Population Fluctuation Mechanism of the Super-Thermal Photon Statistic of Quantum LEDs with Collective Effects

Abstract

The analytical procedure is developed for the calculation of the quantum second-order autocorrelation function $g_2$ of a small super-radiant LED, where the field, polarisation, and population of the active medium cannot be eliminated adiabatically. The Langevin force, which describes the effect of population fluctuations on the LED polarisation and preserves the operator commutation relations, is found. It is demonstrated that the super-thermal photon statistics with $g_2>2$ of a small quantum LED with large photon number fluctuations, emitter-field coupling, bad cavity, and operating in the limit $n\to 0$, is the result of a combined effect of the spontaneous emission, collective effects and population fluctuations. Analytical expressions for $g_2$ and $n$ are derived.