Charging dynamics of quantum batteries under the time-energy uncertainty relation

Abstract

Quantum battery is an emerging field of research that utilizes the principles of quantum mechanics to store energy in quantum systems. In this work, we analytically solve the time-evolution of a battery that is coupled with a charger modelled by a harmonic oscillator in the interaction picture, and we expand the wavefunction using time-dependent basis eigenkets. From the analytic solution, we find that charging two batteries that have direct interaction with each other presents an advantage in terms of the time at which the batteries attain their completely charged state over charging one battery or two non-interacting batteries. This advantage, however is evident only for moderate coupling, and this compromises the maximum charging probability of these batteries. Moreover, in the large-coupling regime, the charging times of three systems approach equality, and the probability approaches certainty. The difference between the charging dynamics of the three systems is illuminated by the time-energy uncertainty relation.