2026-10-28 · arXiv Quantum Physics
arXiv:2610.37665v1 Announce Type: new
Abstract: We study the dynamics of an ensemble of $N$ two-level emitters undergoing collective decay at rate $\Gamma$ 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.
原文链接：https://arxiv.org/abs/2610.37665
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