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:2604.20602 · Physical Review A

Bound, antibound and resonance two-photon states in chiral waveguide QED

Jiaming Shi, Alexander Poddubny

quant-phSubmitted Apr 22, 2026• Announced Apr 23, 2026• 0 citations• Revised May 21, 2026 (v3)
v1 · Apr 22, 2026v2 · May 17, 2026v3 · May 21, 2026
arXivHTMLPDF

Abstract

We present a theoretical study of the two-particle spectrum $ω(K)$ for the chiral waveguide QED setup of an array of two-level atoms directionally interacting with photons propagating along the waveguide. We demonstrate that for each pair center-of-mass momentum $K$ there exist distinct solutions with $\Imω\le 0$ in the two-particle spectrum, corresponding to bound, antibound and resonance states, in addition to the continuum of scattering states. Contrary to previous studies, which showed the bound and resonance-state spectra only over a limited range of $K$, the calculated spectrum is consistent across all $K$ values. An interesting finding is that the real part of the spectrum $\Re ω(K)$ in the chiral model is gapless. The calculated dispersion law $ω(K)$ provides an effective model for the bound photon pairs also in a finite-size array, manifesting the topological non-Hermitian skin effect.

DOI
10.1103/dhdw-m239
Comments
v3: misprint in Eq. (8) corrected compared to v2. Code publicly available at Zenodo and Github, https://doi.org/10.5281/zenodo.19675093

Related papers

Photonic Bound States and Scattering Resonances in Waveguide QED

Bastian Bakkensen, Yu-Xiang Zhang, J. Bjerlin +1 more

We study the emergence of two types of two-photon bounds states in waveguides of any chirality. Specifically, we present a systematic way of analytically determining the eigenstates of a system consisting of a waveguide coupled to a partially chiral, infinite array of equidistant two-level emitters. Using an effective Hamiltonian approach, we determine the properties of the two-photon bound states by determining their dispersion relation and internal structure. The bound states come in two varieties, depending on the two-photon momentum and emitter spacing. One of these states is a long-lived true bound state, whereas the other, a scattering resonance, decays in time via coupling to free two-photon states, leading to resonances and corresponding phase shifts in the photon-photon scattering.

arXiv:2110.06093•Oct 12, 2021•4 citations

Chiral Dissociation of Bound Photon Pairs for a Non-Hermitian Skin Effect

Jiaming Shi, Alexander N. Poddubny

We theoretically study the bound states of interacting photons propagating in a waveguide chirally coupled to an array of atoms. We demonstrate that the bound photon pairs can concentrate at the edge of the array and link this to the non-Hermitian skin effect. Unlike tight-binding non-Hermitian setups, the bound states in the waveguide-coupled array exhibit infinite radiative lifetimes when the array has an infinite size. However, in a finite array, non-Hermiticity and localization of bound pairs emerge due to their chiral dissociation into scattering states. Counterintuitively, when the photons are preferentially emitted to the right, the bound pairs are localized at the left edge of the array and vice versa.

arXiv:2501.09417•Physical Review Letters•May 27, 2025•6 citations

Dynamics of Many-Body Photon Bound States in Chiral Waveguide QED

Sahand Mahmoodian, Giuseppe Calajò, Darrick E. Chang +2 more

We theoretically study the few-and many-body dynamics of photons in chiral waveguides.In particular, we examine pulse propagation through an ensemble of N two-level systems chirally coupled to a waveguide.We show that the system supports correlated multiphoton bound states, which have a welldefined photon number n and propagate through the system with a group delay scaling as 1=n 2 .This has the interesting consequence that, during propagation, an incident coherent-state pulse breaks up into different bound-state components that can become spatially separated at the output in a sufficiently long system.For sufficiently many photons and sufficiently short systems, we show that linear combinations of n-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency.Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition.Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons.Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters.Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED.

arXiv:1910.05828•Physical Review X•Jul 14, 2020•126 citations

Most Subradiant Bound Photon Pairs from Chirality-Mediated Dispersion Softening

Kailin Tan, Xuanbing Jiang, Dong Wang +1 more

We study the subradiant bound states (BSs) in a two-level atom array chirally coupled to a one-dimensional waveguide. We demonstrate that the chiral interaction can drive BSs to become the most subradiant two-excitation states across a wide spacing range. This phenomenon is rooted in a mechanism of chirality-mediated dispersion softening, where the BS band distortion suppresses the band curvature $|α_2|$ at an extremum point. We rigorously prove that the BS decay rate follows the scaling $Γ\sim |α_2|/N^3$, revealing that the reduction of $|α_2|$ is key to suppressing emission and enhancing subradiance. We also show the existence of chiral BSs in a realistic nanofiber interface.

quant-pharXiv:2606.01146•Jun 2, 2026•0 citations

Dynamics of Many-Body Photon Bound States in Chiral Waveguide QED

Sahand Mahmoodian, Calajó, Guiseppe, Darrick E. Chang +2 more

We theoretically study the few- and many-body dynamics of photons in chiral waveguides. In particular, we examine pulse propagation through an ensemble of N two-level systems chirally coupled to a waveguide. We show that the system supports correlated multiphoton bound states, which have a well-defined photon number n and propagate through the system with a group delay scaling as 1/n2. This has the interesting consequence that, during propagation, an incident coherent-state pulse breaks up into different bound-state components that can become spatially separated at the output in a sufficiently long system. For sufficiently many photons and sufficiently short systems, we show that linear combinations of n-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency. Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition. Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons. Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters. Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED. © 2020 authors.

•Jan 1, 2020•101 citations

Topology and Interactions in a Qubit Array Coupled to a Waveguide

Janet Zhong

Waveguide quantum electrodynamic (waveguide QED) systems (arrays of qubits coupled to a waveguide) can exhibit a vast array of phenomena from collective effects, non-trivial topology to novel localisation effects. This thesis is the first study of a long-range coupled topological waveguide QED system. The existence of topological edge states for when one photon is incident on a spatially modulated qubit array is numerically verified and the results are analogous to a photonic crystal set-up in Ref. [1]. This thesis then goes beyond the single photon regime to consider the effect of interactions for when two photons are incident in the qubit array. Bound photon pairs and bound pair edge states are readily observed. Numerical results suggest that the bound pair edge states are topologically non-trivial, however, a topological invariant should be calculated before making stronger conclusive statements. Even more interestingly, the two-photon qubit array can also exhibit a self-induced localised state. This appears to be a completely unexplored effect that can connect many body physics, collective effects as well as topological properties. The exotic topological properties of these waveguide QED systems are promising developments in the growing field of quantum topological photonics which is said to have large potential for quantum computing technologies. The novel localised states also reveals that the physics of waveguide QED systems are richer than expected with many unexplored phenomena.

•Jan 1, 2019•0 citations
We present a theoretical study of the two-particle spectrum ω(K)ω(K)ω(K) for the chiral waveguide QED setup of an array of two-level atoms directionally interacting with photons propagating along the waveguide. We demonstrate that for each pair center-of-mass momentum KKK there exist distinct solutions with ℑω≤0\Imω\le 0ℑω≤0 in the two-particle spectrum, corresponding to bound, antibound and resonance states, in addition to the continuum of scattering states. Contrary to previous studies, which showed the bound and resonance-state spectra only over a limited range of KKK, the calculated spectrum is consistent across all KKK values. An interesting finding is that the real part of the spectrum ℜω(K)\Re ω(K)ℜω(K) in the chiral model is gapless. The calculated dispersion law ω(K)ω(K)ω(K) provides an effective model for the bound photon pairs also in a finite-size array, manifesting the topological non-Hermitian skin effect.
We study the emergence of two types of two-photon bounds states in waveguides of any chirality. Specifically, we present a systematic way of analytically determining the eigenstates of a system consisting of a waveguide coupled to a partially chiral, infinite array of equidistant two-level emitters. Using an effective Hamiltonian approach, we determine the properties of the two-photon bound states by determining their dispersion relation and internal structure. The bound states come in two varieties, depending on the two-photon momentum and emitter spacing. One of these states is a long-lived true bound state, whereas the other, a scattering resonance, decays in time via coupling to free two-photon states, leading to resonances and corresponding phase shifts in the photon-photon scattering.
We theoretically study the bound states of interacting photons propagating in a waveguide chirally coupled to an array of atoms. We demonstrate that the bound photon pairs can concentrate at the edge of the array and link this to the non-Hermitian skin effect. Unlike tight-binding non-Hermitian setups, the bound states in the waveguide-coupled array exhibit infinite radiative lifetimes when the array has an infinite size. However, in a finite array, non-Hermiticity and localization of bound pairs emerge due to their chiral dissociation into scattering states. Counterintuitively, when the photons are preferentially emitted to the right, the bound pairs are localized at the left edge of the array and vice versa.
We theoretically study the few-and many-body dynamics of photons in chiral waveguides.In particular, we examine pulse propagation through an ensemble of N two-level systems chirally coupled to a waveguide.We show that the system supports correlated multiphoton bound states, which have a welldefined photon number n and propagate through the system with a group delay scaling as 1=n 2 .This has the interesting consequence that, during propagation, an incident coherent-state pulse breaks up into different bound-state components that can become spatially separated at the output in a sufficiently long system.For sufficiently many photons and sufficiently short systems, we show that linear combinations of n-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency.Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition.Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons.Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters.Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED.
We study the subradiant bound states (BSs) in a two-level atom array chirally coupled to a one-dimensional waveguide. We demonstrate that the chiral interaction can drive BSs to become the most subradiant two-excitation states across a wide spacing range. This phenomenon is rooted in a mechanism of chirality-mediated dispersion softening, where the BS band distortion suppresses the band curvature ∣α2∣|α_2|∣α2​∣ at an extremum point. We rigorously prove that the BS decay rate follows the scaling Γ∼∣α2∣/N3Γ\sim |α_2|/N^3Γ∼∣α2​∣/N3, revealing that the reduction of ∣α2∣|α_2|∣α2​∣ is key to suppressing emission and enhancing subradiance. We also show the existence of chiral BSs in a realistic nanofiber interface.
We theoretically study the few- and many-body dynamics of photons in chiral waveguides. In particular, we examine pulse propagation through an ensemble of N two-level systems chirally coupled to a waveguide. We show that the system supports correlated multiphoton bound states, which have a well-defined photon number n and propagate through the system with a group delay scaling as 1/n2. This has the interesting consequence that, during propagation, an incident coherent-state pulse breaks up into different bound-state components that can become spatially separated at the output in a sufficiently long system. For sufficiently many photons and sufficiently short systems, we show that linear combinations of n-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency. Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition. Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons. Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters. Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED. © 2020 authors.
Waveguide quantum electrodynamic (waveguide QED) systems (arrays of qubits coupled to a waveguide) can exhibit a vast array of phenomena from collective effects, non-trivial topology to novel localisation effects. This thesis is the first study of a long-range coupled topological waveguide QED system. The existence of topological edge states for when one photon is incident on a spatially modulated qubit array is numerically verified and the results are analogous to a photonic crystal set-up in Ref. [1]. This thesis then goes beyond the single photon regime to consider the effect of interactions for when two photons are incident in the qubit array. Bound photon pairs and bound pair edge states are readily observed. Numerical results suggest that the bound pair edge states are topologically non-trivial, however, a topological invariant should be calculated before making stronger conclusive statements. Even more interestingly, the two-photon qubit array can also exhibit a self-induced localised state. This appears to be a completely unexplored effect that can connect many body physics, collective effects as well as topological properties. The exotic topological properties of these waveguide QED systems are promising developments in the growing field of quantum topological photonics which is said to have large potential for quantum computing technologies. The novel localised states also reveals that the physics of waveguide QED systems are richer than expected with many unexplored phenomena.