Formation of hybrid parametric cavity polariton solitons

We study the nonlinear dynamics of exciton-polaritons in semiconductor microcavities operating in the strong-coupling regime and driven by a coherent optical pump above the exciton resonance. Provided that the exciton dispersion is accounted for, parametric mixing of polaritons from the upper and the lower polariton branches gives rise to modulational instability of the homogeneous solution. This instability leads to the formation of quasiperiodic patterns. Our analytical analysis shows that there are domains in parameter space where these patterns and stable homogeneous solution may exist simultaneously. This is the prerequisite for the existence of cavity polariton solitons---single-peak solutions on a homogeneous background. Because they originate from parametric mixing of polaritons from both branches of the dispersion relation we term them hybrid parametric cavity solitons. There are two kinds of these resting solitons---stationary and breathing ones. Both types require for stability that the cavity resonance be redshifted to the exciton resonance.