Pseudo-conservative dynamics of coupled polariton condensates

Open-dissipative systems obeying parity-time ($\mathcal{PT}$) symmetry are capable of demonstrating oscillatory dynamics akin to the conservative systems. In contrast to limit cycle solutions characteristic of nonlinear systems, the $\mathcal{PT}$-symmetric oscillations form a continuum of non-isolated orbits. However, precise sculpturing of the real potential and the gain-loss spatial profiles required for establishing of the $\mathcal{PT}$-symmetry is practically challenging. The optical devices, such as lasers, exhibit relaxation dynamics and do not operate as the $\mathcal{PT}$-symmetric systems. Here we demonstrate how these constraints can be overcome. We predict that a pair of optically trapped polariton condensates (a polariton dimer) can be excited and operated in the oscillating regime typical of the isolated systems. This regime can be realized in the presence of both dissipative and conservative coupling between the condensates and can be maintained at an arbitrary external pump intensity. Every orbit is characterised by a frequency comb appearing in the spectrum of a dimer in the presence of the conservative nonlinearity. Our results pave the way for the creation of the optical computing devices operating under the constant-wave external pumping.