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arXiv:2302.08824 · Physical Review A

Coherence buildup and laser thresholds from nanolasers to macroscopic lasers

Mark Anthony Carroll, Giampaolo D’Alessandro, Gian Luca Lippi, Gian‐Luca Oppo, F. Papoff

Published Jun 26, 2023• 10 citations
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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 multielectron 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 numbers of emitters and 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.

DOI
10.1103/physreva.107.063710

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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.
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We study the stationary photon output and statistics of small lasers. Our closed-form expressions clarify the contribution of collective effects due to the interaction between quantum emitters. We generalize laser rate equations and explain photon trapping: a decrease of the photon number output below the lasing threshold, derive an expression for the stationary cavity mode autocorrelation function g2g_2g2​, which implies that collective effects may strongly influence the photon statistics. We identify conditions for coherent, thermal and superthermal radiation, the latter being a unique fingerprint for collective emission in lasers. These generic analytical results agree with recent experiments, complement numerical results, and provide insight into and design rules for nanolasers.