Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System

TL;DR

This paper reports an experimental verification of the quantum Jarzynski equality using a single trapped ytterbium ion, demonstrating its validity in an isolated quantum system through precise measurements of work and transition probabilities.

Contribution

First experimental test of the quantum Jarzynski equality in a trapped ion system, confirming its applicability in quantum non-equilibrium processes.

Findings

Verified the quantum Jarzynski equality in a trapped ion system

Demonstrated the equality holds from equilibrium to far-from-equilibrium regimes

Used projective measurements to accurately determine work distributions

Abstract

The past two decades witnessed important developments in the field of non-equilibrium statistical mechanics. Among these developments, the Jarzynski equality, being a milestone following the landmark work of Clausius and Kelvin, stands out. The Jarzynski equality relates the free energy difference between two equilibrium states and the work done on the system through far from equilibrium processes. While experimental tests of the equality have been performed in classical regime, the verification of the quantum Jarzynski equality has not yet been fully demonstrated due to experimental challenges. Here, we report an experimental test of the quantum Jarzynski equality with a single \Yb ion trapped in a harmonic potential. We perform projective measurements to obtain phonon distributions of the initial thermal state. Following that we apply the laser induced force on the projected energy eigenstate, and find transition probabilities to final energy eigenstates after the work is done. By varying the speed of applying the force from equilibrium to far-from equilibrium regime, we verified the quantum Jarzynski equality in an isolated system.