Nondegenerate two-photon lasing in a single quantum dot

We propose two-mode two-photon microlaser using a single semiconductor quantum dot grown inside a two-mode microcavity. We explore both incoherent and coherent pumping at low temperatures to achieve suitable conditions for two-mode two-photon lasing. The two-mode two-photon stimulated emission is strongly suppressed but the single-photon stimulated emission is enhanced by exciton-phonon interactions. In coherently pumped quantum dot one can achieve large two-mode two-photon lasing where single-photon lasing is almost absent. We also discuss generation of steady state two-mode entangled state using two-photon resonant pumping.