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arXiv:1005.2274 · Physical Review A

Multiatomic mirror for perfect reflection of single photons in a wide band of frequency

Yue Chang, Z. R. Gong, C. P. Sun

Published Jan 31, 2011• 55 citations
arXivHTMLPDF

Abstract

A resonant two-level atom doped in a one-dimensional waveguide behaves as a mirror, but this single-atom ``mirror'' can only reflect single photons perfectly at a specific frequency. For a one-dimensional coupled-resonator waveguide, we propose to extend the perfect-reflection region from a specific frequency point to a wide band by placing many atoms individually in the resonators in a finite coordinate region of the waveguide. Such a doped resonator array promises to control the propagation of a practical photon wave packet with a certain momentum distribution instead of a single photon, which is ideally represented by a plane wave with a specific momentum. The studies based on the discrete-coordinate scattering theory indicate that such a hybrid structure with finite atoms indeed provides a near-perfect reflection for a single photon in a wide band. We also calculated the photon group velocity distribution, which shows that the perfect-reflection wide band exactly corresponds to the stopping light region.

DOI
10.1103/physreva.83.013825

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A resonant two-level atom doped in a one-dimensional waveguide behaves as a mirror, but this single-atom ``mirror'' can only reflect single photons perfectly at a specific frequency. For a one-dimensional coupled-resonator waveguide, we propose to extend the perfect-reflection region from a specific frequency point to a wide band by placing many atoms individually in the resonators in a finite coordinate region of the waveguide. Such a doped resonator array promises to control the propagation of a practical photon wave packet with a certain momentum distribution instead of a single photon, which is ideally represented by a plane wave with a specific momentum. The studies based on the discrete-coordinate scattering theory indicate that such a hybrid structure with finite atoms indeed provides a near-perfect reflection for a single photon in a wide band. We also calculated the photon group velocity distribution, which shows that the perfect-reflection wide band exactly corresponds to the stopping light region.
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.
Abstract We study single photon scattering in a one-dimensional coupled resonator waveguide, which is dressed by a small and a giant artificial atom simultaneously. Here, we have set the small atom to be a neighbor to one leg of the giant atom, and the giant atom couples to the waveguide via two distant sites. When the small and giant atoms are both resonant with the bare resonator in the waveguide, we observe the perfect reflection of the resonant incident photon. On the other hand, when the small atom is detuned from the giant atom, the single photon reflection is characterized by a wide window and Fano line shape. We hope our work will pave the way for the potential application of small and giant atom hybrid systems in the study of photonic control in the low-dimensional waveguide structure.
Slowing/stopping the light travelling in free space with electromagnetically induced transparency to im- plement the optical quantum information processings and store information has been paid much attention in recent years. For the waveguide photons, here, we propose an approach to stop them with a controllable atomic cavity generated by a pair of atomic mirrors; one of them reflects the photon completely and an- other one with the adjustable reflected/transmitted probability of the photons. Based on the full quantum mechanical theory in real space, we show that the reflected/transmitted probability of the waveguide photon with a fixed frequency can be controlled by adjusting the energy-splitting of the driven two-level atomic scatters (i.e., atomic mirrors). As a consequence, the photon can be controllably transmitted/reflected along the waveguide by the aside atomic mirrors with the adjustable atomic energy levels. Ideally, the photons could be stopped in the atomic cavity. This provides a novel mechanism to stop/retravel the waveguide photon in a controllable ways. The feasibility of the proposal with the current integrated optical devices is also discussed.
An atomic chain coupled to a one-dimensional (1D) photonic waveguide can become a very good atom mirror. This atom mirror can have a very high reflectivity for a single-photon pulse due to the collective interaction between the atoms. Two atom arrays coupled to a 1D waveguide can form a good cavity. When a single-photon pulse is incident from one side of the cavity, only a discrete subset of photon frequencies can transmit the cavity and the transmitted frequencies are almost equally spaced, which is similar to a frequency comb. The linewidth of the comb frequency can be reduced if we increase the atom number in the atomic arrays. More interestingly, if the photon pulse is initially inside the cavity, the photon spectrum after a long time of interaction is also discretized with the comb frequencies being significantly amplified while other frequencies being largely suppressed. This single-photon frequency comb may be useful for precision measurement.
We theoretically investigate single-photon coherent transport through a finite waveguide quantum electrodynamics (QED) array with spatially modulated emitter-waveguide couplings. By combining exact scattering calculations with spectral factorization and a semiclassical WKB analysis, we identify how the coupling profile controls the reflection bandwidth and its finite-size dependence. A Gaussian transverse displacement produces an exponential-of-Gaussian decay-rate profile that broadens the high-reflectivity window and suppresses the boundary-induced Fabry-Perot oscillations compared with a uniform array. The transmission zeros remain exactly degenerate at the atomic resonance for arbitrary positive coupling profiles at non-Bragg spacings. In contrast, the collective poles reorganize under the spatial modulation, redistributing their radiative widths and preventing individual subradiant resonances from terminating the reflection window. We further derive an algebraic 1/N scaling law for the contraction of the bandwidth toward its bulk value. The bulk bandwidth is determined by the largest local decay rate, whereas the finite-size correction increases as the profile becomes sharper, leading to an optimal profile width. These results establish spatial coupling engineering as a practical tool for designing broadband atomic mirrors in atom-nanofiber and circuit-QED platforms.
We propose a special cavity design that is constructed by terminating a one-dimensional waveguide with a perfect mirror at one end and doping a two-level atom at the other. We show that this atom plays the intrinsic role of a semitransparent mirror for single-photon transports such that quasinormal modes emerge spontaneously in the cavity system. This atomic mirror has its reflection coefficient tunable through its level spacing and its coupling to the cavity field, for which the cavity system can be regarded as a two-end resonator with a continuously tunable leakage. The overall investigation predicts the existence of quasibound states in the waveguide continuum. Solid-state implementations based on a dc-superconducting quantum interference device circuit and a defected line resonator embedded in a photonic crystal are illustrated to show the experimental accessibility of the generic model.