  We realize a one-dimensional Josephson junction using quantum degenerate Bose
gases in a tunable double well potential on an atom chip. Matter wave
interferometry gives direct access to the relative phase field, which reflects
the interplay of thermally driven fluctuations and phase locking due to
tunneling. The thermal equilibrium state is characterized by probing the full
statistical distribution function of the two-point phase correlation.
Comparison to a stochastic model allows to measure the coupling strength and
temperature and hence a full characterization of the system.
