Experimental test of fluctuation relations for driven open quantum systems with an NV center

TL;DR

This paper experimentally verifies quantum fluctuation relations in a driven open quantum system using an NV center in diamond, demonstrating their validity under cyclic driving and energy exchange with reservoirs.

Contribution

It is the first experimental study confirming quantum fluctuation relations in driven open quantum systems with an NV center, including scenarios with thermal gradients and external work.

Findings

Quantum fluctuation relations hold during cyclic driving.

Validation in cases with an effective infinite-temperature reservoir.

Work can vanish at stroboscopic times despite non-zero power.

Abstract

The experimental verification of quantum fluctuation relations for driven open quantum system is currently a challenge, due to the conceptual and operative difficulty of distinguishing work and heat. The Nitrogen-Vacancy center in diamond has been recently proposed as a controlled test bed to study fluctuation relations in the presence of an engineered dissipative channel, in absence of work [Hern\'andez-G\'omez et al., Phys. Rev. Research 2, 023327 (2020)]. Here, we extend those studies to exploring the validity of quantum fluctuation relations in a driven-dissipative scenario, where the spin exchanges energy both with its surroundings because of a thermal gradient, and with an external work source. We experimentally prove the validity of the quantum fluctuation relations in the presence of cyclic driving in two cases, when the spin exchanges energy with an effective infinite-temperature reservoir, and when the total work vanishes at stroboscopic times -- although the power delivered to the NV center is non-null. Our results represent the first experimental study of quantum fluctuation relation in driven open quantum systems.