  We demonstrate a regime in which matter-wave condensates of
exciton-polaritons trapped in an elliptically shaped two-dimensional potential
appear as a coherent mixture of ground and first-excited state of the quantum
harmonic oscillator. This system resembles an optically controllable two-level
system and produces near terahertz harmonic oscillations of the condensate's
center of mass along the major axis of the elliptical trapping potential. The
population ratio between the two trap levels is tunable through the excitation
laser power and is shown to follow Lotka-Volterra dynamics. We demonstrate
coherence formation between two spatially displaced trapped condensate
oscillators - the polaritonic analogue of Huygen's clock synchronization for
coupled condensate oscillators.
