Theory of Polariton Solitons in Semiconductor Microcavities

Abstract

We review the physics behind the formation of localized states of exciton-polaritons, or polariton solitons, in semiconductor microresonators operating in the strong coupling regime. We describe the properties of polariton solitons existing in the vicinity of both the lower- and upper-polariton branches and discuss their linear stability. Strength and sign of polariton dispersion can be controlled by changing the transverse momentum of the pump beam which leads to new degrees of freedom in soliton formation. In particular, we show that pump momenta associated with a positive polariton mass, occurring near the bottom of the lower-polariton branch, favor the formation of stable two- (2D) and one-dimensional (1D) dark solitons. Polaritons with a large momentum exhibit a negative effective mass and lead to the formation of moving 1D bright solitons. An important feature of the strong light–matter interaction is that it allows the existence of 2D bright solitons having a negative effective mass along the direction of the pump momentum and a positive effective mass along the orthogonal direction. Saturation of photon–exciton coupling can support stable bright solitons near the upper-polariton branch above the excitonic resonance. Taking into account the finite mass of excitons leads to modulational instability (filamentation) of the transverse soliton profile and the generation of free excitons. This instability either entails the generation of stationary nanoscale periodic patterns localized on the soliton background or to an explosive oscillatory soliton dynamics.