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arXiv:1506.01176 · Optics Letters

Theoretical treatment of the interaction between two-level atoms and periodic waveguides

Xiaorun Zang, Philippe Lalanne

Published Aug 10, 2015• 7 citations
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Abstract

Light transport in periodic waveguides coupled to two-level atoms is investigated theoretically. By using optical Bloch equations and a photonic modal formalism, we derive a convenient semi-analytical expression for calculating the scattering matrix of single atoms trapped in periodic waveguides. The expression that holds for both photonic and plasmonic waveguides represents a basic building block toward the study of collective effects arising from photon-mediated multi-atom interactions in periodic waveguides.

DOI
10.1364/ol.40.003869

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Light transport in periodic waveguides coupled to two-level atoms is investigated theoretically. By using optical Bloch equations and a photonic modal formalism, we derive a convenient semi-analytical expression for calculating the scattering matrix of single atoms trapped in periodic waveguides. The expression that holds for both photonic and plasmonic waveguides represents a basic building block toward the study of collective effects arising from photon-mediated multi-atom interactions in periodic waveguides.
We have theoretically studied the scattering of two-photon pulses from a spatially-separated array of two-level atoms coupled to the waveguide. A general analytical expression for the scattered pulse has been obtained. The contributions of various single-eigenstate and double-excited eigenstates of the array have been analyzed. We have also calculated the dependence of the time incident photons are stored in the array on its period and the number of atoms. The largest storage times correspond to the structures with the anti-Bragg period, equal to the quarter of the wavelength of light at the atom resonance frequency λ/4λ/4λ/4.
We theoretically studied the scattering of short two-photon pulses from a spatially separated array of two-level atoms coupled to the waveguide. A general analytical expression for the scattered pulse has been obtained. The contributions of various single-eigenstate and double-excited eigenstates of the array have been analyzed. We also calculated how the time, during which the incident photons are stored in the array, depends on the array period and the number of atoms. The largest storage times correspond to the structures with the anti-Bragg period, equal to the quarter of the wavelength of light at the atom resonance frequency $\ensuremath{\lambda}/4$.
In this work we considered light interaction with two-level quantum systems chirally coupled to a single guided mode with account for a spin-locking effect. The chiral coupling allows achieving asymmetric interaction between the two-level systems, which strongly affects the light scattering of a guided mode of an optical nanofiber by one-dimensional atomic chain. We have also build an analytical model of unidirectional transport of quantum excitation and verified it with modelling of atoms coupled with surface plasmon polariton mode of a metallic nanowire. In particularly, we showed the tolerance of the unidirectionally coupled systems over the positional disorder of the two-level systems.
We present a full multimode treatment of the interaction of the quantized radiation field with a single two-level atom in a one-dimensional waveguide configuration. Starting with an incident pulse consisting of an arbitrary (finite) number of photons in a general initial state, we derive the equations of motion and a closed-form expression for the shape of the pulse after its interaction with the atom. We then specialize our results to the two-photon case where a number of analytical results can be derived, for both unidirectional and bidirectional systems. We study the effects of different pulse shapes, the manifestations of the entangled, so-called bound state of the two photons, single- and two-photon detection probabilities, and provide simple approximate results for the strong-coupling (or adiabatic, or long-pulse) regime. We also discuss the requirements for a true unidirectional setup, and the application of such a setup to photon sorting proposed by Witthaut, Lukin, and S\o{}rensen [Europhys. Lett. 97, 50007 (2012)].
We study one- and two-photon scattering from a qubit embedded in a one-dimensional waveguide in the presence of modal dispersion. We use a resolvent based analysis and utilize techniques borrowed from the Lee model studies. Modal dispersion leads to atom-photon bound states which necessitate the use of multichannel scattering theory. We present multichannel scattering matrix elements in terms of the solution of a Fredholm integral equation of the second kind. Through the use of the Lippmann-Schwinger equation, we derive an infinite series of Feynman diagrams that represent the solution to the integral equation. We use the Feynman diagrams as vertex correction terms to come up with closed-form formulas that successfully predict the trapping rate of a photon in the atom-photon bound state. We verify our formalism through Krylov-subspace based numerical studies with pulsed excitations. Our results provide the tools to calculate the complex correlations between scattered photons in a dispersive environment.