Lotka-Volterra population dynamics in coherent and tunable oscillators of trapped polariton condensates

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 states 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. Furthermore, we demonstrate coherence formation between two spatially displaced trapped condensate oscillators---the polaritonic analog of Huygen's clock synchronization for coupled condensate oscillators.