Matter-wave propagation in optical lattices

ISSN： 1071-2836

Source： Journal of Russian Laser Research, Vol.31, Iss.3, 2010-05, pp. : 281-293

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Abstract

Coherent propagation of atomic-matter waves in a one-dimensional optical lattice is studied. Wave packets of cold two-level atoms propagate simultaneously in two optical potentials in a dressed-state basis. Three regimes of the wave-packet propagation are specified by the quantity ∆² /ω _D, where ∆ and ω _D are the dimensionless atom–laser detuning and the Doppler shift, respectively. At ∆² /ω _D ≫ 1, the propagation is essentially adiabatic, at ∆² /ω _D ≪ 1, it is (almost) resonant, and at ∆² ≃ ω _D, the wave packets propagate nonadiabatically, splitting at each node of the standing wave. The latter means that the atom makes a transition from one potential to the other one when crossing each node, and the probability of that transition is given by a Landau–Zener-like formula. All the regimes of propagation are studied with δ-like and Gaussian wave packets in the momentum and position spaces. Varying the control parameters, we can create wave packets trapped in a well of optical potentials and moving ballistically in a given direction in close analogy with point-like atoms. Within some range of the parameters, we force the atom to move in a pure quamtum-mechanical manner in such a way that a part of the packet is trapped in a well, and the other part propagates ballistically. The propagation modes are found to be characterized by different types of time evolution of the uncertainty product and the Wigner function.