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

• URL: http://arxiv.org/abs/2205.13473v1
• Date: Thu, 26 May 2022 16:33:51 GMT
• Title: Quantum density matrix theory for a laser without adiabatic elimination of the population inversion: transition to lasing in the class-B limit
• Authors: Alejandro M. Yacomotti, Zakari Denis, Alberto Biella, Cristiano Ciuti
• Abstract summary: No class-B quantum density-matrix model is available to date, capable of accurately describing coherence and photon correlations within a unified theory. 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. 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.
• Score: 62.997667081978825
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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