Spin oscillations of a single-mode polariton system driven by a plane wave

Theoretical study is performed of a single-mode polariton system with linear coupling of spin components. Such coupling results in the spontaneous breakdown of the spin symmetry under coherent driving, which is usually accompanied by a switch from linear to circular polarization. Here, it is found that each of the states with broken symmetry can undergo the Hopf bifurcation into a zero-amplitude limit cycle that gradually expands upon varying excitation parameters. Within a finite range of excitation powers, two equally possible limit cycles corresponding to opposite spin states remain separate in the phase space, however, at some point they unite and produce the full-range oscillations of the circular-polarization degree. Depending on excitation frequency and spin coupling strength, the oscillations can either be regular and robust against arbitrary perturbations or show a transition to chaos through a series of the period-doubling events.