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Article Dans Une Revue Laser Photonics Rev. Année : 2023

Quantum density matrix theory for a laser without adiabatic elimination of the population inversion: transition to lasing in the class-B limit

Résumé

Despite the enormous technological interest in micro and nanolasers, surprisingly, no class-B quantum density-matrix model is available to date, capable of accurately describing coherence and photon correlations within a unified theory. In class-B lasers $-$applicable for most solid-state lasers at room temperature$-$, the macroscopic polarization decay rate is larger than the cavity damping rate which, in turn, exceeds the upper level population decay rate. Here we carry out a density-matrix theoretical approach for generic class-B lasers, and provide closed equations for the photonic and atomic reduced density matrix in the Fock basis of photons. Such a relatively simple model can be numerically integrated in a straightforward way, and exhibits all the expected phenomena, from one-atom photon antibunching, to the well-known S-shaped input-output laser emission and super-Poissonian autocorrelation for many atoms ($1\leq g^{(2)}(0)\leq 2$), and from few photons (large spontaneous emission factors, $\beta\sim1$) to the thermodynamic limit ($N\gg1$ and $\beta\sim 0$). Based on the analysis of $g^{(2)}(\tau)$, we conclude that super-Poissonian fluctuations are clearly related to relaxation oscillations in the photon number. We predict a strong damping of relaxation oscillations with an atom number as small as $N\sim 10$. This model enables the study of few-photon bifurcations and non-classical photon correlations in class-B laser devices, also leveraging quantum descriptions of coherently coupled nanolaser arrays.

Dates et versions

hal-03693083 , version 1 (10-06-2022)

Identifiants

Citer

Alejandro M. Yacomotti, Zakari Denis, Alberto Biella, Cristiano Ciuti. Quantum density matrix theory for a laser without adiabatic elimination of the population inversion: transition to lasing in the class-B limit. Laser Photonics Rev., 2023, 17 (1), pp.2200377. ⟨10.1002/lpor.202200377⟩. ⟨hal-03693083⟩
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