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Dynamical tunnelling of ultracold atoms

Nature volume 412, pages 52–55 (2001)Cite this article

Abstract

The divergence of quantum and classical descriptions of particle motion is clearly apparent in quantum tunnelling1,2 between two regions of classically stable motion. An archetype of such non-classical motion is tunnelling through an energy barrier. In the 1980s, a new process, ‘dynamical’ tunnelling1,2,3, was predicted, involving no potential energy barrier; however, a constant of the motion (other than energy) still forbids classically the quantum-allowed motion. This process should occur, for example, in periodically driven, nonlinear hamiltonian systems with one degree of freedom4,5,6. Such systems may be chaotic, consisting of regions in phase space of stable, regular motion embedded in a sea of chaos. Previous studies predicted4 dynamical tunnelling between these stable regions. Here we observe dynamical tunnelling of ultracold atoms from a Bose–Einstein condensate in an amplitude-modulated optical standing wave. Atoms coherently tunnel back and forth between their initial state of oscillatory motion (corresponding to an island of regular motion) and the state oscillating 180° out of phase with the initial state.

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Figure 1: Poincaré section for position q and momentum p of a classical particle in an amplitude-modulated optical lattice.
Figure 2: Diagram of period-one resonances of an atom in an amplitude-modulated sinusoidal potential.
Figure 3: Atomic momentum distributions after n modulation periods, showing dynamical tunnelling.
Figure 4: Mean momentum as a function of the number of modulation periods, n.
Figure 5: Momentum distributions as a function of the number of modulation periods, showing the tunnelling oscillation between negative and positive momenta.

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Acknowledgements

We thank C. Holmes for discussions. The NIST group was supported by the ONR, NASA and ARDA, and the University of Queensland group was supported by the ARC. A.B. was partially supported by DGA (France), and H. H. was partially supported by the A. v. Humboldt Foundation. W.K.H. and B.U. thank NIST for hospitality during the experiments.

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Authors and Affiliations

  1. National Institute of Standards and Technology, Gaithersburg, 20899, Maryland, USA

    W. K. Hensinger, H. Häffner, A. Browaeys, K. Helmerson, C. McKenzie, W. D. Phillips, S. L. Rolston & B. Upcroft

  2. Centre for Laser Science, Department of Physics, The University of Queensland, Brisbane, 4072, Queensland, Australia

    W. K. Hensinger, N. R. Heckenberg, H. Rubinsztein-Dunlop & B. Upcroft

  3. Centre for Quantum Computer Technology, The University of Queensland, Brisbane, 4072, Queensland, Australia

    G. J. Milburn

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  1. W. K. Hensinger
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Correspondence to W. K. Hensinger.

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Hensinger, W., Häffner, H., Browaeys, A. et al. Dynamical tunnelling of ultracold atoms. Nature 412, 52–55 (2001). https://doi.org/10.1038/35083510

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