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arXiv · 2503.10463

Solving Dicke superradiance analytically: A compendium of methods

Raphael Holzinger·Nico S. Bassler·Julian Lyne·Fidel G. Jimenez·Julius T. Gohsrich·Claudiu Genes
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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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Raphael Holzinger, Nico S. Bassler, Julian Lyne, Fidel G. Jimenez, Julius T. Gohsrich, Claudiu Genes. 2025-03-19. Solving Dicke superradiance analytically: A compendium of methods. https://doi.org/10.1103/9p44-kwfl

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