Thermal, Quantum Antibunching and Lasing Thresholds from Single Emitters to Macroscopic Devices

Abstract

Starting from a fully quantized Hamiltonian for an ensemble of identical emitters coupled to the modes of an optical cavity, we determine analytically regimes of thermal, collective anti-bunching and laser emission that depend explicitly on the number of emitters. The lasing regime is reached for a number of emitters above a critical number-which depends on the light-matter coupling, detuning and the dissipation rates-via a universal transition from thermal emission to collective anti-bunching to lasing as the pump increases. Cases where the second order intensity correlation fails to predict laser action are also presented.

Photon-number squeezing in nano- and microlasers

“…In line with these developments, the recent quantum-dot based Coherent-Incoherent model (CIM), where the coherent and incoherent field components are independently described 35 , predicts from first principles the existence of a prethreshold regime where photon antibunching, thus squeezing 36 , is naturally observed. The CIM model has been derived under the experimentally verified conditions 37 that the decay rate of the material polarization is much larger than that of the photons in the cavity.…”

“…Antibunching has been experimentally observed and modeled 39 for a low number of emitters. In this letter we predict that squeezing with large photon number occurs at extremely low power supply for nano and micro laser with emitter numbers up to 10 3 in the anti-bunching region 35 . The advantage of this prediction is that the photon antibunched behaviour appears to naturally precede lasing, in a cw regime of operation, without the need for any special experimental arrangements and promises to provide photon fluxes comparable or larger than those of more complex, pulsed techniques.…”

“…[40][41][42] and references therein), in the photon number for macroscopic signals. These qualitative considerations point to a potential interest even in a moderate amount of antibunching emerging from the model 35 .…”

“…We test the idea by using a quantum model 35 , derived using the cluster expansion technique 44,45 , that includes both coherent and incoherent field components; previous cluster expansion based models neglect the expectation values of the coherent variables [46][47][48] .Its key feature resides in the univocal determination of a lasing threshold irrespective of cavity characteristics (even for β = 1, the fraction of spontaneous emission coupled into the lasing mode), thus establishing a clear boundary between the squeezed and coherent emission regime. The medium is assumed to be an ensemble of iden- tical but independent two-level emitters coupled with a single cavity lasing mode.…”

“…for which squeezing can occur and this becomes narrower as the number of intra-cavity emitters increases 35 . As we later show, this constraint does not strongly affect the scheme's implementability.…”