Solving Dicke superradiance analytically: A compendium of methods
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913033907863552 |
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| author | Holzinger, Raphael Bassler, Nico S. Lyne, Julian Jimenez, Fidel G. Gohsrich, Julius T. Genes, Claudiu |
| author_facet | Holzinger, Raphael Bassler, Nico S. Lyne, Julian Jimenez, Fidel G. Gohsrich, Julius T. Genes, Claudiu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10463 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving Dicke superradiance analytically: A compendium of methods Holzinger, Raphael Bassler, Nico S. Lyne, Julian Jimenez, Fidel G. Gohsrich, Julius T. Genes, Claudiu Quantum Physics Optics 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. |
| title | Solving Dicke superradiance analytically: A compendium of methods |
| topic | Quantum Physics Optics |
| url | https://arxiv.org/abs/2503.10463 |