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

Quantum Mechanical Treatment of Two-Level Atoms Coupled to Continuum

Fatih Dinç, İlke Ercan

Published Nov 5, 2017• 0 citations
OpenAlex

Abstract

In this paper, we provide a rigorous quantum mechanical derivation for the coherent photon transport characteristics of a two-level atom coupled to a waveguide without linearizing the coupling coefficient between the light and the atom. We propose a novel single frequency sampling method that allows us to treat the singularities in real space scattering potential despite the non-convergence property. We also study the conditions under which the linearization of the coupling coefficient is an accurate assumption. This allows us to confirm and expand on the findings of the existing literature while obtaining the dynamic electronic polarizability for the two-level atom confined to a 1-D waveguide while using an interaction Hamiltonian with rotating-wave approximation.

Related papers

Quantum mechanical treatment of two-level atoms coupled to continuum with an ultraviolet cutoff

Fatih Dinç, İlke Ercan

Abstract In this paper, we provide a rigorous quantum mechanical derivation for the coherent photon transport characteristics of a two-level atom coupled to a waveguide without linearizing the coupling coefficient between the light and the atom. We propose a novel single frequency sampling method utilizing a UV-cutoff that allows us to treat the singularities in real space scattering potential despite the non-convergence property. We also study the conditions under which the linearization of the coupling coefficient is an accurate assumption and find the resulting spontaneous emission and transport characteristics taking the radiative and non-radiative decay rates into account. This allows us to confirm and expand on the findings of the existing literature while obtaining the dynamic electronic polarizability for the two-level atom confined to a 1D waveguide while using an interaction Hamiltonian with rotating-wave approximation.

arXiv:1711.01615•Journal of Physics A Mathematical and Theoretical•Jul 5, 2018•2 citations

Fully quantum-mechanical analytic results for single-photon transport in a single-mode waveguide coupled to a whispering-gallery resonator interacting with a two-level atom

Jung‐Tsung Shen, Shanhui Fan

We analyze the single-photon transport in a single-mode waveguide coupled to a whispering-gallery-type resonator interacting with a two-level atom. The single-photon transport properties such as the transmission and reflection amplitudes, as well as the resonator and the atom responses, are solved exactly via a real-space approach. The treatment includes the inter-mode backscattering between the two degenerate whispering gallery modes of the resonator, and the dissipations of the resonator and the atom. We also show that a generalized critical coupling condition, that the single-photon transmission at the output of the waveguide goes to zero on resonance for a matched system, holds for the full coupled waveguide-ring resonator-atom system.

arXiv:0901.3940•Jan 26, 2009•0 citations

Quantum Rabi oscillations of a qubit strongly coupled to a one-dimensional waveguide

Ya. S. Greenberg, A. A. Shtygashev, O. A. Chuikin +2 more

We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.

quant-pharXiv:2608.16077•Aug 18, 2026•0 citations

Theory of single-photon transport in a single-mode waveguide. II. Coupling to a whispering-gallery resonator containing a two-level atom

Jung‐Tsung Shen, Shanhui Fan

We analyze the single-photon transport in a single-mode waveguide coupled to a whispering-gallery-type resonator interacting with a two-level atom. The single-photon transport properties such as the transmission and reflection amplitudes, as well as the resonator and the atom responses, are solved exactly via a real-space approach. The treatment includes the intermode backscattering between the two degenerate whispering-gallery modes of the resonator, and the dissipations of the resonator and the atom. We also show that a generalized critical coupling condition, that the single-photon transmission at the output of the waveguide goes to zero on resonance for a matched system, holds for the full coupled waveguide-ring resonator-atom system.

Physical Review A•Feb 26, 2009•148 citations

The Two Level Atom System Dissipation Influence to Single Photon Propagating Properties

Lingyun Xie, Lian-Fu Wei

The studies of interactions of electromagnetic fields with two level atom systems is a main theme of quantum optics. Here, we shows how the inherent dissipation of atom influences the interaction between atom and single photon propagating in the waveguide. Based on a fully quantum mechanical theory in real space, we exactly calculated the transportation probability of a single photon for a two-level atom system next to the waveguide. We find that the existence of a dissipated atom can be utilized to act as the light router as well as the beam splitter, if properly adjust relationship of atom dissipation 􀟛􀯤and coupling strengthV between atom and single photon in waveguide.

DEStech Transactions on Computer Science and Engineering•Mar 17, 2017•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
In this paper, we provide a rigorous quantum mechanical derivation for the coherent photon transport characteristics of a two-level atom coupled to a waveguide without linearizing the coupling coefficient between the light and the atom. We propose a novel single frequency sampling method that allows us to treat the singularities in real space scattering potential despite the non-convergence property. We also study the conditions under which the linearization of the coupling coefficient is an accurate assumption. This allows us to confirm and expand on the findings of the existing literature while obtaining the dynamic electronic polarizability for the two-level atom confined to a 1-D waveguide while using an interaction Hamiltonian with rotating-wave approximation.
Abstract In this paper, we provide a rigorous quantum mechanical derivation for the coherent photon transport characteristics of a two-level atom coupled to a waveguide without linearizing the coupling coefficient between the light and the atom. We propose a novel single frequency sampling method utilizing a UV-cutoff that allows us to treat the singularities in real space scattering potential despite the non-convergence property. We also study the conditions under which the linearization of the coupling coefficient is an accurate assumption and find the resulting spontaneous emission and transport characteristics taking the radiative and non-radiative decay rates into account. This allows us to confirm and expand on the findings of the existing literature while obtaining the dynamic electronic polarizability for the two-level atom confined to a 1D waveguide while using an interaction Hamiltonian with rotating-wave approximation.
We analyze the single-photon transport in a single-mode waveguide coupled to a whispering-gallery-type resonator interacting with a two-level atom. The single-photon transport properties such as the transmission and reflection amplitudes, as well as the resonator and the atom responses, are solved exactly via a real-space approach. The treatment includes the inter-mode backscattering between the two degenerate whispering gallery modes of the resonator, and the dissipations of the resonator and the atom. We also show that a generalized critical coupling condition, that the single-photon transmission at the output of the waveguide goes to zero on resonance for a matched system, holds for the full coupled waveguide-ring resonator-atom system.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.
We analyze the single-photon transport in a single-mode waveguide coupled to a whispering-gallery-type resonator interacting with a two-level atom. The single-photon transport properties such as the transmission and reflection amplitudes, as well as the resonator and the atom responses, are solved exactly via a real-space approach. The treatment includes the intermode backscattering between the two degenerate whispering-gallery modes of the resonator, and the dissipations of the resonator and the atom. We also show that a generalized critical coupling condition, that the single-photon transmission at the output of the waveguide goes to zero on resonance for a matched system, holds for the full coupled waveguide-ring resonator-atom system.
The studies of interactions of electromagnetic fields with two level atom systems is a main theme of quantum optics. Here, we shows how the inherent dissipation of atom influences the interaction between atom and single photon propagating in the waveguide. Based on a fully quantum mechanical theory in real space, we exactly calculated the transportation probability of a single photon for a two-level atom system next to the waveguide. We find that the existence of a dissipated atom can be utilized to act as the light router as well as the beam splitter, if properly adjust relationship of atom dissipation 􀟛􀯤and coupling strengthV between atom and single photon in waveguide.
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.