Nondegenerate two-photon lasing in a single quantum dot

We propose a two-mode, two-photon microlaser using a single semiconductor quantum dot (QD) grown inside a two-mode microcavity. We explore both incoherent and coherent pumping at low temperatures to achieve suitable conditions for the lasing. The two-mode, two-photon-stimulated emission is strongly suppressed when exciton-phonon interactions occur, but the single-photon-stimulated emission is enhanced in this case. In coherently pumped QDs, one can achieve large two-mode, two-photon lasing, while the single-photon lasing is almost absent here. We further extend our study for the generation of a two-mode entangled state using two-photon resonant pumping.