Coherent population oscillations and an effective spin-exchange interaction in a $\mathcal{PT}$ symmetric polariton mixture

We study a two-species mixture of exciton-polaritons with self- and cross-interaction nonlinearities in a double well structure, in the presence of relaxation and continuous pumping. We identify the conditions that render the system parity-time ($\mathcal{PT}$) symmetric, and investigate its dynamic and static properties. We show that the system can exhibit long-term coherent oscillations of populations of the two polaritonic components between the two potential wells, and can simulate the dynamics of a pair of spin-1/2 particles (qubits) in the presence of exchange interaction.