Multi-Photon Lasing Phenomena in Quantum Dot-Cavity QED

Multi-photon lasing has been realized in systems with strong nonlinear interactions between emitters and cavity modes, where single-photon processes are suppressed. Coherence between the internal states of a quantum emitter, or among multiple emitters, plays a key role. Such continuous nonclassical sources of light can find applications in quantum computation, quantum sensing, quantum metrology, and quantum communication. This thesis explores the multi-photon lasing phenomena in various quantum dot-photonic crystal cavity quantum electrodynamic (QED) setups. Exciton-phonon interactions are inevitable in such systems and are incorporated using the polaron-transformed master equation. The Born-Markov approximation is employed to obtain the reduced density matrix rate equation. Using quantum laser theory, we derived the Scully-Lamb laser rate equations and evaluated the single- and multi-photon excess emission rates defined as the difference between emission and absorption rates into the cavity mode without mean-field approximations. We investigated cooperative two-photon lasing, correlated emission lasing, hyperradiant lasing, non-degenerate two-mode two-photon lasing, and continuous variable entanglement in open quantum systems with single or multiple semiconductor quantum dots (two-level, three-level, and four-level) driven coherently/incoherently and coupled to single/ bimodal cavities.