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arXiv:2509.05290 · Physical Review A

Excitable quantum systems: The bosonic avalanche laser

Louis Garbe, Peter Rabl

Published Jun 30, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the dynamics of a lasing system driven by a current of bosonic (quasi-)particles via a dissipative three-mode mixing process. A semiclassical analysis of this system predicts distinct dynamical regimes, where both the cavity mode and the gain medium can undergo lasing transitions. Of particular interest is an intermediate self-pulsing phase that exhibits the characteristics of an excitable system and converts random input signals into separated, quasi-periodic pulses at the output. By performing exact Monte Carlo simulations, we extend this analysis into the quantum regime and show that despite being dominated by huge bosonic particle number fluctuations, this effect survives even for rather low average photon numbers. Our system thus represents an intriguing model of an excitable quantum many-body system, with practical relevance for quantum detectors or autonomous quantum machines. As an illustration, we discuss the realization of this system with superconducting quantum circuits and its application as a number-resolved avalanche detector for microwave photons.

DOI
10.1103/xn1v-mwvm

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We investigate the dynamics of a lasing system driven by a current of bosonic (quasi-)particles via a dissipative three-mode mixing process. A semiclassical analysis of this system predicts distinct dynamical regimes, where both the cavity mode and the gain medium can undergo lasing transitions. Of particular interest is an intermediate self-pulsing phase that exhibits the characteristics of an excitable system and converts random input signals into separated, quasi-periodic pulses at the output. By performing exact Monte Carlo simulations, we extend this analysis into the quantum regime and show that despite being dominated by huge bosonic particle number fluctuations, this effect survives even for rather low average photon numbers. Our system thus represents an intriguing model of an excitable quantum many-body system, with practical relevance for quantum detectors or autonomous quantum machines. As an illustration, we discuss the realization of this system with superconducting quantum circuits and its application as a number-resolved avalanche detector for microwave photons.
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The dominant role of quantum fluctuations in determining the steady-state and transient response of a laser is demonstrated when there is a small number of particles in the system. In this regime, quantum fluctuations are found to suppress the lasing threshold and create a non-Poisson probability distribution for n discrete excited electronic states and s discrete photons. The correlation between n and s damps the averaged dynamic response of laser emission. Random walk calculations verify the master equation predictions and are used to connect to systems containing larger numbers of particles.
We theoretically investigate the response of a coherently-driven nonlinear optical cavity to an additional incident single photon. Using a quantum description of the nonlinear dynamics that fully accounts for the quantum fluctuations of the cavity field and for the discrete nature of the incident photon, we characterize the quantum dynamics of single-photon-stimulated jumps from the low-photon-number to the high-photon-number state of the optical bistability loop. We find that the system can exhibit a giant response to this single quantum of excitation, rooted in the phase-transition picture of optical bistability. In addition to shedding light on the role of quantum fluctuations in the non-equilibrium dynamics of a nonlinear optical cavity, our results suggest a strategy for an all-optical single-photon avalanche detector.
In the strong coupling regime of cavity QED where the characteristic damping rates are orders of magnitude below the coherent coupling, resolved multi-photon resonances can be observed for strong enough driving strength. In a certain frequency range, the external coherent drive field hits multi-photon resonances which correspond to very high order transitions that cannot be excited at the given power of the driving field. We found that in this range the cavity field evolves into a robust semiclassical solution which is the mixture of the vacuum and an excited quasi-classical state. The system is reminiscent of optical bistability, however, here a single atom produces a telegraph signal for the outgoing intensity by switching between two states with large photon number difference. We calculate this behavior also for the Tavis-Cummings model representing three qubits in an existing circuit QED experimental setting.
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In the first part of this thesis, a detailed analysis of lasing in random multiple-light-scattering media with gain is presented. Random laser emission is analyzed using a time-dependent diffusion model for light propagating in the medium containing active atoms. We demonstrate the effects of scatterers to narrow the emission spectral linewidth and to shorten the emitted pulse duration at a specific threshold pump intensity. This threshold pump intensity decreases with scatterer density and excitation spot diameter, in excellent agreement with experimental results. The coherence properties of the random laser are studied using a generalized master equation. The random laser medium is treated as a collection of low quality-factor cavities, coupled by random photon diffusion. Laser-like coherence, on average, is demonstrated above a specific pumping threshold. We demonstrate that with stronger scattering, the pumping threshold for the transition from chaotic to isotropic coherent light emission decreases and enhanced optical coherence for the emitted light is achieved above threshold. The second part of this thesis presents a study of lasing in photonic crystals (PCs). The emission from an incoherently pumped atomic system in interaction with the electro-magnetic reservoir of a PC is analyzed using a set of generalized semiclassical Maxwell-Bloch equations. We demonstrate that the photonic band edge facilitates the enhancement of stimulated emission and the reduction of internal losses, leading to an important lowering of the laser threshold. In addition, an increase of the laser output at a photonic band edge is demonstrated. We next develop a detailed quantum theory of a coherently pumped two-level atom in a photonic band gap material, coupled to both a multi-mode wave-guide channel and a high-quality micro-cavity embedded within the PC. The cavity field characteristics are highly distinct from that of a corresponding high-Q cavity in ordinary vacuum. We demonstrate enhanced, inversionless, and nearly coherent light generation when the photon density of states (DOS) jump between the Mollow spectral components of atomic resonance fluorescence is large. In the case of a vanishing photon DOS on the lower Mollow sideband and no dipolar dephasing, the emitted photon statistics is Poissonian and the cavity field exhibits quadrature coherence.