[Paper Review] Lasing in Strong Coupling

Fabrice P. Laussy, Elena del Valle+1 more|arXiv (Cornell University)|Jun 2, 2011

Laser-Matter Interactions and Applications3 citations

TL;DR

This paper demonstrates that lasing in the strong-coupling regime of light-matter interaction can achieve thresholdless operation with Poissonian photon statistics across all pumping powers, but a universal quantum nonlinearity induces a discontinuous jump in second-order coherence ($g^{(2)}$) during the transition to stimulated emission lasing, preventing ideal thresholdless behavior. The maximum $g^{(2)}$ value of approximately 1.10282 is universal and occurs at a well-defined pumping rate, providing a fundamental standard for identifying lasing in strong coupling systems.

ABSTRACT

An almost ideal thresholdless laser can be realized in the strong-coupling regime of light-matter interaction, with Poissonian fluctuations of the field at all pumping powers and all intensities of the field. This ideal scenario is thwarted by quantum nonlinearities when crossing from the linear to the stimulated emission regime, resulting in a universal jump in the second order coherence, which measurement could however be used to establish a standard of lasing in strong coupling.

Motivation & Objective

• To investigate the transition from strong-coupling dynamics to conventional lasing in a single emitter system.
• To identify whether ideal thresholdless lasing is achievable in the strong-coupling regime despite quantum nonlinearities.
• To establish a universal, experimentally measurable signature—specifically, a peak in $g^{(2)}$—that defines the onset of lasing in strong coupling.
• To provide a quantitative standard for characterizing lasing in strong coupling systems using measurable coherence statistics.

Proposed method

• The study employs the fully quantized Jaynes–Cummings Hamiltonian coupled to a dissipative environment via a master equation with Lindblad terms for decay and pumping.
• Photon statistics are analyzed through the $n$th-order coherence function $g^{(n)}(0) = N_a[n]/n_a^n$, with focus on $g^{(2)}(0)$ as the key observable.
• The steady-state photon number distribution $p(n) = \langle n|\rho|n \rangle$ is compared to Poissonian statistics to quantify deviations.
• The system is analyzed in the strong-coupling limit, where the Purcell rate $\kappa_\sigma = 4g^2/\gamma_a$ governs the effective coupling strength.
• Numerical solutions of the master equation are used to compute $N_a[n]$ and $g^{(2)}$ across varying pumping rates $P_\sigma$ and decay rates $\gamma_\sigma$, revealing universal scaling.
• The transition region is characterized by a universal shape in $g^{(2)}$ and a universal maximum value of $\approx 1.10282$, independent of system parameters when strong coupling is optimal.

Experimental results

Research questions

• RQ1 Can lasing in the strong-coupling regime achieve truly thresholdless operation with Poissonian statistics across all pumping powers?
• RQ2 What causes the breakdown of ideal thresholdless lasing despite favorable strong-coupling conditions?
• RQ3 Is there a universal, measurable signature marking the transition from strong-coupling dynamics to stimulated emission lasing?
• RQ4 Can the maximum value of $g^{(2)}$ be used as a fundamental standard to identify lasing in strong coupling?
• RQ5 How do quantum nonlinearities in the strong-coupling regime affect photon statistics during the lasing transition?

Key findings

• The maximum value of the second-order coherence function $g^{(2)}$ reaches a universal peak of approximately 1.10282 in the optimal strong-coupling regime, independent of system parameters.
• This peak occurs at a well-defined pumping rate of $P_\sigma \approx 2.115\gamma_a$ when $\gamma_\sigma = \gamma_a$, marking a universal transition point.
• The transition from strong coupling to lasing is characterized by a universal shape in $g^{(2)}$ that is invariant under dimensionless scaling of $P_\sigma/\gamma_a$ and $\gamma_\sigma/\gamma_a$, regardless of $g$.
• The deviation from Poissonian statistics, quantified by $\delta_n = p(n) - e^{-\bar{n}}\bar{n}^n/n!$, grows linearly in the one-photon lasing region and spreads across multiple photon number states during the transition.
• The universal $g^{(2)}$ peak is only observed when strong coupling is sufficiently good; if not, the maximum value drops and the shape deviates, indicating incomplete realization of the transition.
• The peak in $g^{(2)}$ provides a robust, unambiguous experimental standard for identifying lasing in strong coupling, even when traditional thresholds are absent.