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arXiv:1203.0451 · New Journal of Physics

Scattering of massless particles in one-dimensional chiral channel

Mikhail Pletyukhov, Vladimir Gritsev

Published Sep 27, 2012• 58 citations
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Abstract

We present a general formalism describing the propagation of an arbitrary multi-particle wave packet in a one-dimensional multimode chiral channel coupled to an ensemble of emitters which are distributed at arbitrary positions. The formalism is based on a direct and exact resummation of a diagrammatic series for the multi-particle scattering matrix. It is complementary to the Bethe Ansatz approach and to approaches based on equations of motion, and it reveals a simple and transparent structure of scattering states. In particular, we demonstrate how this formalism works on various examples, including the scattering of one- and two-photon states off two- and three-level emitters, off an array of emitters, as well as the scattering of coherent light. We argue that this formalism can be used constructively for the study of the scattering of an arbitrary initial photonic state off emitters with an arbitrary degree of complexity.

DOI
10.1088/1367-2630/14/9/095028

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We present a general formalism describing the propagation of an arbitrary multi-particle wave packet in a one-dimensional multimode chiral channel coupled to an ensemble of emitters which are distributed at arbitrary positions. The formalism is based on a direct and exact resummation of a diagrammatic series for the multi-particle scattering matrix. It is complementary to the Bethe Ansatz approach and to approaches based on equations of motion, and it reveals a simple and transparent structure of scattering states. In particular, we demonstrate how this formalism works on various examples, including the scattering of one- and two-photon states off two- and three-level emitters, off an array of emitters, as well as the scattering of coherent light. We argue that this formalism can be used constructively for the study of the scattering of an arbitrary initial photonic state off emitters with an arbitrary degree of complexity.
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Recent experimental progress has realized strong, efficient coupling of effective two level systems to waveguides. We study the scattering of multimode photons from such emitters coupled losslessly to the confined geometry of a one dimensional waveguide. We develop novel techniques for describing the scattered state of both single and multi-photon wavepackets and explore how such wavepackets interact with arrays of emitters coupled to a one dimensional waveguide. Finally, we apply these techniques and analyze the capability of two particular systems to act as a quantum conditional logic gate.
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We give exact solutions for correlated two-photon transport in one-dimensional waveguide coupled to a two-level system, using a Bethe-Ansatz-like approach. The S-matrix is explicitly constructed to account for the transport properties of the photons. We show that the scattering eigenstates of this system include a two-photon bound state that passes through the two-level system as a composite single particle. Also, the two-level system can induce effective attractive or repulsive interactions in space for photons. This general procedure can be applied to the Anderson model as well.