  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.
