Solving Dicke superradiance analytically: A compendium of methods

Holzinger R.; Bassler N.S.; Lyne J.; Jimenez F.G.; Gohsrich J.T.; Genes C. · Physical Review A (2026) · DOI: 10.1103/9p44-kwfl

Resumen

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 emitters. 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.

Instituciones: Pontificia Universidad Católica del Perú