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Journal of Modern Optics

Inelastic time-dependent tunnelling of matter waves

Maria Luisa Chiofalo, M. Artoni, Giuseppe Carlo La Rocca

Published Apr 1, 2004• 2 citations
Publisher

Abstract

Tunnelling of ultra-cold atoms across a periodically displaced optical barrier exhibits characteristic inelastic effects as well as remarkable transparency at energies for which the same barrier, if stationary, would be opaque. Such phenomena could be observed with sodium Bose-Einstein condensate wavepackets and could be exploited for atom-laser sideband generation.

DOI
10.1080/09500340408233632

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Tunnelling of ultra-cold atoms across a periodically displaced optical barrier exhibits characteristic inelastic effects as well as remarkable transparency at energies for which the same barrier, if stationary, would be opaque. Such phenomena could be observed with sodium Bose-Einstein condensate wavepackets and could be exploited for atom-laser sideband generation.
The criteria for validity of adiabaticity for nonlinear wave equations are considered within the context of atomic matter waves tunneling from macroscopically populated optical standing-wave traps loaded from a Bose-Einstein condensate. We show that, even when the optical standing wave is slowly turned on and the condensate behaves adiabatically during this turn-on, once the tunneling time between wells in the optical lattice becomes longer than the nonlinear time scale, adiabaticity breaks down and a significant spatially varying phase develops across the condensate wave function from well to well. This phase drastically affects the contrast of the fringe pattern in Josephson-effect interference experiments, and the condensate coherence properties in general.
Abstract Quantum tunnelling is a phenomenon of non-equilibrium quantum dynamics and its detailed process is largely unexplored. We report the experimental observation of macroscopic quantum tunnelling of Bose–Einstein condensate in a hybrid trap. By exerting a non-adiabatic kick to excite a collective rotation mode of the trapped condensate, a periodic pulse train, which remains as condensate, is then out-coupled by quantum tunnelling. This non-equilibrium dynamics is analogue to tunnelling ionization. The imaged tunnelling process shows the splitting of matter wave packet by the potential barrier. The controversial “tunnelling time" question is found inadequate, from the point of view of wave propagation. The realized matter wave pulse train can also be a passive pulsed atom laser for atom interferometer applications.
The quantum-mechanical transport properties of cold atoms in an optical lattice are described in terms of an analytically tractable model. The atoms are cooled down to the lowest energy band in the periodic optical potential, in the tight- binding limit. The transport mechanisms are coherent tunneling through potential barriers, and momentum recoil at optical pumping. Expressions are obtained for the time-dependent population distributions over the energy eigenstates and over localized states. These expressions are modified in the presence of a dark atomic state, that is uncoupled to the field.
We realize textbook experiments on Bose-Einstein condensate tunnelling through thin repulsive potential barriers. In particular, we demonstrate atom tunnelling though a single optical barrier in the quantum scattering regime where the De Broglie wavelength of the atoms is larger than the barrier width. Such a beam splitter can be used for atom interferometry and we study the case of two barriers creating an atomic Fabry-P{é}rot cavity. Technically, the velocity of the atoms is reduced thanks to the use of a 39K Bose-Einstein condensate with no interactions. The potential barriers are created optically and their width is tunable thanks to the use of a digital micro-mirror device. In addition, our scattering experiments enable in-situ characterization of the optical aberrations of the barrier optical system.
We study the one-dimensional dynamical behaviour of an atomic wavepacket moving across an opaque and spatially oscillating optical barrier. The tunnelling probability shows a dramatic dependence on the frequency of the barrier oscillation. Transmission of the atomic wavepacket is, in fact, dominated by inelastic or elastic effects, depending on whether the oscillation period is comparable to or shorter than the atom–barrier interaction time. In the elastic regime, in particular, we find that full transparency becomes possible at energies where the stationary barrier would otherwise be essentially opaque. We predict that both inelastic and elastic resonant tunnelling regimes could be observed with atomic condensates impinging on a spatially oscillating optical barrier. A few applications will also be discussed.