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Optics Letters

Coherent photon transport from spontaneous emission in one-dimensional waveguides

Jung‐Tsung Shen, Shanhui Fan

Published Aug 1, 2005• 529 citations
Publisher

Abstract

A two-level system coupled to a one-dimensional continuum is investigated. By using a real-space model Hamiltonian, we show that spontaneous emission can coherently interfere with the continuum modes and gives interesting transport properties. The technique is applied to various related problems with different configurations, and analytical solutions are given.

DOI
10.1364/ol.30.002001

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A two-level system coupled to a one-dimensional continuum is investigated. By using a real-space model Hamiltonian, we show that spontaneous emission can coherently interfere with the continuum modes and gives interesting transport properties. The technique is applied to various related problems with different configurations, and analytical solutions are given.
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.
We provide a theoretical and computational framework for fully quantum mechanical studies of few-photon transport phenomena in arbitrary waveguiding structures in the presence of coherent interaction with optically active emitters. The reduced dimensionality of such systems leads to pronounced quantum interference effects that may be exploited for a number of applications and we apply our framework to the case of single-photon transport through a two-level atom. In this system, the atom's emission dynamics leads to strong interference effects that can be used for the realization of nanomirrors.
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.
A recent theoretical analysis and experimental results show that interesting transport properties of a single microwave photon emerge when a quantum bit in a cavity is coupled to a one-dimensional waveguide. Here we adopt a real-space model Hamiltonian to give a unified approach which accounts for the experimental results, and make new predictions on the properties of single photon transport, such as the general Fano line shape, symmetric vacuum Rabi splitting for a leaky cavity at resonance, and a one-photon switching capability.
The spontaneous emission of a four-level atom embedded in a one-dimensional photonic crystal is investigated. The atom has two upper levels coupled by the same vacuum modes to a common lower level and is driven by a coherent field to an auxiliary level. Spontaneous emission can be suppressed significantly due to the combinational influences of the interference effect and the band edge effect. The radiation field emitted by the atom is also studied. Spontaneous emission can be modified by controlling the Rabi frequency of the driving.
Spontaneous emission of photons by an atom placed near the dielectric waveguide is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the waveguide boundaries 1. These modes include modes extended over the whole space (travelling) and modes trapped to the waveguide. To describe angular properties of the spontaneous emission, a parameterization of the travelling modes by the outgoing waves has been proposed. Otherwise, using a more common parameterization of these modes by the incoming waves, one has to take into account the interference of different reflected and transmitted waves accompanying photons incoming from both sides of the waveguide 2, what was overlooked in 3. Angular characteristics of the travelling photon emission (a), distributions of the trapped photon emission (b), as well as global decay rates (c), have been calculated using the quantum approach and standard perturbation theory. Enhancement and suppression of radiative decay rates in various configurations have been shown. A certain calculational error, in the treatment of the density of trapped states, in an earlier paper by Khosravi and Loudon 4, affecting emission rates for thin waveguides, has been corrected.