  We theoretically analyze exciton-photon oscillatory dynamics within a
homogenous polariton gas in presence of energy detuning between the cavity and
quantum well modes. Whereas pure Rabi oscillations consist of the particle
exchange between the photon and excitons states in the polariton system without
any oscillations of the phases of the two sub-condensates, we demonstrate that
any non-zero detuning results in oscillations of the relative phase of the
photon and exciton macroscopic wave functions. Different initial conditions
reveal a variety of behaviors of the relative phase between the two
condensates, and a crossover from Rabi-like to Josephson-like oscillations is
predicted.
