Strongly-correlated multi-particle transport in one-dimension through a quantum impurity: an outline of exact and complete solutions

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 non-trivial correlations between the multi-particles. 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 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 novel 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.