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Experimental evidence for non-exponential decay in quantum tunnelling

Nature volume 387, pages 575–577 (1997)Cite this article

Abstract

An exponential decay law is the universal hallmark of unstable systems and is observed in all fields of science. This law is not, however, fully consistent with quantum mechanics and deviations from exponential decay have been predicted for short as well as long times1,2,3,4,5,6,7,8. Such deviations have not hitherto been observed experimentally. Here we present experimental evidence for short-time deviation from exponential decay in a quantum tunnelling experiment. Our system consists of ultra-cold sodium atoms that are trapped in an accelerating periodic optical potential created by a standing wave of light. Atoms can escape the wells by quantum tunnelling, and the number that remain can be measured as a function of interaction time for a fixed value of the well depth and acceleration. We observe that for short times the survival probability is initially constant before developing the characteristics of exponential decay. The conceptual simplicity of the experiment enables a detailed comparison with theoretical predictions.

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Figure 1: Distribution of atoms after exposure to a three-stage accelerating standing wave for V0/h = 80kHz.
Figure 2: Typical example of experimentally measured survival probability for a small acceleration of 1,200ms−2, a large acceleration of 4,500ms−2, and V0/h = 50kHz as a function of the duration of the large acceleration.
Figure 3: Survival probability as a function of duration of the large acceleration.
Figure 4: Survival probability as a function of duration of the large acceleration.

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References

  1. Khalfin, L. A. Contribution to the decay theory of a quasi-stationary state. JETP 6, 1053–1063 (1958).

    ADS  MATH  Google Scholar 

  2. Winter, R. G. Evolution of a quasi-stationary state. Phys. Rev. 123, 1503–1507 (1961).

    Article  ADS  Google Scholar 

  3. Fonda, L., Ghirardi, G. C. & Rimini, A. Decay theory of unstable quantum systems. Rep. Prog. Phys. 41, 587–631 (1978).

    Article  ADS  CAS  Google Scholar 

  4. Ballentine, L. E. Quantum Mechanics (Prentice Hall, Englewood Cliffs, NJ, (1990)).

    MATH  Google Scholar 

  5. Greenland, P. T. Seeking non-exponential decay. Nature 335, 298 (1988).

    Article  ADS  Google Scholar 

  6. Chiu, C. B., Sudarshan, E. C. G. & Misra, B. Time evolution of unstable quantum states and a resolution of Zeno's paradox. Phys. Rev. D 16, 520–529 (1977).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  7. Sudarshan, E. C. G., Chiu, C. B. & Bhamathi, G. in Advances in Chemical Physics Vol. XCIX(eds Prigogine, I. & Rice, S. A.) 121–209 (Wiley, New York, (1997)).

    Google Scholar 

  8. Petrosky, T. & Prigogine, I. in Advances in Chemical Physics Vol. XCIX(eds Prigogine, I. & Rice, S. A.) 1–120 (Wiley, New York, (1997)).

    Google Scholar 

  9. Kazantsev, A. P., Surdutovich, G. I. & Yakovlev, V. P. Mechanical Action of Light on Atoms (World Scientific, Singapore, (1990)).

    Book  Google Scholar 

  10. Niu, Q., Zhao, X., Georgakis, G. A. & Raizen, M. G. Atomic Landau-Zener tunneling and Wannier-Stark ladders in optical potential. Phys. Rev. Lett. 76, 4504–4507 (1996).

    Article  ADS  CAS  Google Scholar 

  11. Wilkinson, S. R., Bharucha, C. F., Madison, K. W., Niu, Q. & Raizen, M. G. Observation of atomic Wannier-Stark ladders in an accelerating optical potential. Phys. Rev. Lett. 76, 4512–4515 (1996).

    Article  ADS  CAS  Google Scholar 

  12. Ben Dahan, M., Peik, E., Reichel, J., Castin, Y. & Salomon, C. Bloch oscillations of atoms in an optical potential. Phys. Rev. Lett. 76, 4508–4511 (1996).

    Article  ADS  CAS  Google Scholar 

  13. Bharucha, C. F. et al. Observation of atomic tunneling in an accelerating optical potential. Phys. Rev. A 55, R857–R860 (1997).

    Article  ADS  CAS  Google Scholar 

  14. Cohen-Tannoudji, C. in Fundamental Systems in Quantum Optics (eds Dalibard, J., Raimond, J. M. & Zinn-Justin, J.) 1–164 (Elsevier, Amsterdam, (1992)).

    Google Scholar 

  15. Moore, F. L., Robinson, J. C., Bharucha, C., Williams, P. E. & Raizen, M. G. Observation of dynamical localization in atomic momentum transfer: a new testing ground for quantum chaos. Phys. Rev. Lett. 73, 2974–2977 (1994).

    Article  ADS  CAS  Google Scholar 

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Acknowledgements

M.G.R. was supported by the US Office of Naval Research, the Robert A. Welch Foundation, and the US National Science Foundation; B.S. was supported by the US National Science Foundation; Q.N. was supported by the Robert A. Welch Foundation.

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Author notes

  1. Bala Sundaram

    Present address: Department of Mathematics, CSI-CUNY, Staten Island, New York, 10314, USA

Authors and Affiliations

  1. Department of Physics, The University of Texas at Austin, Austin, 78712-1081, Texas, USA

    Steven R. Wilkinson, Cyrus F. Bharucha, Martin C. Fischer, Kirk W. Madison, Patrick R. Morrow, Qian Niu & Mark G. Raizen

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Correspondence to Mark G. Raizen.

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Wilkinson, S., Bharucha, C., Fischer, M. et al. Experimental evidence for non-exponential decay in quantum tunnelling. Nature 387, 575–577 (1997). https://doi.org/10.1038/42418

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