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arXiv:2603.04591

Photon statistics in chiral waveguide QED: I Mean field and perturbative expansions

M. Eltohfa, F. Robicheaux

quant-phphysics.atom-phSubmitted Mar 4, 2026• Announced Mar 6, 2026• 0 citations
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Abstract

Waveguide Quantum Electrodynamics (WQED) offers a suitable stage for controlling the interaction of light with atoms, allowing for collective phenomena such as super- and subradiance. In a chiral waveguide setup, the quantum state evolves through all the Hilbert space, rendering an exact theoretical treatment exponentially hard and unobtained to date for more than $\sim 20$ atoms. In this work, we use a computationally efficient higher order mean-field approximation to model the radiation dynamics in a chirally coupled array of atoms, showing good agreement with recent experimental results. Further, based on a perturbative approximation of the full dynamics, we develop an analytical solution that captures photon statistics for a moderate atom number, $N$, and a homogeneous atom-waveguide coupling, $β$. Finally, we show that capturing the onset of second-order coherence from a fully inverted state requires a fourth-order mean-field approximation, as lower-order treatments fail to account for the necessary four-body correlations. These results illustrate the complex behavior of a symmetry-lacking system, and the methods discussed here provide systematic analytical solutions to which semi-classical methods such as the cumulant expansion or the truncated Wigner approximation can be benchmarked.

Related papers

Photon statistics in waveguide QED: II Exact solutions in a thermodynamic limit

M. Eltohfa, F. Robicheaux

Waveguide quantum electrodynamics (WQED) offers a powerful framework for controlling light-matter interactions and realizing collective phenomena such as super- and subradiance. In general waveguide settings, the quantum dynamics spans the full Hilbert space, rendering exact theoretical treatments exponentially difficult and currently out of reach, and only a few models have exact, analytical solutions. Motivated by recent experiments, we treat the thermodynamic limit of the number of atoms, $N \rightarrow \infty$, while the homogeneous atom-waveguide coupling $β\rightarrow 0$ keeping the optical depth $4Nβ$ fixed. In this limit, a second order mean field method is exact, giving analytical solutions for the statistics of the photons emitted in the waveguide both for chiral and symmetric configurations starting from full inversion. As $N \rightarrow \infty$, the emission in freespace approaches that of an independent ensemble. However, until a special time, $\approx 1.59 \times$ the lifetime of a single-atom, we show an exponentially enhanced superradiance in the waveguide as the optical depth increases. After the special time, the emission into the waveguide exhibits subradiance. We also show that the initial shot-to-shot fluctuations in the rate of emission into the waveguide diminish in a chiral system and vanish in a symmetric system as $N$ approaches $\infty$. Additionally, the equal-time second-order correlation becomes trivial, showing that finite-size effects are essential to observe the emergence of second-order coherence. Finally, going beyond the thermodynamic limit requires higher order mean field methods. Our results illustrate finite- and infinite-body collective effects in symmetric and symmetry-lacking systems.

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Waveguide QED with cold atoms provides a potent platform for the study of non-equilibrium, many-body, and open-system quantum dynamics. Even with weak coupling and strong photon loss, the collective enhancement of light-atom interactions leads to strong correlations of photons arising in transmission, as shown in recent experiments. Here we apply an improved mean-field theory based on higher-order cumulant expansions to describe the experimentally relevant, but theoretically elusive, regime of weak coupling and strong driving of large ensembles. We determine the transmitted power, squeezing spectra and the degree of second-order coherence, and systematically check the convergence of the results by comparing expansions that truncate cumulants of few-particle correlations at increasing order. This reveals the important role of many-body and long-range correlations between atoms in steady state. Our approach allows to quantify the trade-off between anti-bunching and output power in previously inaccessible parameter regimes. Calculated squeezing spectra show good agreement with measured data, as we present here.

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Fast and high excitation transport in waveguide quantum electrodynamics

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Abstract Waveguide quantum electrodynamics (wQED) with underlying collective and long-range atom-atom interactions has led to many distinct dynamical phenomena, including modified collective radiations and intriguing quantum correlations. It stands out as a unique platform to illustrate correlated photon transport, as well as to promise applications in quantum information processing. Here we manifest a fast and high atomic excitation transport by employing two separated chirally-coupled atomic arrays. This enhanced waveguide-mediated transport of excitations emerges due to the dominance of few subradiant right eigenstates that are spectrally isolated and spatially localized in the system’s dynamics. Contrary to the instinct of applying the cascaded systems with unidirectional couplings to expedite direct and high excitation transport, the optimal system configurations in open wQED systems demand slight or finite nonreciprocal decay channels to facilitate energy transport by exploiting waveguide-mediated couplings. We also investigate the effect of the couplings’ directionality and the scaling of atom number on the transport properties. Our results showcase the wide applicability in wQED platforms and provide insights into quantum engineering and quantum information applications.

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Three-Body Thermalization in One Dimension & Realistic Effects on Subradiance and Superradinace in Many-Atom Systems

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This thesis investigates two largely independent topics in many-body and quantum optical physics. The first concerns the thermalization of classical one-dimensional (1D) gases through three-body collisions, while the second explores collective light–matter interactions in atomic arrays and waveguide quantum electrodynamics, with an emphasis on subradiance, superradiance, and computational methods for many-body dynamics. The first part studies thermalization in dilute classical 1D gases, where conventional twobody collisions cannot establish thermal equilibrium. Using Monte Carlo calculations of the three-body collision kernel together with the Boltzmann equation and molecular dynamics simulations, we characterize the thermalization dynamics for particles interacting through inverse power-law and Lennard–Jones potentials. We show that the Boltzmann and molecular dynamics approaches agree in the dilute limit and derive the thermalization rate for inverse power-law interactions.The second part investigates realistic effects in collective light–matter systems. We first study the influence of finite trapping potentials on subradiant states in atomic arrays coupled through free space or a one-dimensional waveguide. We show that atomic motion fundamentally limits subradiant lifetimes through wavefunction delocalization, recoil heating, and dipole-force-induced motion, leading to decoherence and reduced quantum memory fidelity. These results identify optimal trapping and array configurations for long-lived collective excitations.The final chapters develop theoretical methods for describing photon emission in chiral and symmetric waveguide QED systems. Using higher-order mean-field approximations, we model collective emission in experimentally relevant chiral waveguides, obtaining agreement with recent experiments and deriving analytical expressions for photon statistics. We demonstrate that fourth-order correlations are required to capture the emergence of second-order coherence from a fully inverted state. Finally, in the thermodynamic limit of large atom number and fixed optical depth, we show that a second-order mean-field theory becomes exact, yielding analytical solutions for photon emission statistics in both chiral and symmetric waveguides. We characterize the crossover between enhanced superradiant and subradiant emission, establish the suppression of emission fluctuations in the large-system limit, and clarify the role of finite-size effects in generating nontrivial photon correlations.

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Manipulating excitation dynamics in structured waveguide quantum electrodynamics

I Gusti Ngurah Yudi Handayana, Ya-Tang Yu, Wei-Hsuan Chung +1 more

Waveguide quantum electrodynamics (wQED) has become a central platform for studying collective light-matter interactions in low-dimensional photonic environments. While conventional wQED systems rely on uniform chirality or reciprocal emitter-waveguide coupling, we propose a structured wQED framework, where the coupling directionality of each emitter can be engineered locally to control excitation transport in an atom-nanophotonic interface. For different combinations of patterned coupling directionalities of the emitters, we identify four representative configurations that exhibit distinct dynamical behaviors: centering, wave-like, leap-frog, and dispersion excitations. Spectral analysis of the effective non-Hermitian Hamiltonian reveals that these dynamics originate from interferences among subradiant eigenmodes. Variance analysis further quantifies the spreading of excitation as functions of interatomic spacing and global chirality, showing tunable localization-delocalization transitions. Including nonguided losses, we find that the transport characteristics remain robust for realistic coupling efficiencies (beta >= 0.99). These results establish structured wQED as a practical route to manipulate excitation localization, coherence, and transport through programmable directionality patterns, paving the way for controllable subradiant transport and chiral quantum information routing.

arXiv:2510.27310•Physical Review A•Mar 23, 2026•0 citations
Waveguide Quantum Electrodynamics (WQED) offers a suitable stage for controlling the interaction of light with atoms, allowing for collective phenomena such as super- and subradiance. In a chiral waveguide setup, the quantum state evolves through all the Hilbert space, rendering an exact theoretical treatment exponentially hard and unobtained to date for more than ∼20\sim 20∼20 atoms. In this work, we use a computationally efficient higher order mean-field approximation to model the radiation dynamics in a chirally coupled array of atoms, showing good agreement with recent experimental results. Further, based on a perturbative approximation of the full dynamics, we develop an analytical solution that captures photon statistics for a moderate atom number, NNN, and a homogeneous atom-waveguide coupling, βββ. Finally, we show that capturing the onset of second-order coherence from a fully inverted state requires a fourth-order mean-field approximation, as lower-order treatments fail to account for the necessary four-body correlations. These results illustrate the complex behavior of a symmetry-lacking system, and the methods discussed here provide systematic analytical solutions to which semi-classical methods such as the cumulant expansion or the truncated Wigner approximation can be benchmarked.
Waveguide quantum electrodynamics (WQED) offers a powerful framework for controlling light-matter interactions and realizing collective phenomena such as super- and subradiance. In general waveguide settings, the quantum dynamics spans the full Hilbert space, rendering exact theoretical treatments exponentially difficult and currently out of reach, and only a few models have exact, analytical solutions. Motivated by recent experiments, we treat the thermodynamic limit of the number of atoms, N→∞N \rightarrow \inftyN→∞, while the homogeneous atom-waveguide coupling β→0β\rightarrow 0β→0 keeping the optical depth 4Nβ4Nβ4Nβ fixed. In this limit, a second order mean field method is exact, giving analytical solutions for the statistics of the photons emitted in the waveguide both for chiral and symmetric configurations starting from full inversion. As N→∞N \rightarrow \inftyN→∞, the emission in freespace approaches that of an independent ensemble. However, until a special time, ≈1.59×\approx 1.59 \times≈1.59× the lifetime of a single-atom, we show an exponentially enhanced superradiance in the waveguide as the optical depth increases. After the special time, the emission into the waveguide exhibits subradiance. We also show that the initial shot-to-shot fluctuations in the rate of emission into the waveguide diminish in a chiral system and vanish in a symmetric system as NNN approaches ∞\infty∞. Additionally, the equal-time second-order correlation becomes trivial, showing that finite-size effects are essential to observe the emergence of second-order coherence. Finally, going beyond the thermodynamic limit requires higher order mean field methods. Our results illustrate finite- and infinite-body collective effects in symmetric and symmetry-lacking systems.
Waveguide QED with cold atoms provides a potent platform for the study of non-equilibrium, many-body, and open-system quantum dynamics. Even with weak coupling and strong photon loss, the collective enhancement of light-atom interactions leads to strong correlations of photons arising in transmission, as shown in recent experiments. Here we apply an improved mean-field theory based on higher-order cumulant expansions to describe the experimentally relevant, but theoretically elusive, regime of weak coupling and strong driving of large ensembles. We determine the transmitted power, squeezing spectra and the degree of second-order coherence, and systematically check the convergence of the results by comparing expansions that truncate cumulants of few-particle correlations at increasing order. This reveals the important role of many-body and long-range correlations between atoms in steady state. Our approach allows to quantify the trade-off between anti-bunching and output power in previously inaccessible parameter regimes. Calculated squeezing spectra show good agreement with measured data, as we present here.
Waveguide QED with cold atoms provides a potent platform for the study of non-equilibrium, many-body, and open-system quantum dynamics. Even with weak coupling and strong photon loss, the collective enhancement of light-atom interactions leads to strong correlations of photons arising in transmission, as shown in recent experiments. Here we apply an improved mean-field theory based on higher-order cumulant expansions to describe the experimentally relevant, but theoretically elusive, regime of weak coupling and strong driving of large ensembles. We determine the transmitted power, squeezing spectra and the degree of second-order coherence, and systematically check the convergence of the results by comparing expansions that truncate cumulants of few-particle correlations at increasing order. This reveals the important role of many-body and long-range correlations between atoms in steady state. Our approach allows to quantify the trade-off between anti-bunching and output power in previously inaccessible parameter regimes. Calculated squeezing spectra show good agreement with measured data, as we present here.
Abstract Waveguide quantum electrodynamics (wQED) with underlying collective and long-range atom-atom interactions has led to many distinct dynamical phenomena, including modified collective radiations and intriguing quantum correlations. It stands out as a unique platform to illustrate correlated photon transport, as well as to promise applications in quantum information processing. Here we manifest a fast and high atomic excitation transport by employing two separated chirally-coupled atomic arrays. This enhanced waveguide-mediated transport of excitations emerges due to the dominance of few subradiant right eigenstates that are spectrally isolated and spatially localized in the system’s dynamics. Contrary to the instinct of applying the cascaded systems with unidirectional couplings to expedite direct and high excitation transport, the optimal system configurations in open wQED systems demand slight or finite nonreciprocal decay channels to facilitate energy transport by exploiting waveguide-mediated couplings. We also investigate the effect of the couplings’ directionality and the scaling of atom number on the transport properties. Our results showcase the wide applicability in wQED platforms and provide insights into quantum engineering and quantum information applications.
This thesis investigates two largely independent topics in many-body and quantum optical physics. The first concerns the thermalization of classical one-dimensional (1D) gases through three-body collisions, while the second explores collective light–matter interactions in atomic arrays and waveguide quantum electrodynamics, with an emphasis on subradiance, superradiance, and computational methods for many-body dynamics. The first part studies thermalization in dilute classical 1D gases, where conventional twobody collisions cannot establish thermal equilibrium. Using Monte Carlo calculations of the three-body collision kernel together with the Boltzmann equation and molecular dynamics simulations, we characterize the thermalization dynamics for particles interacting through inverse power-law and Lennard–Jones potentials. We show that the Boltzmann and molecular dynamics approaches agree in the dilute limit and derive the thermalization rate for inverse power-law interactions.The second part investigates realistic effects in collective light–matter systems. We first study the influence of finite trapping potentials on subradiant states in atomic arrays coupled through free space or a one-dimensional waveguide. We show that atomic motion fundamentally limits subradiant lifetimes through wavefunction delocalization, recoil heating, and dipole-force-induced motion, leading to decoherence and reduced quantum memory fidelity. These results identify optimal trapping and array configurations for long-lived collective excitations.The final chapters develop theoretical methods for describing photon emission in chiral and symmetric waveguide QED systems. Using higher-order mean-field approximations, we model collective emission in experimentally relevant chiral waveguides, obtaining agreement with recent experiments and deriving analytical expressions for photon statistics. We demonstrate that fourth-order correlations are required to capture the emergence of second-order coherence from a fully inverted state. Finally, in the thermodynamic limit of large atom number and fixed optical depth, we show that a second-order mean-field theory becomes exact, yielding analytical solutions for photon emission statistics in both chiral and symmetric waveguides. We characterize the crossover between enhanced superradiant and subradiant emission, establish the suppression of emission fluctuations in the large-system limit, and clarify the role of finite-size effects in generating nontrivial photon correlations.
Waveguide quantum electrodynamics (wQED) has become a central platform for studying collective light-matter interactions in low-dimensional photonic environments. While conventional wQED systems rely on uniform chirality or reciprocal emitter-waveguide coupling, we propose a structured wQED framework, where the coupling directionality of each emitter can be engineered locally to control excitation transport in an atom-nanophotonic interface. For different combinations of patterned coupling directionalities of the emitters, we identify four representative configurations that exhibit distinct dynamical behaviors: centering, wave-like, leap-frog, and dispersion excitations. Spectral analysis of the effective non-Hermitian Hamiltonian reveals that these dynamics originate from interferences among subradiant eigenmodes. Variance analysis further quantifies the spreading of excitation as functions of interatomic spacing and global chirality, showing tunable localization-delocalization transitions. Including nonguided losses, we find that the transport characteristics remain robust for realistic coupling efficiencies (beta >= 0.99). These results establish structured wQED as a practical route to manipulate excitation localization, coherence, and transport through programmable directionality patterns, paving the way for controllable subradiant transport and chiral quantum information routing.