Optimal state for a Tavis-Cummings quantum battery via the Bethe ansatz method

TL;DR

This paper analyzes the impact of initial optical field states on a Tavis-Cummings quantum battery's performance, introducing a new method to determine optimal initial states and examining effects like decoherence.

Contribution

It introduces a fast Bethe ansatz solution for the system's dynamics and identifies the optimal initial optical states for maximum energy and power.

Findings

Maximum stored energy proportional to initial photon number

Quantum battery can be fully charged with large initial photon number

Stored energy is hypersensitive to the number-state cavity field

Abstract

In this paper, we investigate the effect of different optical field initial states on the performance of the Tavis-Cummings (T-C) quantum battery. In solving the dynamical evolution of the system, we found a fast way to solve the Bethe ansatz equation. We find that the stored energy and the average charging power of the T-C quantum battery are closely related to the probability distribution of the optical field initial state in the number states. We define a quantity called the number-state stored energy. With this prescribed quantity, we only need to know the probability distribution of the optical field initial state in the number states to obtain the stored energy and the average charging power of the T-C quantum battery at any time. We propose an equal probability and equal expected value splitting method by which we can obtain two inequalities, and the two inequalities can be reduced to Jensen's inequalities. By this method, we found the optimal initial state of the optical field. We found that the maximum stored energy and the maximum average charging power of the T-C quantum battery are proportional to the initial average photon number, and the quantum battery can be fully charged when the initial average photon number is large enough. We found two phenomena, which can be described by two empirical inequalities. These two phenomena imply the hypersensitivity of the stored energy of the T-C quantum battery to the number-state cavity field. Finally, we discussed the impact of decoherence on battery performance.