Low- and high-$\beta$ lasers in Class-A limit: photon statistics, linewidth, and the laser-phase transition analogy

Abstract

Nanocavity lasers are commonly characterized by the spontaneous coupling coefficient $\beta$ that represents the fraction of photons emitted into the lasing mode. While $\beta$ is conventionally discussed in semiconductor lasers where the photon lifetime is much shorter than the carrier lifetime (class-B lasers), little is known about $\beta$ in atomic lasers where the photon lifetime is much longer than the other lifetimes and only the photon degree of freedom exists (class-A lasers). We investigate the impact of the spontaneous coupling coefficient $\beta$ on lasing properties in the class-A limit by extending the well-known Scully-Lamb master equation. We demonstrate that, in the class-A limit, all the photon statistics are uniquely characterized by $\beta$ and that the laser phase transition-like analogy becomes transparent. In fact, $\beta$ perfectly represents the "system size" in phase transition. Finally, we investigate the laser-phase transition analogy from the standpoint of a quantum dissipative system. Calculating a Liouvillian gap, we clarify the relation between $\beta$ and the continuous phase symmetry breaking.

References in corpus (20)

• Spectral theory of Liouvillians for dissipative phase transitions
• Dissipative Phase Transition in Central Spin Systems
• Boundary time crystals
• Algebraic versus exponential decoherence in dissipative many-particle systems
• Polariton quantum blockade in a photonic dot
• Probing a dissipative phase transition via dynamical optical hysteresis
• Critical dynamical properties of a first-order dissipative phase transition
• Signatures of a dissipative phase transition in photon correlation measurements
• Fast Purcell-enhanced single photon source in 1,550-nm telecom band from a resonant quantum dot-cavity coupling
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Controlling the dynamics of a coupled atom-cavity system by pure dephasing : basics and potential applications in nanophotonics
• Pure emitter dephasing : a resource for advanced solid-state single photon sources
• On thresholdless lasing features in high-$\beta$ nitride nanobeam cavities: a quantum optical study
• Scully-Lamb quantum laser model for parity-time-symmetric whispering-gallery microcavities: Gain saturation effects and non-reciprocity
• Higher-order photon correlations in pulsed photonic crystal nanolasers
• Superthermal light emission and nontrivial photon statistics in small lasers
• Delayed transition to coherent emission in nanolasers with extended gain media
• Optical Bistability in a Low Photon-Density Regime
• Laser theory in manifest Lindblad form
• Spontaneous symmetry breaking in the laser transition

Cited by in corpus (12)

• Continuous Dissipative Phase Transitions without Symmetry Breaking
• The driven-dissipative Bose-Hubbard dimer: phase diagram and chaos
• Dissipative phase transitions in $n$-photon driven quantum nonlinear resonators
• Liouvillian spectral collapse in the Scully-Lamb laser model
• Quantum density matrix theory for a laser without adiabatic elimination of the population inversion: transition to lasing in the class-B limit
• "Phase Transitions" in small systems: why standard threshold definitions fail for nanolasers
• A stochastic approach to the quantum noise of a single-emitter nanolaser
• Emulating the local Kuramoto model with an injection-locked photonic crystal laser array
• Probing the Ginzburg-Landau Potential for Lasers Using Higher-order Photon Correlations
• Simple yet Accurate Stochastic Approach to the Quantum Phase Noise of Nanolasers
• Modeling Quantum Noise in Nanolasers using Markov Chains
• Second-order correlation function supported optical sensing for particle detection