The maximum photon emission rate in atomic ensembles scales universally as atom number times optical depth at fixed density, unifying ordered and disordered systems from independent emission to the Dicke limit.
Solving Dicke superradiance analytically: A compendium of methods
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abstract
We present several analytical approaches to the Dicke superradiance problem, which involves determining the time evolution of the density operator for an initially inverted ensemble of $N$ identical two-level systems undergoing collective spontaneous emission. This serves as one of the simplest cases of open quantum system dynamics that allows for a fully analytical solution. We explore multiple methods to tackle this problem, yielding a solution valid for any time and any number of spins. These approaches range from solving coupled rate equations and identifying exceptional points in non-Hermitian evolution to employing combinatorial and probabilistic techniques, as well as utilizing a quantum jump unraveling of the master equation. The analytical solution is expressed as a residue sum obtained from a contour integral in the complex plane, suggesting the possibility of fully analytical solutions for a broader class of open quantum system dynamics problems.
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quant-ph 2verdicts
UNVERDICTED 2representative citing papers
A symbolic quantum-trajectory construction produces closed-form exponential sums for populations and observables in multichannel Dicke superradiance, including first-order phase transition resemblance for two channels and scaling laws for balanced multi-channel cases.
citing papers explorer
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Optical depth dictates universal bounds on many-body decay in atomic ensembles
The maximum photon emission rate in atomic ensembles scales universally as atom number times optical depth at fixed density, unifying ordered and disordered systems from independent emission to the Dicke limit.
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Symbolic Quantum-Trajectory Method for Multichannel Dicke Superradiance
A symbolic quantum-trajectory construction produces closed-form exponential sums for populations and observables in multichannel Dicke superradiance, including first-order phase transition resemblance for two channels and scaling laws for balanced multi-channel cases.