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Experimental evidence for non-exponential decay in quantum tunnelling

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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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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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  1. Steven R. Wilkinson
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  2. Cyrus F. Bharucha
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  3. Martin C. Fischer
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  4. Kirk W. Madison
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  6. Qian Niu
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  7. Bala Sundaram
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  8. 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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