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Physical Review A

Interacting laser and Bose-Einstein-condensate atomic beams: Mutual guiding structures

Federica Cattani, Vasily Geyko, Arkady V. Kim, D. Anderson, M. Lisak

Published Apr 22, 2010• 7 citations
Publisher

Abstract

A basic set of equations describing the interaction of a Bose-Einstein condensate (BEC) with a laser field is derived based on a semiclassical model and applied to the problem of mutual guiding of laser and BEC atomic beams. Within this framework we have studied stationary spatially localized solutions of the nonlinear system which describe possible laser and BEC atomic beam guiding and have shown their stability as well. It is also shown that a self-guiding effect can be realized through both single- and multiple-scaled structures of a BEC atomic and a laser beam.

DOI
10.1103/physreva.81.043623

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A basic set of equations describing the interaction of a Bose-Einstein condensate (BEC) with a laser field is derived based on a semiclassical model and applied to the problem of mutual guiding of laser and BEC atomic beams. Within this framework we have studied stationary spatially localized solutions of the nonlinear system which describe possible laser and BEC atomic beam guiding and have shown their stability as well. It is also shown that a self-guiding effect can be realized through both single- and multiple-scaled structures of a BEC atomic and a laser beam.
A semi-classical model is derived for describing the interaction between coherent electromagnetic radiation and a Bose–Einstein condensate in the limit of zero temperature, including the back action of the atoms on the radiation. This model is used to analyse the problem of the self-consistent evolution of a laser beam and a BEC atomic beam. The mutual propagation is studied numerically and demonstrates not only the possibility of a stationary regime of mutual guiding, but also of generating a collapse-like phenomenon.
We have studied the details of the formation of mutually guided and localized structures of co-propagating coherent electromagnetic radiation and a Bose-Einstein condensate (BEC). In the limit of zero temperature and large detuning, we have used a semiclassical model based on Maxwell equations coupled to the Schr\"odinger equation which includes the back action of the atoms on the radiation. Following numerically the two systems, we have found that a variety of effects can be displayed depending on the initial conditions: The formation of single-hump mutually guided structures of atoms and radiation seems to be only one of the possible outcomes of the interaction. Other effects we have observed via numerical simulations are, for instance, the creation of atom-laser solitarylike structures which are then symmetrically ejected from the initial central peak or similar symmetrical structures trapped in a bound state and thus oscillating about the central point in a way somehow reminiscent of purely nonlinear optics effect.
The formation of Bose-Einstein condensate (BEC) structures via electromagnetically induced interactions is analyzed within a semiclassical approach, wherein an improved interaction potential is obtained. This analysis shows how the laser-induced forces can lead to self-confinement of the ground state even with a homogeneous field. It furthermore indicates that the vector character of the field can be crucially important, since it can change the type of nonlinearity, thus strongly modifying the BEC structures.
We give a general formulation of the semiclassical approach to solving the problem of interaction between a Bose-Einstein condensate of dilute gas and electromagnetic radiation without using the commonly applied mean-field approximation. We suggest variants of the systems of Maxwell-Schrödinger equations whose solution describes such effects as superradiant light scattering, light beam amplification, atomic wave (atomic laser) amplification, induced transparency, and reduction in the group velocity of light.
We apply the concepts of nonlinear guided-wave optics to a Bose-Einstein condensate (BEC) trapped in an external potential. As an example, we consider a parabolic double-well potential and derive coupled-mode equations for the complex amplitudes of the BEC macroscopic collective modes. Our equations describe different regimes of the condensate dynamics, including the nonlinear Josephson effect for any separation between the wells. We demonstrate macroscopic self-trapping for both repulsive and attractive interactions, and confirm our results by direct numerical solution of the Gross-Pitaevskii-equation.