Quantum battery supercharging via counter-diabatic dynamics

TL;DR

This paper presents a counter-diabatic method to design Hamiltonians for quantum batteries that enables supercharging with a limited number of global interactions, achieving quadratic scaling in power with system size.

Contribution

It introduces a novel counter-diabatic approach for quantum battery supercharging, demonstrating that maximum power can be achieved with only O(n) multipartite interactions.

Findings

Supercharging requires multipartite interactions, but not necessarily many.

A spin chain model achieves quadratic power scaling with O(n) interactions.

Counter-diabatic expansion surpasses adiabatic time constraints with limited many-body terms.

Abstract

We introduce a counter-diabatic approach for deriving Hamiltonians modeling superchargable quantum batteries (QBs). A necessary requirement for the supercharging process is the existence of multipartite interactions among the cells of the battery. Remarkably, this condition may be insufficient no matter the number of multipartite terms in the Hamiltonian. We analytically illustrate this kind of insufficiency through a model of QB based on the adiabatic version for the Grover search problem. On the other hand, we provide QB supercharging with just a mild number of global connections in the system. To this aim, we consider a spin-$1/2$ chain with $n$ sites in the presence of Ising multipartite interactions. We then show that, by considering the validity of the adiabatic approximation and by adding $n$ terms of $(n-1)$-site interactions, we can achieve a Hamiltonian exhibiting maximum QB power, with respect to a normalized evolution time, growing quadratically with $n$. Therefore, supercharging can be achieved by $O(n)$ terms of multipartite connections. The time constraint required by the adiabatic approximation can be surpassed by considering a counter-diabatic expansion in terms of the gauge potential for the original Hamiltonian, with a limited $O(n)$ many-body interaction terms assured via a Floquet approach for the counter-diabatic implementation.