Images of a Bose-Einstein condensate in position and momentum space

Details Images of a Bose-Einstein condensate in position and momentum space Images of a Bose-Einstein condensate in position and momentum space

2005-12-15

arxiv.org/abs/cond-mat/0512359v1

Physics

Condensed Matter

Other Condensed Matter

4 pages; Talk given at the Laser Physics Workshop, July 2005, Kyoto, Japan

Scientific paper

10.1134/S1054660X06120188

In the Bogoliubov theory a condensate initially prepared in its ground state described by stationary Bogoliubov vacuum and later perturbed by a time-dependent potential or interaction strength evolves into a time-dependent excited state which is dynamical Bogoliubov vacuum. The dynamical vacuum has a simple diagonal form in a time-dependent orthonormal basis of single particle modes. This diagonal representation leads to a gaussian probability distribution for possible outcomes of density measurements in position and momentum space. In these notes we also discuss relations with the U(1) symmetry breaking version of the Bogoliubov theory and give two equivalent gaussian integral representations of the dynamical vacuum state.

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