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


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.

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Figure 1: Experimental set-up for testing the Jarzynski equality and equilibrium and non-equilibrium work processes.
Figure 2: Thermal state preparation of the phonon and measurement results.
Figure 3: Experimental scheme for the projective measurement of the phonon state.
Figure 4: Dissipated work Wdiss = WΔ F = νΔ n and probabilities for three different ramping speeds of the force.


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We thank C. Jarzynski for careful reading of the manuscript and helpful comments. This work was supported in part by the National Basic Research Program of China Grants 2011CBA00300, 2011CBA00301, the National Natural Science Foundation of China Grants 61073174, 61033001, 61061130540, 11374178, 11375012 and 11105136. K.K. and H.T.Q. acknowledge the recruitment program of Global Youth Experts of China.

Author information




S.A., M.U., D.L. and Y.L. developed the experimental system and performed the experiments. Y.L. and S.A. analysed the results. J.Z. developed the adiabatic protocol for the projective measurement. J-N.Z. provided the concrete model for the experiment. J-N.Z., Z-Q.Y. and H.T.Q. provided theoretical support to the project. K.K. supervised the project. All authors contributed to writing the manuscript.

Corresponding authors

Correspondence to H. T. Quan or Kihwan Kim.

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The authors declare no competing financial interests.

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An, S., Zhang, JN., Um, M. et al. Experimental test of the quantum Jarzynski equality with a trapped-ion system. Nature Phys 11, 193–199 (2015).

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