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AIP conference proceedings

Photon transport in one-dimensional systems coupled to three-level quantum impurities

Christoph Martens, Paolo Longo, Kurt Busch

Published Jan 1, 2012• 4 citations
Publisher

Abstract

We discuss a model for single-photon scattering in a tight-binding waveguide with an embedded three-level quantum impurity. To this end, we calculate stationary scattering solutions of plane wave states and compare the results with non-stationary numerical simulations of single-photon pulses. Using the example of a driven Λ-three-level system we show how numerical investigations can lead to a more realistic picture at extremal scattering conditions.

DOI
10.1063/1.4750125

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We discuss a model for single-photon scattering in a tight-binding waveguide with an embedded three-level quantum impurity. To this end, we calculate stationary scattering solutions of plane wave states and compare the results with non-stationary numerical simulations of single-photon pulses. Using the example of a driven Λ-three-level system we show how numerical investigations can lead to a more realistic picture at extremal scattering conditions.
We discuss the transport properties of a single photon in a onedimensional waveguide with an embedded three-level atom and utilize both stationary plane-wave solutions and time-dependent transport calculations to investigate the interaction of a photon with driven and undriven V-and -systems.Specifically, for the case of an undriven V-system, we analyze the phenomenon of long-time occupation of the upper atomic levels in conjunction with almost dark states.For the undriven -system, we find non-stationary dark states and we explain how the photon's transmittance can be controlled by an initial phase difference between the energetically lower-lying atomic states.With regard to the driven three-level systems, we discuss electromagnetically induced transparency in terms of the pulse propagation of a single photon through a -type atom.In addition, we demonstrate how a driven V-type atom can be utilized to control the momentum distribution of the scattered photon.
In a preceding paper we introduced a formalism to study the scattering of low-intensity fields from a system of multilevel emitters embedded in a three-dimensional (3D3\mathrm{D}3D) dielectric medium. Here we show how this photon-scattering relation can be used to analyze the scattering of single photons and weak coherent states from any generic multilevel quantum emitter coupled to a one-dimensional (1D1\mathrm{D}1D) waveguide. The reduction of the photon-scattering relation to 1D1\mathrm{D}1D waveguides provides a direct solution of the scattering problem involving low-intensity fields in the waveguide QED regime. To show how our formalism works, we consider examples of multilevel emitters and evaluate the transmitted and reflected field amplitude. Furthermore, we extend our study to include the dynamical response of the emitters for scattering of a weak coherent photon pulse. As our photon-scattering relation is based on the Heisenberg picture, it is quite useful for problems involving photodetection in the waveguide architecture. We show this by considering a specific problem of state generation by photodetection in a multilevel emitter, where our formalism exhibits its full potential. Since the considered emitters are generic, the 1D1\mathrm{D}1D results apply to a plethora of physical systems such as atoms, ions, quantum dots, superconducting qubits, and nitrogen-vacancy centers coupled to a 1D1\mathrm{D}1D waveguide or transmission line.
We investigate theoretically the single-photon scattering by a Λ-type three-level system interacting with a whispering-gallery-type resonator which is coupled to a one-dimensional waveguide by full quantum-mechanical approach. The single-photon transmission amplitude and reflection amplitude are obtained exactly via real-space approach. The single-photon transport properties controlling by classic optical field are discussed. The critical coupling condition in the coupled waveguide-whispering-gallery resonator-atom with three-level system is also analyzed.
We study the coherent scattering process of photons in two waveguides chiral coupling to a Λ-type three-level system (3LS). The 3LS acts as a few-photon router that can direct photons with unity. By adjusting the classical field applied to the 3LS, the tunneling paths between two waveguides can be turned off and on, but two photons can not be routed simultaneously from one port of the incident waveguide to an arbitrarily selected port of the other waveguide. Moreover, driven field controls the number of the bi-photon bound states and the interference pattern of the bi-photon bound states.