Strongly correlated multiparticle transport in one dimension through a quantum impurity

Jung-Tsung Shen and Shanhui Fan
Phys. Rev. A 76, 062709 – Published 27 December 2007

Abstract

We consider the transport properties of multiple-particle quantum states in a class of one-dimensional systems with a single quantum impurity. In these systems, the local interaction at the quantum impurity induces strong and nontrivial correlations between the multiparticles. We outline an exact theoretical approach, based upon real-space equations of motion and the Bethe ansatz, that allows one to construct the full scattering matrix (S matrix) for these systems. In particular, we emphasize the need for a completeness check upon the eigenstates of the S matrix, when these states obtained from Bethe ansatz are used for describing the scattering properties. As a detailed example of our approach, we solve the transport properties of two photons incident on a single two-level atom, when the photons are restricted to a one-dimensional system such as a photonic crystal waveguide. Our approach predicts a number of nonlinear effects involving only two photons, including background fluorescence, spatial attraction and repulsion between the photons, as well as the emergence of a two-photon bound state.

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  • Received 26 July 2007
  • Publisher error corrected 5 February 2008

DOI:https://doi.org/10.1103/PhysRevA.76.062709

©2007 American Physical Society

Corrections

5 February 2008

Erratum

Authors & Affiliations

Jung-Tsung Shen and Shanhui Fan*

  • Department of Electrical Engineering and Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

  • *shanhui@stanford.edu

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Issue

Vol. 76, Iss. 6 — December 2007

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