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Physical Review A

Single-photon scattering on Λ -type three-level atoms in a one-dimensional waveguide

T. S. Tsoi, C. K. Law

Published Sep 15, 2009• 80 citations
Publisher

Abstract

We investigate the quantum scattering involving a single photon and a chain of $N$ polarized $\ensuremath{\Lambda}$-type three-level atoms inside a one-dimensional waveguide. By using a transfer matrix method, we obtain analytic expressions of eigenvectors of the Hamiltonian, which determine the polarization dependent transmission and reflection spectra for a single photon. We show that the scattering is most significant when the interatomic distance equals an integer multiple plus a quarter of the resonance wavelength. In such a configuration, an incident photon with an unknown polarization can be converted into a specified polarization with a transmission probability higher than that in polarizers obeying Malus's law.

DOI
10.1103/physreva.80.033823

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We investigate the quantum scattering involving a single photon and a chain of NNN polarized \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type three-level atoms inside a one-dimensional waveguide. By using a transfer matrix method, we obtain analytic expressions of eigenvectors of the Hamiltonian, which determine the polarization dependent transmission and reflection spectra for a single photon. We show that the scattering is most significant when the interatomic distance equals an integer multiple plus a quarter of the resonance wavelength. In such a configuration, an incident photon with an unknown polarization can be converted into a specified polarization with a transmission probability higher than that in polarizers obeying Malus's law.
The single photon scattering in one-dimensional waveguide coupled to two separated atoms is investigated. The first atom is considered as a Λ system and the second one is taken as V -type configuration. The analytical expressions of the single photon scattering spectra are obtained. The calculated results show that the polarization conversion of single photon can be realized by controlling the distance between the two atoms due to the interference effects. The conversion efficiency can reach unit in the ideal case. Furthermore, the polarization conversion of the single photon also depends on the initial state of the Λ system. The influences of dissipations on the single photon polarization conversion are also shown.
We investigate the interaction between a single photon and a chain of NNN equally spaced two-level atoms inside a one-dimensional waveguide. By solving the eigenvectors of the Hamiltonian in the subspace with a single excitation, we address quantum interference effects in two physical processes. First, we analyze the scattering of a single photon when atoms are all initially at their ground states. We discover a set of transmission peaks determined by NNN. These transmission peaks are narrow and sensitive to the relative position between atoms. Second, we examine the spontaneous emission of a photon from an excited atom in the chain in vacuum. The characteristic atomic decay rates are found to be enhanced and reduced by increasing the number of atoms. In particular, the slowest decay rate scales approximately as ${N}^{\ensuremath{-}3}$.
Traditional polarizer provides a way to convert an unknown polarization into a specified polarization. According to Malus, the intensity of the transmission is directly proportional to the square of the cosine of angle between the transmission axes of the polarizer and the incident polarization. There, the intensity refers to the collective behavior of many photons. Here we propose a novel approach to realizing polarization-filtering at single-photon level. We discuss how a single planepolarized photon transports through a polarized analyzer generated by a single atom (the so-called "single-atom polarizer"), and provide a single quantum version of Malus's law. We investigate the quantum scattering of a single photon by a controllable four-level atom inside a one-dimensional waveguide. By using real-space theoretical approach, we obtain analytic expressions of the transmission spectrum of the photon. Then, our numerical experiments show that the transmitted probability of the incident photon can be controlled by selecting the polarized-dependent transition configuration of the driven atom. The application of such a single-atom polarizer to linear optical quantum information processing is also discussed.
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 investigate theoretically quantum scattering of two distinguishable photon wave packets from a $\ensuremath{\Xi}$-type three-level atom in a one-dimensional waveguide. The quantum state of scattered photons is solved analytically, and the solution indicates how the two photons become strongly correlated after the scattering. We determine the two-photon reflection and transmission properties, and analyze the quantum entanglement between the scattered photons. In particular, we show that the degree of entanglement can be enhanced by decreasing the spectral width of the incident photon wave packets.
We consider the coherent propagation of nnn photons in a one-dimensional coupled-resonator waveguide for n=2,3,4….n=2,3,4\dots{}.n=2,3,4…. The scattering by a three-level atom, which resides in one of the resonators of the waveguide and gives rise to only two-photon transitions, results in a perfect quantum switch that allows either total reflection or total transmission. This is to be contrasted to the case of a single photon inside a one-dimensional resonant waveguide scattered by a two-level system with single-photon transitions where only total reflection can be accomplished; viz. the system behaves only as a perfect mirror but not as an ideal, transparent medium.