Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2504.09985

Superradiant Peak Emission Rate and Time in Quantum Emitter Arrays

Raphael Holzinger, Susanne F. Yelin

Published Apr 14, 2025• 0 citations
arXivHTMLPDF

Abstract

Determining the peak photon emission time and rate for an ensemble of $N$ quantum systems undergoing collective superradiant decay typically requires tracking the time evolution of the density operator. Generally, the dimension of the density operator grows exponentially ($\sim \! 2^N$) with the number of emitters, in the absence of any symmetries such as in Dicke superradiance with full or partial permutational symmetry. We present a detailed study of the superradiant peak emission rate and time for initially fully excited quantum emitter ensembles, for one-, two- and three-dimensional arrays in free-space and emitter chains coupled to waveguide reservoirs. For few emitters ($N\lesssim 14$) we utilize the full quantum master equation, and for mesoscopic emitter numbers ($N\lesssim 400$) we use a second- and third-order cumulant expansion of the operator averages to track the time evolution of the system.

DOI
10.48550/arxiv.2504.09985

Related papers

Scaling of Superradiant Peak Emission in Spatially Extended Emitter Arrays

Raphael Holzinger, Susanne F. Yelin

In quantum optics, superradiance is a phenomenon in which a system of $N$ fully excited quantum emitters radiate intense flashes of light during collective decay. However, computing its peak intensity exactly for many spatially separated emitters remains challenging due to the exponential growth of the underlying Hilbert space with system size $N$. Based on third-order cumulant expansion methods, we present general scaling laws for the expononent of the peak emission rate as a function of the emitter number in free-space emitter arrays and arrays coupled to one-dimensional waveguide reservoirs. We find, that for 1D chains in free-space the peak emission rate scales linearly with $N$, while for 2D and 3D arrays with finite emitter spacing it scales superlinearly but sub-quadratically. For emitter chains coupled to waveguide reservoirs we find that the peak emission rate scales quadratically with $N$.

arXiv:2506.12649•Jun 14, 2025•0 citations

Benchmarking the Cumulant Expansion Method Using Dicke Superradiance

Martin Fasser, Claudiu Genes, Helmut Ritsch +1 more

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.

Photonics•Oct 10, 2025•0 citations

Characterizing superradiant dynamics in atomic arrays via a cumulant expansion approach

Oriol Rubies-Bigordà, Stefan Ostermann, Susanne F. Yelin

Ordered atomic arrays with subwavelength lattice spacing emit light collectively. For fully inverted atomic arrays, this results in an initial burst of radiation and a fast buildup of coherences between the atoms at initial times. Based on a cumulant expansion of the equations of motion, we derive exact analytical expressions for the emission properties and numerically analyze the full many-body problem resulting in the collective decay process for unprecedented system sizes of up to a few hundred atoms. We benchmark the cumulant expansion approach and show that it correctly captures the cooperative dynamics resulting in superradiance. For fully inverted arrays, this allows us to extract the scaling of the superradiant peak with particle number. For partially excited arrays where no coherences are shared among atoms, we also determine the critical number of excitations required for the emergence of superradiance in one- and two-dimensional geometries. In addition, we study the robustness of superradiance in the case of non-unit filling and position disorder.

arXiv:2211.11895•Physical Review Research•Feb 8, 2023•49 citations

Superradiant decay in non-Markovian Waveguide Quantum Electrodynamics

Rosa Lucia Capurso, Giuseppe Calajó, Simone Montangero +5 more

An array of initially excited emitters coupled to a one-dimensional waveguide exhibits superradiant decay under the Born-Markov approximation, manifested as a coherent burst of photons in the output field. In this work, we employ tensor-network methods to investigate its non-Markovian dynamics induced by finite time delays in photon exchange among the emitters. We find that the superradiant burst breaks into a structured train of correlated photons, each intensity peak corresponding to a specific photon number. We quantify the emitter-photon and emitter-emitter entanglement generated during this process and show that the latter emerges in the long-time limit, as part of the excitation becomes trapped within the emitters' singlet subspace. We finally consider the decay of the system's most radiant state, the symmetric Dicke state, and show that time delay can lead to decay rates exceeding those predicted by the Markovian approximation.

quant-pharXiv:2511.22332•Communications Physics•Nov 28, 2025•2 citations

Benchmarking the Cumulant Expansion Method using Dicke Superradiance

Helmut Ritsch, Raphael Holzinger

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 needing approximate methods for large ensembles. Here, we benchmark the cumulant expansion method for describing collective superradiant decay against a new, recently found exact solution. Applying two variants of the cumulant expansion exhibits reliable convergence of time and magnitude of the maximum emission power with increasing truncation order. The longterm 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 even qualitatively nonphysical behavior. At sufficiently high spin numbers, both chosen cumulant methods agree, but still fail to reliably converge to the numerically exact result. Generally, at a longer time scale, the expansions substantially overestimate the remaining population. While numerically fast and efficient, cumulant expansion methods need to be treated with sufficient caution when applied for long-time evolution or reliably finding steady states.

•Sep 15, 2025•0 citations

Solving Dicke superradiance analytically: A compendium of methods

R. Holzinger, Nico S. Bassler, Julian Lyne +3 more

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.

arXiv:2503.10463•Physical Review A•Feb 18, 2026•6 citations
Determining the peak photon emission time and rate for an ensemble of NNN quantum systems undergoing collective superradiant decay typically requires tracking the time evolution of the density operator. Generally, the dimension of the density operator grows exponentially (∼ ⁣2N\sim \! 2^N∼2N) with the number of emitters, in the absence of any symmetries such as in Dicke superradiance with full or partial permutational symmetry. We present a detailed study of the superradiant peak emission rate and time for initially fully excited quantum emitter ensembles, for one-, two- and three-dimensional arrays in free-space and emitter chains coupled to waveguide reservoirs. For few emitters (N≲14N\lesssim 14N≲14) we utilize the full quantum master equation, and for mesoscopic emitter numbers (N≲400N\lesssim 400N≲400) we use a second- and third-order cumulant expansion of the operator averages to track the time evolution of the system.
In quantum optics, superradiance is a phenomenon in which a system of NNN fully excited quantum emitters radiate intense flashes of light during collective decay. However, computing its peak intensity exactly for many spatially separated emitters remains challenging due to the exponential growth of the underlying Hilbert space with system size NNN. Based on third-order cumulant expansion methods, we present general scaling laws for the expononent of the peak emission rate as a function of the emitter number in free-space emitter arrays and arrays coupled to one-dimensional waveguide reservoirs. We find, that for 1D chains in free-space the peak emission rate scales linearly with NNN, while for 2D and 3D arrays with finite emitter spacing it scales superlinearly but sub-quadratically. For emitter chains coupled to waveguide reservoirs we find that the peak emission rate scales quadratically with NNN.
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.
Ordered atomic arrays with subwavelength lattice spacing emit light collectively. For fully inverted atomic arrays, this results in an initial burst of radiation and a fast buildup of coherences between the atoms at initial times. Based on a cumulant expansion of the equations of motion, we derive exact analytical expressions for the emission properties and numerically analyze the full many-body problem resulting in the collective decay process for unprecedented system sizes of up to a few hundred atoms. We benchmark the cumulant expansion approach and show that it correctly captures the cooperative dynamics resulting in superradiance. For fully inverted arrays, this allows us to extract the scaling of the superradiant peak with particle number. For partially excited arrays where no coherences are shared among atoms, we also determine the critical number of excitations required for the emergence of superradiance in one- and two-dimensional geometries. In addition, we study the robustness of superradiance in the case of non-unit filling and position disorder.
An array of initially excited emitters coupled to a one-dimensional waveguide exhibits superradiant decay under the Born-Markov approximation, manifested as a coherent burst of photons in the output field. In this work, we employ tensor-network methods to investigate its non-Markovian dynamics induced by finite time delays in photon exchange among the emitters. We find that the superradiant burst breaks into a structured train of correlated photons, each intensity peak corresponding to a specific photon number. We quantify the emitter-photon and emitter-emitter entanglement generated during this process and show that the latter emerges in the long-time limit, as part of the excitation becomes trapped within the emitters' singlet subspace. We finally consider the decay of the system's most radiant state, the symmetric Dicke state, and show that time delay can lead to decay rates exceeding those predicted by the Markovian approximation.
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 needing approximate methods for large ensembles. Here, we benchmark the cumulant expansion method for describing collective superradiant decay against a new, recently found exact solution. Applying two variants of the cumulant expansion exhibits reliable convergence of time and magnitude of the maximum emission power with increasing truncation order. The longterm 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 even qualitatively nonphysical behavior. At sufficiently high spin numbers, both chosen cumulant methods agree, but still fail to reliably converge to the numerically exact result. Generally, at a longer time scale, the expansions substantially overestimate the remaining population. While numerically fast and efficient, cumulant expansion methods need to be treated with sufficient caution when applied for long-time evolution or reliably finding steady states.
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 NNN 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.