Experimental verification of a Jarzynski-related information-theoretic equality using a single trapped ion

Most non-equilibrium processes in thermodynamics are quantified only by inequalities, however the Jarzynski relation presents a remarkably simple and general equality relating non-equilibrium quantities with the equilibrium free energy, and this equality holds in both classical and quantum regimes. We report a single-spin test and confirmation of the Jarzynski relation in quantum regime using a single ultracold $^{40}Ca^{+}$ ion trapped in a harmonic potential, based on a general information-theoretic equality for a temporal evolution of the system sandwiched between two projective measurements. By considering both initially pure and mixed states, respectively, we verify, in an exact and fundamental fashion, the non-equilibrium quantum thermodynamics relevant to the mutual information and Jarzynski equality.