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We propose a scheme to investigate the nonequilibrium work distribution of aquantum particle under well controlled transformations of the externalpotential, exploiting the versatility of a single ion in a segmented linearPaul trap. We describe in detail how the motional quantum state of a single ioncan be prepared, manipulated and finally read out to fully determine the freeenergy difference in both harmonic and anharmonic potentials. Uniquely to oursystem, we show how an ion may be immersed in an engineered laser--fieldreservoir. Trapped ions therefore represent an ideal tool for investigating theJarzynski equality in open and closed quantum systems.

Employing trapped cold ions to verify the quantum Jarzynski equality