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≈0.5ℏω_⊥ (transverse oscillator eigenfrequency ω_⊥) 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.