Symbolic Quantum-Trajectory Method for Multichannel Dicke Superradiance

TL;DR

This paper introduces a symbolic quantum-trajectory method to analyze multichannel Dicke superradiance, providing exact solutions for populations and observables in complex decay scenarios.

Contribution

The authors develop a novel symbolic quantum-trajectory approach that extends Dicke superradiance analysis to multiple competing decay channels with tunable rates.

Findings

Closed-form expressions for populations and observables as finite sums of exponentials.

Identification of a phase transition-like behavior in the stationary ground-state distribution.

Scaling laws for superradiant peak time and intensity in balanced multichannel decay.

Abstract

We solve Dicke superradiance with two or more competing collective decay channels of tunable rates using a symbolic quantum-trajectory construction. The method yields closed time-domain populations and observables as finite sums of exponentials for arbitrary numbers of emitters and arbitrary decay rates. For two channels, the behavior of the stationary ground-state distribution resembles a first-order phase transition at the point where the channel-rate ratio is equal to unity. For balanced $d$-channel decay, we obtain scaling laws for the superradiant peak time and intensity. These results unify and extend single-channel Dicke dynamics to multilevel emitters and provide a compact tool for cavity and waveguide experiments, where permutation-symmetric reservoirs engineer multiple collective decay paths.