Bosons in Cigar-Shaped Traps: Thomas-Fermi Regime, Tonks-Girardeau Regime, and In Between

Abstract
We present a quantitative analysis of the experimental accessibility of the Tonks-Girardeau gas in present-day experiments with cigar-trapped alkalis. For this purpose we derive, using a Bethe ansatz generated local equation of state, a set of hydrostatic equations describing one-dimensional, δ-interacting Bose gases trapped in a harmonic potential. The resulting solutions cover the entire range of atomic densities.