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:1904.13004 · Physical Review A

Bound states in the continuum for an array of quantum emitters

Paolo Facchi A, Davide Lonigro, Saverio Pascazio, Francesco Vincenzo Pepe, Domenico Pomarico

Published Aug 22, 2019• 39 citations
arXivHTMLPDF

Abstract

We study the bound states in the continuum for a system of $n$ two-level quantum emitters, coupled with a one-dimensional photon field, when a single excitation is shared among the different components of the system. The emitters are equally spaced at fixed positions. We first consider the approximation of distant emitters and exhibit degenerate eigenspaces of bound states corresponding to resonant discrete values of the energy. We then consider the full form of the eigenvalue equation, in which the effects of the finite spacing and the field dispersion relation become relevant, yielding significant nonperturbative effects that can lift some degeneracies. We explicitly solve the cases $n=3$ and $n=4$ emitters.

DOI
10.1103/physreva.100.023834

Related papers

Stationary excitation waves and multimerization in arrays of quantum emitters

Davide Lonigro, Paolo Facchi A, Saverio Pascazio +2 more

We explore the features of an equally-spaced array of two-level quantum emitters, that can be either natural atoms (or molecules) or artificial atoms, coupled to a field with a single continuous degree of freedom (such as an electromagnetic mode propagating in a waveguide). We investigate the existence and characteristics of bound states, in which a single excitation is shared among the emitters and the field. We focus on bound states in the continuum, occurring in correspondence of excitation energies in which a single excited emitter would decay. We characterize such bound states for an arbitrary number of emitters, and obtain two main results, both ascribable to the presence of evanescent fields. First, the excitation profile of the emitter states is a sinusoidal wave. Second, we discuss the emergence of multimers, consisting in subsets of emitters separated by two lattice spacings in which the electromagnetic field is approximately vanishing.

arXiv:2106.08213•New Journal of Physics•Oct 1, 2021•11 citations

Photon-emitter dressed states in a closed waveguide

Davide Lonigro, Paolo Facchi A, Andrew D. Greentree +3 more

We study a system made up of one or two two-level quantum emitters, coupled to a single transverse mode of a closed waveguide, in which photon wavenumbers and frequencies are discretized, and characterize the states in which one excitation is steadily shared between the field and the emitters. We unearth finite-size effects in the field-emitter interactions and identify a family of dressed bound states that represent the forerunners of bound states in the continuum in the limit of an infinite waveguide. We finally consider the potential interest of such states for applications in the field of quantum information.

arXiv:2103.10926•Physical Review A•Nov 8, 2021•7 citations

Controlling atom-photon bound states in a coupled resonator array with a two-level quantum emitter

Zhongling Lu, Jing Li, Jing Lü +1 more

We consider a one-dimensional (1D) coupled-resonator array (CRA), where a two-level quantum emitter (2LE) is electric-dipole coupled to the modes of two adjacent resonators. We investigate the energy spectrum, the photon probability distribution of the bound states, and the emission process of the 2LE into the CRA vacuum. A quantum phase transition is found which is characterized by the change of the number of the out-of-band discrete levels. The condition for this change is also presented. The photon wave functions of bound states are found to be asymmetry around the position of the 2LE when the coupling strengths between the 2LE and the resonator are not equal, and they have the same preferred directions which are primarily determined by the larger one among the coupling strengths. The presence of the atom-photon bound states is manifested in the form of a stationary oscillation or a non-vanishing constant in the long enough time.

arXiv:2401.09688•Optics Letters•Jan 2, 2024•8 citations

Quasi-Degenerate Resonant Eigenstate Doublets of Two Quantum Emitters in a Closed Waveguide

Ammara Ammara, Paolo Facchi A, Saverio Pascazio +2 more

The physics of systems of quantum emitters in waveguide quantum electrodynamics is significantly influenced by the relation between their spatial separation and the wavelength of the emitted photons. If the distance that separates a pair of emitters meets specific resonance conditions, the photon amplitudes produced from decay may destructively interfere. In an infinite-waveguide setting, this effect gives rise to bound states in the continuum, where a photon remains confined between the emitters. In the case of a finite-length waveguide with periodic boundary conditions, there exist two such relevant distances for a given arrangement of the quantum emitters, leading to states in which a photon is confined to either the shorter or the longer path that connects the emitters. If the ratio of the shorter and the longer path is a rational number, these two kinds of resonant eigenstates are allowed to co-exist for the same Hamiltonian. In this paper, we investigate the existence of quasi-degenerate resonant doublets of a pair of identical emitters coupled to a linear waveguide mode. The states that form the doublet are searched among the ones in which a single excitation tends to remain bound to the emitters. We investigate the spectrum in a finite range around degeneracy points to check whether the doublet remains well separated from the closest eigenvalues in the spectrum. The identification of quasi-degenerate doublets opens the possibility to manipulate the emitters-waveguide system as an effectively two-level system in specific energy ranges, providing an innovative tool for quantum technology tasks.

arXiv:2507.14371•Photonics•Aug 27, 2025•0 citations

Quantum plasmonics with N emitters: bright hybrid continuum selection

Georgii Semin, Hans-Rudolf Jauslin, Gérard Colas des Francs +1 more

We construct mode-selective effective models describing the interaction of the quantum plasmon-polariton field supported by a finite dielectric medium and one or several quantum emitters. The construction of the effective model is based on the decomposition of the field into bright modes relevant to the interaction with the emitters and dark modes, which do not interact with the emitters. We show that the quantum plasmon-polariton field can be represented equivalently by a double-continuum spectrum or by a single hybrid continuum spectrum for each emitter. The system of the electromagnetic field coupled to a finite medium is composed of two families of continuum modes, each of them with an infinite degeneracy. The two families are deformations of the free electromagnetic field and the free medium, induced by the interaction between them, as described by the Lippmann-Schwinger equations. We show that if there are $N$ emitters interacting with this plasmon-polariton field, the effective interaction involves a much smaller set of bosonic continuum modes: the interacting part of the continuum can be described by $N$ non-degenerate one-dimensional continua, one for each emitter. The representation of the interaction in terms of a single hybrid continuum spectrum coincides with the one within the macroscopic Langevin model with bulk medium. This coincidence is explained by an exact compensation of two terms, one in the coupling term of the Hamiltonian and the other one in a Green tensor identity.

quant-pharXiv:2604.21560•Apr 24, 2026

Bound state in the continuum by spatially separated ensembles of atoms in a coupled-cavity array

P. T. Fong, C. K. Law

We present an analytic solution of bound states in the continuum (BICs) for photons and atoms in a one-dimensional coupled-cavity array. These bound states are formed by two ensembles of two-level atoms confined in separated cavities of the array. We show that in the regime where the photon hopping rate between neighboring cavities is high compared with the collective Rabi frequency the BIC corresponds to a nonradiating collective atomic state in which the two ensembles of atoms are strongly entangled. On the other hand, in the low photon hopping rate regime, the BIC behaves as a quantum cavity in which photons can be trapped between the two ensembles of atoms.

arXiv:1705.04021•Physical Review A•Aug 18, 2017•28 citations
We study the bound states in the continuum for a system of nnn two-level quantum emitters, coupled with a one-dimensional photon field, when a single excitation is shared among the different components of the system. The emitters are equally spaced at fixed positions. We first consider the approximation of distant emitters and exhibit degenerate eigenspaces of bound states corresponding to resonant discrete values of the energy. We then consider the full form of the eigenvalue equation, in which the effects of the finite spacing and the field dispersion relation become relevant, yielding significant nonperturbative effects that can lift some degeneracies. We explicitly solve the cases n=3n=3n=3 and n=4n=4n=4 emitters.
We explore the features of an equally-spaced array of two-level quantum emitters, that can be either natural atoms (or molecules) or artificial atoms, coupled to a field with a single continuous degree of freedom (such as an electromagnetic mode propagating in a waveguide). We investigate the existence and characteristics of bound states, in which a single excitation is shared among the emitters and the field. We focus on bound states in the continuum, occurring in correspondence of excitation energies in which a single excited emitter would decay. We characterize such bound states for an arbitrary number of emitters, and obtain two main results, both ascribable to the presence of evanescent fields. First, the excitation profile of the emitter states is a sinusoidal wave. Second, we discuss the emergence of multimers, consisting in subsets of emitters separated by two lattice spacings in which the electromagnetic field is approximately vanishing.
We study a system made up of one or two two-level quantum emitters, coupled to a single transverse mode of a closed waveguide, in which photon wavenumbers and frequencies are discretized, and characterize the states in which one excitation is steadily shared between the field and the emitters. We unearth finite-size effects in the field-emitter interactions and identify a family of dressed bound states that represent the forerunners of bound states in the continuum in the limit of an infinite waveguide. We finally consider the potential interest of such states for applications in the field of quantum information.
We consider a one-dimensional (1D) coupled-resonator array (CRA), where a two-level quantum emitter (2LE) is electric-dipole coupled to the modes of two adjacent resonators. We investigate the energy spectrum, the photon probability distribution of the bound states, and the emission process of the 2LE into the CRA vacuum. A quantum phase transition is found which is characterized by the change of the number of the out-of-band discrete levels. The condition for this change is also presented. The photon wave functions of bound states are found to be asymmetry around the position of the 2LE when the coupling strengths between the 2LE and the resonator are not equal, and they have the same preferred directions which are primarily determined by the larger one among the coupling strengths. The presence of the atom-photon bound states is manifested in the form of a stationary oscillation or a non-vanishing constant in the long enough time.
The physics of systems of quantum emitters in waveguide quantum electrodynamics is significantly influenced by the relation between their spatial separation and the wavelength of the emitted photons. If the distance that separates a pair of emitters meets specific resonance conditions, the photon amplitudes produced from decay may destructively interfere. In an infinite-waveguide setting, this effect gives rise to bound states in the continuum, where a photon remains confined between the emitters. In the case of a finite-length waveguide with periodic boundary conditions, there exist two such relevant distances for a given arrangement of the quantum emitters, leading to states in which a photon is confined to either the shorter or the longer path that connects the emitters. If the ratio of the shorter and the longer path is a rational number, these two kinds of resonant eigenstates are allowed to co-exist for the same Hamiltonian. In this paper, we investigate the existence of quasi-degenerate resonant doublets of a pair of identical emitters coupled to a linear waveguide mode. The states that form the doublet are searched among the ones in which a single excitation tends to remain bound to the emitters. We investigate the spectrum in a finite range around degeneracy points to check whether the doublet remains well separated from the closest eigenvalues in the spectrum. The identification of quasi-degenerate doublets opens the possibility to manipulate the emitters-waveguide system as an effectively two-level system in specific energy ranges, providing an innovative tool for quantum technology tasks.
We construct mode-selective effective models describing the interaction of the quantum plasmon-polariton field supported by a finite dielectric medium and one or several quantum emitters. The construction of the effective model is based on the decomposition of the field into bright modes relevant to the interaction with the emitters and dark modes, which do not interact with the emitters. We show that the quantum plasmon-polariton field can be represented equivalently by a double-continuum spectrum or by a single hybrid continuum spectrum for each emitter. The system of the electromagnetic field coupled to a finite medium is composed of two families of continuum modes, each of them with an infinite degeneracy. The two families are deformations of the free electromagnetic field and the free medium, induced by the interaction between them, as described by the Lippmann-Schwinger equations. We show that if there are NNN emitters interacting with this plasmon-polariton field, the effective interaction involves a much smaller set of bosonic continuum modes: the interacting part of the continuum can be described by NNN non-degenerate one-dimensional continua, one for each emitter. The representation of the interaction in terms of a single hybrid continuum spectrum coincides with the one within the macroscopic Langevin model with bulk medium. This coincidence is explained by an exact compensation of two terms, one in the coupling term of the Hamiltonian and the other one in a Green tensor identity.
We present an analytic solution of bound states in the continuum (BICs) for photons and atoms in a one-dimensional coupled-cavity array. These bound states are formed by two ensembles of two-level atoms confined in separated cavities of the array. We show that in the regime where the photon hopping rate between neighboring cavities is high compared with the collective Rabi frequency the BIC corresponds to a nonradiating collective atomic state in which the two ensembles of atoms are strongly entangled. On the other hand, in the low photon hopping rate regime, the BIC behaves as a quantum cavity in which photons can be trapped between the two ensembles of atoms.