Experimental test of the quantum Jarzynski equality with a trapped-ion system

Abstract

The Jarzynski equality relates the free-energy difference between two equilibrium states to the work done on a system through far-from-equilibrium processes—a milestone that builds on the pioneering work of Clausius and Kelvin. Although experimental tests of the equality have been performed in the classical regime, the quantum Jarzynski equality has not yet been fully verified owing to experimental challenges in measuring work and work distributions in a quantum system. Here, we report an experimental test of the quantum Jarzynski equality with a single 171Yb+ ion trapped in a harmonic potential. We perform projective measurements to obtain phonon distributions of the initial thermal state. We then apply a laser-induced force to the projected energy eigenstate and find transition probabilities to final energy eigenstates after the work is done. By varying the speed with which we apply the force from the equilibrium to the far-from-equilibrium regime, we verify the quantum Jarzynski equality in an isolated system. The Jarzynski equality, relating non-equilibrium processes to free-energy differences between equilibrium states, has been verified in a number of classical systems. An ion-trap experiment now succeeds in demonstrating its quantum counterpart.