Coherence build up and laser thresholds from nanolasers to macroscopic lasers

Abstract

We detail the derivation of nanolaser models that include coherent and incoherent variables and predict the existence of a laser threshold, irrespective of cavity size and emitter number, for both single- and multi-electron systems. The growth in photon number in the lasing mode is driven by an increase in correlation between absorption and emission processes, leading to the onset of self-sustained stimulated emission (laser threshold), followed, in turn, by a correlation decrease and ending with the dominance of coherent emission. The first-order coherence $g^{(1)}$ steadily increases, as the pump grows towards the laser threshold value, and reaches unity at or beyond threshold. The transition toward coherent emission becomes increasingly sharp as the number of emitters and of the coupled electromagnetic cavity modes increase, continuously connecting, in the thermodynamic limit, the physics of nano- and macroscopic lasers at threshold. Our predictions are in remarkable agreement with experiments whose first-order coherence measurements have so far been explained only phenomenologically. A consistent evaluation of different threshold indicators provides a tool for a correct interpretation of experimental measurements at the onset of laser action.

arXiv comment11 pages, 5 figures

References in corpus (8)

• Transport equations including many-particle correlations for an arbitrary quantum system. General formalism
• Emission from quantum-dot high- microcavities: transition from spontaneous emission to lasing and the effects of superradiant emitter coupling
• Single-electron quantum dot in Si/SiGe with integrated charge-sensing
• Measurement of the second-order coherence function for metallic nanolasers
• Unequivocal differentiation of coherent and chaotic light through interferometric photon correlation measurements
• Superthermal light emission and nontrivial photon statistics in small lasers
• Thermal, quantum anti-bunching and lasing thresholds from single emitters to macroscopic devices
• "Phase Transitions" in small systems: why standard threshold definitions fail for nanolasers

Cited by in corpus (1)

• Identifying and anticipating the threshold bifurcation of a complex laser with permutation entropy