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Optics Communications

Perturbative and iterative methods for photon transport in one-dimensional waveguides

Kenechukwu C. Obi, Jung‐Tsung Shen

Published Jan 9, 2015• 5 citations
Publisher
DOI
10.1016/j.optcom.2015.01.022

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Abstract The waveguide quantum electrodynamics (QED) system may have important applications in quantum device and quantum information technology. In this article we review the methods being proposed to calculate photon transport in a one-dimensional (1D) waveguide coupled to quantum emitters. We first introduce the Bethe ansatz approach and the input–output formalism to calculate the stationary results of a single photon transport. Then we present a dynamical time-dependent theory to calculate the real-time evolution of the waveguide QED system. In the longtime limit, both the stationary theory and the dynamical calculation give the same results. Finally, we also briefly discuss the calculations of the multiphoton transport problems.
We investigate the transport properties of two photons inside a one-dimensional waveguide side-coupled to a single-mode nonlinear cavity. The cavity is filled with a nonlinear Kerr medium. Based on the Laplace transform method, we present an analytic solution for the quantum states of the two transmitted and reflected photons, which are initially prepared in a Lorentzian wave packet. The solution reveals how quantum correlation between the two photons emerges after the scattering by the nonlinear cavity. In particular, we show that the output wave function of the two photons in position space can be localized in relative coordinates, which is a feature that might be interpreted as a two-photon bound state in this waveguide-cavity system.