumped into the battery by external forces (direct charging) or transferred into it from an external charger (mediated charging). In this article we focus on particular systems that consist of coupled qubits and harmonic oscillators, for which the optimal charging problem can be explicitly solved using a combined analytical-numerical approach based on our optimal control techniques. However, our approach can be applied to more complex setups, thus fostering the study of many-body effects in the charging process.