  We investigate an optically trapped exciton-polariton condensate and observe
temporal coherence beyond 1~ns duration. Due to the reduction of the spatial
overlap with the thermal reservoir of excitons, the coherence time of the
trapped condensate is more than an order of magnitude longer than that of an
untrapped condensate. This ultralong coherence enables high precision
spectroscopy of the trapped condensate, and we observe periodic beats of the
field correlation function due to a fine energy splitting of two polarization
modes of the condensate. Our results are important for realizing polariton
simulators with spinor condensates in lattice potentials.
