  We perform Young's double-slit experiment to study the spatial coherence
properties of a two-dimensional dynamic condensate of semiconductor microcavity
polaritons. The coherence length of the system is measured as a function of the
pump rate, which confirms a spontaneous buildup of macroscopic coherence in the
condensed phase. An independent measurement reveals that the position and
momentum uncertainty product of the condensate is close to the Heisenberg
limit. An experimental realization of such a minimum uncertainty wave packet of
the polariton condensate opens a door to coherent matter-wave phenomena such as
Josephson oscillation, superfluidity, and solitons in solid state condensate
systems.
