On collective Rabi splitting in nanolasers and nano-LEDs. (arXiv:1810.06098v2 [quant-ph] UPDATED)

We analytically calculate the optical emission spectrum of nanolasers and
nano-LEDs based on a model of many incoherently pumped two-level emitters in a
cavity. At low pump rates we find two peaks in the spectrum for large coupling
strengths and numbers of emitters. We interpret the double-peaked spectrum as a
signature of collective Rabi splitting, and discuss the difference between the
splitting of the spectrum and the existence of two eigenmodes. We show that an
LED will never exhibit a split spectrum, even though it can have distinct
eigenmodes. For systems where the splitting is possible we show that the two
peaks merge into a single one when the pump rate is increased. Finally, we
compute the linewidth of the systems, and discuss the influence of
inter-emitter correlations on the lineshape.

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