Polariton Lasing in a Multilevel Quantum Dot Strongly Coupled To a Single Photon Mode

TL;DR

This paper develops an analytic model for polariton lasing in a quantum dot-cavity system, revealing lasing behavior at lower pump rates than traditional photon lasing through spectral and coherence analysis.

Contribution

It introduces an approximate analytic expression for the spectral function of a strongly coupled quantum dot-photon system, combining numerical diagonalization and master equation techniques.

Findings

Spectral function captures polariton lasing regime at low pump rates.

Second-order coherence functions vary with pumping, indicating lasing onset.

Model aligns qualitatively with experimental polariton lasing observations.

Abstract

We present an approximate analytic expression for the photoluminescence spectral function of a model polariton system, which describes a quantum dot, with a finite number of fermionic levels, strongly interacting with the lowest photon mode of a pillar microcavity. Energy eigenvalues and wavefunctions of the electron-hole-photon system are obtained by numerically diagonalizing the Hamiltonian. Pumping and photon losses through the cavity mirrors are described with a master equation, which is solved in order to determine the stationary density matrix. The photon first-order correlation function, from which the spectral function is found, is computed with the help of the Quantum Regression Theorem. The spectral function qualitatively describes the polariton lasing regime in the model, corresponding to pumping rates two orders of magnitude lower than those needed for ordinary (photon) lasing. The second-order coherence functions for the photon and the electron-hole subsystems are computed as functions of the pumping rate.