Exact Analytical Treatment of Collectively Pumped Dicke Superradiance
Abstract
We study the dynamics of an ensemble of N two-level emitters undergoing collective decay at rate Γ and collective incoherent pumping at rate R, confined to the fully symmetric Dicke ladder. Although the population dynamics are confined to a finite set of rate equations, their quantum-trajectory representation involves infinitely many pump-decay histories. We derive an exact finite continued fraction for the Laplace-transformed Dicke-state populations by resumming the infinitely many quantum trajectories generated by competing pump and decay processes. Our construction provides a physically transparent interpretation of the tridiagonal resolvent and extends to arbitrary permutationally symmetric initial states. In the strong- and weak-pumping regimes, we obtain perturbative transient solutions. We also identify exact relaxation eigenvalues and emission observables at balanced pump and decay strengths. Our solution provides a starting point for extending trajectory-based analytical methods to more general driven-dissipative collective systems.
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BibTeX
@misc{poddar2026exact,
title = {{Exact Analytical Treatment of Collectively Pumped Dicke Superradiance}},
author = {Avishi Poddar and Nico Baßler and Julian Lyne and Susanne F. Yelin and Helmut Ritsch and Claudiu Genes and Raphael Holzinger},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37665},
eprint = {2610.37665},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37665},
}
RIS
TY - UNPB
TI - Exact Analytical Treatment of Collectively Pumped Dicke Superradiance
AU - Avishi Poddar
AU - Nico Baßler
AU - Julian Lyne
AU - Susanne F. Yelin
AU - Helmut Ritsch
AU - Claudiu Genes
AU - Raphael Holzinger
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37665
UR - https://arxiv.org/abs/2610.37665
AB - We study the dynamics of an ensemble of N two-level emitters undergoing collective decay at rate Γ and collective incoherent pumping at rate R, confined to the fully symmetric Dicke ladder. Although the population dynamics are confined to a finite set of rate equations, their quantum-trajectory representation involves infinitely many pump-decay histories. We derive an exact finite continued fraction for the Laplace-transformed Dicke-state populations by resumming the infinitely many quantum trajectories generated by competing pump and decay processes. Our construction provides a physically transparent interpretation of the tridiagonal resolvent and extends to arbitrary permutationally symmetric initial states. In the strong- and weak-pumping regimes, we obtain perturbative transient solutions. We also identify exact relaxation eigenvalues and emission observables at balanced pump and decay strengths. Our solution provides a starting point for extending trajectory-based analytical methods to more general driven-dissipative collective systems.
ER -