Scaling of energy and power in a large quantum battery-charger model

TL;DR

This paper analyzes a large-scale quantum battery-charger model, deriving analytical and numerical results on energy and power scaling, revealing superextensive behavior, and providing insights for experimental realization in superconducting qubit systems.

Contribution

It introduces a comprehensive analysis of energy and power scaling in a large quantum battery model using analytical and numerical methods, highlighting superextensive power growth.

Findings

Superextensive scaling of maximum power $P_B^{ m max}$ observed.

Analytical expressions for energy and power derived via AFM-HP transformation.

System size scaling of energy and power linked to entanglement entropy.

Abstract

We investigate a multi-qubit quantum battery-charger model, focusing on its potential emulation on a superconducting qubit chip. Using a large-spin representation, we first obtain the analytical form of the energy $E_B(t)$, power $P_B(t)$ and their maximum values, $E_B^{\rm max}$ and $P_B^{\rm max}$, of the battery part by means of the antiferromagnetic Holstein-Primakoff (AFM-HP) transformation within the low-energy approximation. In this case, our results show that superextensive scaling behavior of $P_B^{\rm max}$ ensues. By further combining these with the ones obtained via exact diagonalization (ED), we classify the dynamics of various physical quantities, including the entanglement between the battery and charger parts for system sizes encompassing over 10,000 qubits. Finally, by checking a diverse set of system configurations, including either a fixed battery size with growing number of charger qubits, or when both parts simultaneously grow, we classify the system size scalings of $E_B^{\rm max}$ and $P_B^{\rm max}$, relating it with the entanglement entropy in the system. In agreement with the analytical results, robust superextensive behavior of $P_B^{\rm max}$ is also observed in this case. Our work provides an overall guide for expected features in experiments of quantum batteries emulated in superconducting qubit platforms, in particular ones that exhibit long-range couplings.