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Physical Review A

Multiphoton scattering in a one-dimensional waveguide with resonant atoms

Vladimir I. Yudson, P. Reineker

Published Nov 26, 2008• 70 citations
Publisher

Abstract

We study multiphoton scattering inside a one-dimensional waveguide caused by a number of resonant two-level atoms located in a region small compared to the photon wavelength. Applying powerful methods of the theory of integrable quantum systems, we analyze photon correlations caused by scattering. In particular, for the important case of two-photon scattering, we describe explicitly the dependence of the scattering parameters on the number of two-level atoms. Also, we outline the method of describing scattering of an arbitrary number of photons and present explicit expressions for the scattering of three photons in the effective chiral one-dimensional model. The photon wave function is represented as a sum of terms of a different degree of ``entanglement.'' We discuss qualitative distinctions in photon correlations for the single two-level atom case and the case of several atoms.

DOI
10.1103/physreva.78.052713

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We study multiphoton scattering inside a one-dimensional waveguide caused by a number of resonant two-level atoms located in a region small compared to the photon wavelength. Applying powerful methods of the theory of integrable quantum systems, we analyze photon correlations caused by scattering. In particular, for the important case of two-photon scattering, we describe explicitly the dependence of the scattering parameters on the number of two-level atoms. Also, we outline the method of describing scattering of an arbitrary number of photons and present explicit expressions for the scattering of three photons in the effective chiral one-dimensional model. The photon wave function is represented as a sum of terms of a different degree of ``entanglement.'' We discuss qualitative distinctions in photon correlations for the single two-level atom case and the case of several atoms.
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We consider the coherent propagation of nnn photons in a one-dimensional coupled-resonator waveguide for n=2,3,4….n=2,3,4\dots{}.n=2,3,4…. The scattering by a three-level atom, which resides in one of the resonators of the waveguide and gives rise to only two-photon transitions, results in a perfect quantum switch that allows either total reflection or total transmission. This is to be contrasted to the case of a single photon inside a one-dimensional resonant waveguide scattered by a two-level system with single-photon transitions where only total reflection can be accomplished; viz. the system behaves only as a perfect mirror but not as an ideal, transparent medium.
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We analyze the coherent transport of a single photon, which propagates in a one-dimensional coupled-resonator waveguide and is scattered by a controllable two-level system located inside one of the resonators of this waveguide. Our approach, which uses discrete coordinates, unifies low and high energy effective theories for single-photon scattering. We show that the controllable two-level system can behave as a quantum switch for the coherent transport of a single photon. This study may inspire new electro-optical single-photon quantum devices. We also suggest an experimental setup based on superconducting transmission line resonators and qubits.
We give an overview of exactly solvable many-body models of quantum optics. Among them is a system of two-level atoms which interact with photons propagating in a one-dimensional (1D) chiral waveguide; exact eigenstates of this system can be explicitly constructed. This approach is used also for a system of closely located atoms in the usual (non-chiral) waveguide or in 3D space. Moreover, it is shown that for an arbitrary atomic system with a cascade spontaneous radiative decay, the fluorescence spectrum can be described by an exact analytic expression which accounts for interference of emitted photons. Open questions related with broken integrability are discussed.