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:2601.21254

Sampling methods to describe superradiance in large ensembles of quantum emitters

Daniel Eyles, Emmanuel Lassalle, Adam Stokes, Ramón Paniagua-Domínguez, Ahsan Nazir

quant-phSubmitted Jan 29, 2026• Announced Jan 30, 2026• 0 citations
arXivHTMLPDF

Abstract

Superradiance is a quantum phenomenon in which coherence between emitters results in enhanced and directional radiative emission. Many quantum optical phenomena can be characterized by the two-time quantum correlation function $g^{(2)}(t,τ)$, which describes the photon statistics of emitted radiation. However, the critical task of determining $g^{(2)}(t,τ)$ becomes intractable for large emitter ensembles due to the exponential scaling of the Hilbert space dimension with the number of emitters. Here, we analyse and benchmark two approximate numerical sampling methods applicable to emitter arrays embedded within electromagnetic environments, which generally provide upper and lower bounds for $g^{(2)}(t,0)$. We also introduce corrections to these methods (termed offset corrections) that significantly improve the quality of the predictions. The optimal choice of method depends on the total number of emitters, such that taken together, the two approaches provide accurate descriptions across a broad range of important regimes. This work therefore provides new theoretical tools for studying the well-known yet complex phenomenon of superradiance in large ensembles of quantum emitters.

Comments
18 pages, 14 figures

Related papers

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

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

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

Dynamics of Many-Emitter Ensembles: Probing Cooperative Evolution with Scalable Quantum Circuits

Vincent Iglesias-Cardinale, Shreekanth S. Yuvarajan, Herbert F. Fotso

Many-particle quantum systems often give rise to exotic behaviors in their nonequilibrium dynamics that are rather challenging to reveal with analytical methods or with classical computation. Here, we consider the case of a system of many quantum emitters coupled through a radiation bath. By adopting an efficient mapping of the bosonic modes onto a set of quantum bits, we implement quantum circuits, compatible with NISQ (Noisy Intermediate-Scale Quantum) era systems, that allow us to investigate the dynamics of the ensemble as a function of various parameters, including the number of emitters, the spectral inhomogeneity in the system, the emission lifetime of independent emitters, and the spatial separation between emitters. The quantum algorithms afford us the capacity to precisely track the emergence of cooperative dynamics, manifested through superradiant emission, as the system is tuned towards optimal coupling with respect to various parameters. We are particularly able to characterize superradiant emission in an inhomogeneous ensemble as a function of the linewidth of the individual emitters. These quantum algorithms avoid approximations performed in conventional studies of many-emitter systems and provide a robust and intuitive characterization. Despite being limited to a small number of qubits, the present calculations are found to provide a reliable characterization validated by comparison with analytical solutions and classical computation results in their respective regimes of validity. These findings indicate that the approach can be employed to effectively simulate a broad variety of many-emitter systems.

quant-pharXiv:2603.12563•Mar 16, 2026•0 citations

Superradiant Peak Emission Rate and Time in Quantum Emitter Arrays

Raphael Holzinger, Susanne F. Yelin

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.

arXiv:2504.09985•Apr 14, 2025•0 citations

Light-Induced Collective Interactions in Arrays of Quantum Emitters

Oriol Rubies-Bigordà

The interaction between light and matter has captivated physicists for centuries, from early studies of vision and refraction in ancient Greece to the development of quantum mechanics and quantum electrodynamics in the past century. While the response of a single quantum emitter to light is well understood, the radiative properties of an ensemble of closely spaced emitters are far more intricate. Coupling to a shared electromagnetic environment induces coherent and dissipative interactions between emitters, giving rise to a collective response that cannot be captured by treating them independently. In the regime of few excitations, the system hosts delocalized subradiant states, that is, coherent superpositions that are largely decoupled from the electromagnetic field and thus decay at suppressed rates. While this weak coupling makes subradiant states attractive for quantum technologies, it also renders them difficult to manipulate. At higher excitation densities, the intrinsic nonlinearity of emitters and the exponential growth of the Hilbert space make theoretical and numerical descriptions of the system and its dynamics increasingly challenging. This thesis explores two fundamental questions: How can subradiant and dark states be selectively accessed and harnessed for practical applications in quantum technologies? And how can interacting ensembles of quantum emitters be efficiently simulated to uncover their many-body physics? The first part of the thesis develops protocols for controlling and addressing dark states in free-space and waveguide-coupled atomic arrays, demonstrating their utility in quantum storage and the deterministic generation of entangled photonic states. Incorporating atomic motion, we further show that collective subradiant states can enhance cooling in dense atomic arrays, offering new avenues for controlling motional dynamics. In the second part, we introduce cumulant expansions of the equations of motion as a powerful tool to analytically and numerically investigate collective decay in the many-body regime. We first examine the collective decay of fully excited atomic arrays in free space, characterizing the onset and scaling of the superradiant burst across different geometries. In collaboration with experiments on ultracold erbium atoms in optical lattices, we provide the first direct observations of many-body collective effects in free-space ordered arrays, including early-time superradiant bursts, late-time subradiant tails, and the emergence of atomic correlations throughout the dynamics. Finally, we theoretically and numerically explore the transient formation of multi-excitation subradiant states, and demonstrate how the existence of multiple dissipation channels suppresses steady-state superradiance in extended arrays.

•May 1, 2025•0 citations
Superradiance is a quantum phenomenon in which coherence between emitters results in enhanced and directional radiative emission. Many quantum optical phenomena can be characterized by the two-time quantum correlation function g(2)(t,τ)g^{(2)}(t,τ)g(2)(t,τ), which describes the photon statistics of emitted radiation. However, the critical task of determining g(2)(t,τ)g^{(2)}(t,τ)g(2)(t,τ) becomes intractable for large emitter ensembles due to the exponential scaling of the Hilbert space dimension with the number of emitters. Here, we analyse and benchmark two approximate numerical sampling methods applicable to emitter arrays embedded within electromagnetic environments, which generally provide upper and lower bounds for g(2)(t,0)g^{(2)}(t,0)g(2)(t,0). We also introduce corrections to these methods (termed offset corrections) that significantly improve the quality of the predictions. The optimal choice of method depends on the total number of emitters, such that taken together, the two approaches provide accurate descriptions across a broad range of important regimes. This work therefore provides new theoretical tools for studying the well-known yet complex phenomenon of superradiance in large ensembles of quantum emitters.
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.
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 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.
Many-particle quantum systems often give rise to exotic behaviors in their nonequilibrium dynamics that are rather challenging to reveal with analytical methods or with classical computation. Here, we consider the case of a system of many quantum emitters coupled through a radiation bath. By adopting an efficient mapping of the bosonic modes onto a set of quantum bits, we implement quantum circuits, compatible with NISQ (Noisy Intermediate-Scale Quantum) era systems, that allow us to investigate the dynamics of the ensemble as a function of various parameters, including the number of emitters, the spectral inhomogeneity in the system, the emission lifetime of independent emitters, and the spatial separation between emitters. The quantum algorithms afford us the capacity to precisely track the emergence of cooperative dynamics, manifested through superradiant emission, as the system is tuned towards optimal coupling with respect to various parameters. We are particularly able to characterize superradiant emission in an inhomogeneous ensemble as a function of the linewidth of the individual emitters. These quantum algorithms avoid approximations performed in conventional studies of many-emitter systems and provide a robust and intuitive characterization. Despite being limited to a small number of qubits, the present calculations are found to provide a reliable characterization validated by comparison with analytical solutions and classical computation results in their respective regimes of validity. These findings indicate that the approach can be employed to effectively simulate a broad variety of many-emitter systems.
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.
The interaction between light and matter has captivated physicists for centuries, from early studies of vision and refraction in ancient Greece to the development of quantum mechanics and quantum electrodynamics in the past century. While the response of a single quantum emitter to light is well understood, the radiative properties of an ensemble of closely spaced emitters are far more intricate. Coupling to a shared electromagnetic environment induces coherent and dissipative interactions between emitters, giving rise to a collective response that cannot be captured by treating them independently. In the regime of few excitations, the system hosts delocalized subradiant states, that is, coherent superpositions that are largely decoupled from the electromagnetic field and thus decay at suppressed rates. While this weak coupling makes subradiant states attractive for quantum technologies, it also renders them difficult to manipulate. At higher excitation densities, the intrinsic nonlinearity of emitters and the exponential growth of the Hilbert space make theoretical and numerical descriptions of the system and its dynamics increasingly challenging. This thesis explores two fundamental questions: How can subradiant and dark states be selectively accessed and harnessed for practical applications in quantum technologies? And how can interacting ensembles of quantum emitters be efficiently simulated to uncover their many-body physics? The first part of the thesis develops protocols for controlling and addressing dark states in free-space and waveguide-coupled atomic arrays, demonstrating their utility in quantum storage and the deterministic generation of entangled photonic states. Incorporating atomic motion, we further show that collective subradiant states can enhance cooling in dense atomic arrays, offering new avenues for controlling motional dynamics. In the second part, we introduce cumulant expansions of the equations of motion as a powerful tool to analytically and numerically investigate collective decay in the many-body regime. We first examine the collective decay of fully excited atomic arrays in free space, characterizing the onset and scaling of the superradiant burst across different geometries. In collaboration with experiments on ultracold erbium atoms in optical lattices, we provide the first direct observations of many-body collective effects in free-space ordered arrays, including early-time superradiant bursts, late-time subradiant tails, and the emergence of atomic correlations throughout the dynamics. Finally, we theoretically and numerically explore the transient formation of multi-excitation subradiant states, and demonstrate how the existence of multiple dissipation channels suppresses steady-state superradiance in extended arrays.