# Jarzynski equality for superconducting optical cavities: an alternative path to determine Helmholtz free energy

## TL;DR

This paper proposes using superconducting optical cavities and the Jarzynski equality to experimentally determine Helmholtz free energy changes through visibility measurements, offering a novel approach in quantum thermodynamics.

## Contribution

It introduces a new method linking visibility measurements in superconducting cavities to free energy variations via the Jarzynski equality, providing an alternative experimental pathway.

## Key findings

- Established a mathematical relationship between free energy change and visibility.
- Validated the applicability of Jarzynski equality in superconducting cavity systems.
- Proposed a practical method to measure quantum work using visibility.

## Abstract

A superconducting cavity model was proposed as a way to experimentally investigate the work performed in a quantum system. We found a simple mathematical relationship between the free energy variation and visibility measurement in quantum cavity context. If we consider the difference of Hamiltonian at time $t_0$ and $t_\lambda$ (protocol time) as a quantum work, then the Jarzynski equality is valid and the visibility can be used to determine the work done on the cavity.