Finite-size fluctuations and photon statistics near the polariton condensation transition in a single-mode microcavity

Abstract

We consider polariton condensation in a generalized Dicke model, describing a single-mode cavity containing quantum dots, and extend our previous mean-field theory to allow for finite-size fluctuations. Within the fluctuation-dominated regime the correlation functions differ from their ͑trivial͒ mean-field values. We argue that the low-energy physics of the model, which determines the photon statistics in this fluctuation-dominated crossover regime, is that of the ͑quantum͒ anharmonic oscillator. The photon statistics at the crossover are different in the high-temperature and low-temperature limits. When the temperature is high enough for quantum effects to be neglected we recover behavior similar to that of a conventional laser. At low enough temperatures, however, we find qualitatively different behavior due to quantum effects.

Mode locking and mode competition in a nonequilibrium solid-state condensate

“…Our estimates for the critical density of the synchronization transition suggest that it could be cleanly observed in tight traps 11 and is likely to be responsible for the observations of long-range coherence across disorder potentials. 1,14 This latter conclusion could be strengthened by extending the present work to include ͑i͒ a realistic model of the states in a disorder potential, ͑ii͒ thermalization processes, and ͑iii͒ fluctuations beyond the mean-field theory 23 -which lead to linewidths 13 for the condensing modes and hence compete with the synchronization.…”

“…They would be important for a finite system close to the threshold. 23 The phase dynamics is straightforward, obeying…”

Build up of off-diagonal long-range order in microcavity exciton-polaritons across the parametric threshold

“…Despite the lack of spatial fluctuations, the coherence time of our condensate, though long, is clearly finite. In general, such a finite correlation time in a state with perfect spatial order is caused by finite-size fluctuations [28], and reflects the absence of true phase transitions in finite systems. A well-known example is the Schawlow-Townes formula for the coherence time of a single laser mode with an average ofN photons, T c ∝N.…”

Nanolaser with a Single-Graphene-Nanoribbon in a Microcavity

“…It should be noted that the value of the nonlinear excitonic parameter which describes the strength of the interaction between excitons can be estimated to be =0.01 and the details can be found in Ref. [16][17][18]22].…”