Quasi-one-dimensional bosons in three-dimensional traps: From strong-coupling to weak-coupling regime

We analyze a recent experiment on a Tonks-Girardeau gas of 87Rb atoms [ T. Kinoshita, T. Wenger and D.S. Weiss Science 305 1125 (2004)]. We find that the experimental data are compatible with the one-dimensional theory of Lieb, Seiringer and Yngvason Phys. Rev. Lett. 91 150401 (2003) but are better described by a theory that takes into account variations in the transverse width of the atomic cloud. By using this theory we investigate also the free axial expansion of the 87Rb gas in different regimes, Tonks-Girardeau gas, one-dimensional Bose-Einstein condensate and three-dimensional Bose-Einstein condensate