Weakly Interacting Bose Gas in the One-Dimensional Limit

We prepare a chemically and thermally one-dimensional (1D) quantum degenerate Bose gas in a single microtrap. We introduce a new interferometric method to distinguish the quasicondensate fraction of the gas from the thermal cloud at finite temperature. We reach temperatures down to kT approximate to 0.5h omega(perpendicular to) ( transverse oscillator eigenfrequency omega(perpendicular to)) when collisional thermalization slows down as expected in 1D. At the lowest temperatures the transverse-momentum distribution exhibits a residual dependence on the line density n(1D), characteristic for 1D systems. For very low densities the approach to the transverse single-particle ground state is linear in n(1D).