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:0809.1279 · Physical Review B

Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled-resonator arrays

Tao Shi, C. P. Sun

Published May 20, 2009• 160 citations
arXivHTMLPDF

Abstract

We present a quantum field theoretical approach based on the Lehmann-Symanzik-Zimmermann reduction for the multiphoton scattering process in a nanoarchitecture consisting of the coupled-resonator arrays (CRA), which are also coupled to some artificial atoms as a controlling quantum node. By making use of this approach, we find the bound states of a single photon for an elementary unit, the $T$-type CRA, and explicitly obtain its multiphoton scattering $S$ matrix in various situations. We also use this method to calculate the multiphoton $S$ matrices for the more complex quantum network constructed with main $T$-type CRAs, such as a $H$-type CRA waveguide.

DOI
10.1103/physrevb.79.205111

Related papers

Two-Photon Scattering in One Dimension by Localized Two-Level System

Tao Shi, C. P. Sun

We study two-photon scattering in a one-dimensional coupled resonator arrays (CRA) by a two-level system (TLS), which is localized as a quantum controller. The $S$-matrix is analytically calculated for various two-photon scattering processes by TLS, e.g., one photon is confined by TLS to form a bound state while the other is in the scattering state. It is discovered from the poles of the $S$-matrix that there exist two kinds of three-body bound states for describing two bound photons localized around TLS.

arXiv:0907.2776•Jul 16, 2009•6 citations

Transferring and bounding single photon in waveguide controlled by quantum node based on atomic ensemble

Jing Lu, Haohao Dong, Le‐Man Kuang

We study the scattering process of photons confined in a one dimensional optical waveguide by a laser controlled atomic ensemble. The investigation leads to an alternative setup of quantum node controlling the coherent transfer of single photon in such one dimensional continuum. To exactly solve the effective scattering equations by using the discrete coordinate approach, we simulate the linear waveguide as a coupled resonator array at the high energy limit. We generally calculate the transmission coefficients and its vanishing at resonace reflects the good controllability of our scheme. We also show that there exist two bound states to describe the localize photons around the cavity.

arXiv:0809.1540•Sep 9, 2008•0 citations

Transferring and Bounding Single Photon in Waveguide Controlled by Quantum Node Based on Atomic Ensemble

Jing Lu, Dong Hui, Kuang Le-Man

We study the scattering process of photons confined in a one-dimensional optical waveguide by a laser controlled atomic ensemble. The investigation leads to an alternative setup of quantum node controlling the coherent transfer of single photon in such one dimensional continuum. To exactly solve the effective scattering equations by using the discrete coordinate approach, we simulate the linear waveguide as a coupled resonator array at the high energy limit. We generally calculate the transmission coefficients and its vanishing at resonance reflects the good controllability of our scheme. We also show that there exist two bound states to describe the localize photons around the cavity.

Communications in Theoretical Physics•Sep 1, 2009•2 citations

Diagrammatic approach to multiphoton scattering

Tian Feng See, Changsuk Noh, Dimitris G. Angelakis

We present a method to systematically study multiphoton transmission in one-dimensional systems comprised of correlated quantum emitters coupled to input and output waveguides. Within the Green's function approach of the scattering matrix $(S$ matrix), we develop a diagrammatic technique to analytically obtain the system's scattering amplitudes while at the same time visualize all the possible absorption and emission processes. Our method helps to reduce the significant effort in finding the general response of a many-body bosonic system, particularly the nonlinear response embedded in the Green's functions. We demonstrate our proposal through physically relevant examples involving scattering of multiphoton states from two-level emitters as well as from arrays of correlated Kerr nonlinear resonators in the Bose-Hubbard model.

arXiv:1702.01632•Physical Review A•May 18, 2017•19 citations

Single-Photon Transmission Characteristics in a Pair of Coupled-Resonator Waveguides Linked by a Nanocavity Containing a Quantum Emitter

Mu-Tian Cheng, Meng-Ting Ding, Yan‐Yan Song +1 more

Single-photon scattering in a pair of coupled-resonator arrays of waveguides linked by a nanocavity embedded with a two-level system is investigated theoretically. By using the discrete coordinates approach, we deduce the analytical expressions for the transmission and reflection amplitudes. The calculations reveal that the transport properties of the single photon can be controlled by adjusting the coupled strength between the nanocavity and the coupled-resonator array. Quantum switching and a 1/4 beam splitter for the band-edge photon based on this structure are also discussed.

Chinese Physics Letters•May 1, 2013•3 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
We present a quantum field theoretical approach based on the Lehmann-Symanzik-Zimmermann reduction for the multiphoton scattering process in a nanoarchitecture consisting of the coupled-resonator arrays (CRA), which are also coupled to some artificial atoms as a controlling quantum node. By making use of this approach, we find the bound states of a single photon for an elementary unit, the TTT-type CRA, and explicitly obtain its multiphoton scattering SSS matrix in various situations. We also use this method to calculate the multiphoton SSS matrices for the more complex quantum network constructed with main TTT-type CRAs, such as a HHH-type CRA waveguide.
We study two-photon scattering in a one-dimensional coupled resonator arrays (CRA) by a two-level system (TLS), which is localized as a quantum controller. The SSS-matrix is analytically calculated for various two-photon scattering processes by TLS, e.g., one photon is confined by TLS to form a bound state while the other is in the scattering state. It is discovered from the poles of the SSS-matrix that there exist two kinds of three-body bound states for describing two bound photons localized around TLS.
We study the scattering process of photons confined in a one dimensional optical waveguide by a laser controlled atomic ensemble. The investigation leads to an alternative setup of quantum node controlling the coherent transfer of single photon in such one dimensional continuum. To exactly solve the effective scattering equations by using the discrete coordinate approach, we simulate the linear waveguide as a coupled resonator array at the high energy limit. We generally calculate the transmission coefficients and its vanishing at resonace reflects the good controllability of our scheme. We also show that there exist two bound states to describe the localize photons around the cavity.
We study the scattering process of photons confined in a one-dimensional optical waveguide by a laser controlled atomic ensemble. The investigation leads to an alternative setup of quantum node controlling the coherent transfer of single photon in such one dimensional continuum. To exactly solve the effective scattering equations by using the discrete coordinate approach, we simulate the linear waveguide as a coupled resonator array at the high energy limit. We generally calculate the transmission coefficients and its vanishing at resonance reflects the good controllability of our scheme. We also show that there exist two bound states to describe the localize photons around the cavity.
We present a method to systematically study multiphoton transmission in one-dimensional systems comprised of correlated quantum emitters coupled to input and output waveguides. Within the Green's function approach of the scattering matrix (S(S(S matrix), we develop a diagrammatic technique to analytically obtain the system's scattering amplitudes while at the same time visualize all the possible absorption and emission processes. Our method helps to reduce the significant effort in finding the general response of a many-body bosonic system, particularly the nonlinear response embedded in the Green's functions. We demonstrate our proposal through physically relevant examples involving scattering of multiphoton states from two-level emitters as well as from arrays of correlated Kerr nonlinear resonators in the Bose-Hubbard model.
Single-photon scattering in a pair of coupled-resonator arrays of waveguides linked by a nanocavity embedded with a two-level system is investigated theoretically. By using the discrete coordinates approach, we deduce the analytical expressions for the transmission and reflection amplitudes. The calculations reveal that the transport properties of the single photon can be controlled by adjusting the coupled strength between the nanocavity and the coupled-resonator array. Quantum switching and a 1/4 beam splitter for the band-edge photon based on this structure are also discussed.
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.