# Experimental test of exchange fluctuation relations in an open quantum system

## TL;DR

This paper experimentally verifies quantum fluctuation relations in an open quantum system using nitrogen-vacancy centers, revealing how energy exchange can be understood despite incomplete reservoir information, advancing quantum thermodynamics.

## Contribution

It introduces an experimental approach employing NV centers to test energy exchange fluctuation relations in open quantum systems with tunable dissipation.

## Key findings

- Validation of energy exchange fluctuation relation in an NV center system
- Identification of an energy scale factor encoding reservoir information
- Demonstration of steady-state conditions dictating fluctuation relation validity

## Abstract

Elucidating the energy transfer between a quantum system and a reservoir is a central issue in quantum non-equilibrium thermodynamics, which could provide novel tools to engineer quantum-enhanced heat engines. The lack of information on the reservoir inherently limits the practical insight that can be gained on the exchange process of open quantum systems. Here, we investigate the energy transfer for an open quantum system in the framework of quantum fluctuation relations. As a novel toolbox, we employ a nitrogen-vacancy center spin qubit in diamond, subject to repeated quantum projective measurements and a tunable dissipation channel. In the presence of energy fluctuations originated by dissipation and quantum projective measurements, the experimental results, supplemented by numerical simulations, show the validity of the energy exchange fluctuation relation, where the energy scale factor encodes missing reservoir information in the system out-of-equilibrium steady state properties. This result is complemented by a theoretical argument showing that, also for an open three-level quantum system, the existence of an out-of-equilibrium steady state dictates a unique time-independent value of the energy scale factor for which the fluctuation relation is verified. Our findings pave the way to the investigation of energy exchange mechanisms in arbitrary open quantum systems.