Article

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

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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.

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Acknowledgements

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

Affiliations

  1. Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China

    • Shuoming An
    • , Jing-Ning Zhang
    • , Mark Um
    • , Dingshun Lv
    • , Yao Lu
    • , Junhua Zhang
    • , Zhang-Qi Yin
    •  & Kihwan Kim
  2. School of Physics, Peking University, Beijing 100871, China

    • H. T. Quan
  3. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

    • H. T. Quan

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Contributions

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.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to H. T. Quan or Kihwan Kim.

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