Dynamical transition from a quasi-one dimensional Bose-Einstein condensate to a Tonks-Girardeau gas

Details Dynamical transition from a quasi-one dimensional Bose-Einstein condensate to a Tonks-Girardeau gas Dynamical transition from a quasi-one dimensional Bose-Einstein condensate to a Tonks-Girardeau gas

2002-04-29

arxiv.org/abs/cond-mat/0204611v3

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 2 figures, replacement (minor misprint)

Scientific paper

We analyze in detail the expansion of a 1D Bose gas after removing the axial confinement. We show that during its one-dimensional expansion the density of the Bose gas does not follow a self-similar solution, but on the contrary, it asymptotically approaches a Tonks-Girardeau profile. Our analysis is based on a nonlinear Schr\"odinger equation with variable nonlinearity whose validity is discussed for the expansion problem, by comparing with an exact Bose-Fermi mapping for the case of an initial Tonks-Girardeau gas. For this case, the gas is shown to expand self-similarly, with a different similarity law compared to the one-dimensional Thomas-Fermi condensate.

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