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Article

Benchmarking the Cumulant Expansion Method Using Dicke Superradiance

1
Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 21a, A-6020 Innsbruck, Austria
2
Institute for Applied Physics, TU Darmstadt, Hochschulstraße 4A, D-64289 Darmstadt, Germany
3
Department of Physics, Harvard University, Cambridge, MA 02138, USA
*
Authors to whom correspondence should be addressed.
Photonics 2025, 12(10), 996; https://doi.org/10.3390/photonics12100996
Submission received: 4 September 2025 / Revised: 28 September 2025 / Accepted: 30 September 2025 / Published: 10 October 2025
(This article belongs to the Special Issue Collective Effects in Light-Matter Interactions)

Abstract

Collective superradiant decay of a tightly packed inverted quantum emitter ensemble is among the most intensely studied phenomena in quantum optics. Since the seminal work of Dicke more than half a century ago, a plethora of theoretical calculations in quantum many-body physics have followed. Widespread experimental efforts range from the microwave to the X-ray regime. Nevertheless, accurate calculations of the time dynamics of the superradiant emission pulse still remain a challenging task requiring approximate methods for large ensembles. Here, we benchmark the cumulant expansion method for describing collective superradiant decay against a newly found exact solution. The application of two variants of the cumulant expansion exhibits reliable convergence of time and magnitude of the maximum emission power with increasing truncation order. The long-term population evolution is only correctly captured for low emitter numbers, where an individual spin-based cumulant expansion proves more reliable than the collective spin-based variant. Surprisingly, odd orders show unphysical behavior. At sufficiently high spin numbers, both chosen cumulant methods agree, but still fail to reliably converge to the numerically exact result. Generally, on longer time scales the expansions substantially overestimate the remaining population. While numerically fast and efficient, cumulant expansion methods need to be treated with sufficient caution when used for long-time evolution or reliably finding steady states.
Keywords: quantum optics; dicke superradiance; collective light-matter interactions; spontaneous emission quantum optics; dicke superradiance; collective light-matter interactions; spontaneous emission

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MDPI and ACS Style

Fasser, M.; Genes, C.; Ritsch, H.; Holzinger, R. Benchmarking the Cumulant Expansion Method Using Dicke Superradiance. Photonics 2025, 12, 996. https://doi.org/10.3390/photonics12100996

AMA Style

Fasser M, Genes C, Ritsch H, Holzinger R. Benchmarking the Cumulant Expansion Method Using Dicke Superradiance. Photonics. 2025; 12(10):996. https://doi.org/10.3390/photonics12100996

Chicago/Turabian Style

Fasser, Martin, Claudiu Genes, Helmut Ritsch, and Raphael Holzinger. 2025. "Benchmarking the Cumulant Expansion Method Using Dicke Superradiance" Photonics 12, no. 10: 996. https://doi.org/10.3390/photonics12100996

APA Style

Fasser, M., Genes, C., Ritsch, H., & Holzinger, R. (2025). Benchmarking the Cumulant Expansion Method Using Dicke Superradiance. Photonics, 12(10), 996. https://doi.org/10.3390/photonics12100996

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