Precision and Work Fluctuations in Gaussian Battery Charging

TL;DR

This paper investigates the limitations and optimal protocols for charging quantum batteries using Gaussian unitaries, highlighting the trade-offs between practical implementability and charging precision in quantum thermodynamics.

Contribution

It introduces optimal charging protocols within Gaussian unitaries and analyzes their performance, emphasizing practical constraints in quantum battery charging.

Findings

Gaussian unitaries enable asymptotically vanishing charge fluctuations.

Practical Gaussian charging performs less efficiently than ideal protocols.

Optimal Gaussian protocols approach ideal precision in the asymptotic limit.

Abstract

One of the most fundamental tasks in quantum thermodynamics is extracting energy from one system and subsequently storing this energy in an appropriate battery. Both of these steps, work extraction and charging, can be viewed as cyclic Hamiltonian processes acting on individual quantum systems. Interestingly, so-called passive states exist, whose energy cannot be lowered by unitary operations, but it is safe to assume that the energy of any not fully charged battery may be increased unitarily. However, unitaries raising the average energy by the same amount may differ in qualities such as their precision, fluctuations, and charging power. Moreover, some unitaries may be extremely difficult to realize in practice. It is hence of crucial importance to understand the qualities that can be expected from practically implementable transformations. Here, we consider the limitations on charging batteries when restricting to the feasibly realizable family of Gaussian unitaries. We derive optimal protocols for general unitary operations as well as for the restriction to easier implementable Gaussian unitaries. We find that practical Gaussian battery charging, while performing significantly less well than is possible in principle, still offers asymptotically vanishing relative charge variances and fluctuations.