Multi-Photon Lasing Phenomena in Quantum Dot-Cavity QED

TL;DR

The thesis develops a comprehensive open-quantum-systems framework to realize and characterize multi-photon lasing phenomena in semiconductor QD–cavity QED. By employing a polaron-transformed master equation within the Born–Markov approximation, it derives laser-rate equations (without mean-field approximations) that capture the full emitter–cavity dynamics and phonon-mediated processes. The work demonstrates cooperative two-photon lasing and hyperradiant emission in two-QD single-mode setups, extends to two-mode hyperradiant lasing in bimodal cavities, and shows correlated emission lasing that suppresses phase noise and enables continuous-variable entanglement. It further demonstrates nondegenerate two-photon lasing with a biexciton in a nondegenerate bimodal cavity, including CV entanglement under two-photon resonance. Together, the results establish semiconductor QD–cavity QED as a scalable platform for on-chip quantum light sources with applications in quantum metrology, communication, and sensing, while offering exact (vs mean-field) treatments of multi-photon processes and robust phase-noise control through emitter cooperativity and phonon engineering.

Abstract

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.

Figures (66)

• Figure 1: Density of states for (a) Bulk crystal (3D) (b) Quantum well (2D) (c) Quantum wire (1D) (d) Quantum dot (0D)
• Figure 2: A schematic figure showing a quantum dot excited either incoherently (green) or coherently (red) forms an electron–hole pair (exciton) after non-radiative relaxation due to interaction with the surrounding phonon bath. Electron-hole pair whose recombination leads to photon emission.
• Figure 3: (a) Exciton (b) $|X_b\rangle$, $|Y_b\rangle$ fine structure splitting, $\delta$, and along with $|g\rangle$ forming a 3-level system (c) $|XX\rangle$, $|X_b\rangle$, $|Y_b\rangle$, and $|g\rangle$ forming a 4-level system showing transitions between biexcitonic and excitonic states.
• Figure 4: Dashed lines represent planes of atoms in equilibrium, while solid lines show their displacement when a longitudinal wave propagates through the medium.
• Figure 5: Displacement of planes of atoms (solid circles) when a transverse wave passes through the medium.