1. National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
2. Centre for Laser Science, Department of Physics, The University of Queensland, Brisbane, Queensland 4072, Australia
3. Centre for Quantum Computer Technology, The University of Queensland, Brisbane, Queensland 4072, Australia

Correspondence to: W. K. Hensinger^1,2 Correspondence and requests for materials should be addressed to W.K.H. (e-mail: Email: hensinge@physics.uq.edu.au).

Abstract

The divergence of quantum and classical descriptions of particle motion is clearly apparent in quantum tunnelling^{1, 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' tunnelling^{1, 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 freedom^{4, 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.