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Physical Review A

Single-photon frequency-comb generation in a one-dimensional waveguide coupled to two atomic arrays

Zeyang Liao, Hyunchul Nha, Muhammad Suhail Zubairy

Published Mar 28, 2016• 40 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.93.033851

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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 study the emission of a single-photon by a two-level emitter inside an atomic cavity consisting of two atomic mirrors coupled to a one-dimensional waveguide. With proper atomic separations, we realize a frequency comb as well as spectrum narrowing in the waveguide with the symmetric setting, and also unidirectional spectrum narrowing with asymmetric parameters. Within a suitable range, we can control the central frequency of the narrowed spectra by modulating atomic separations. Due to the collective interaction among the emitters, entanglement sudden birth and revival are observed between the mirrors.
We study the dynamics of a single-photon pulse traveling through a linear atomic chain coupled to a one-dimensional (1D) single mode photonic waveguide. We derive a time-dependent dynamical theory for this collective many-body system which allows us to study the real time evolution of the photon transport and the atomic excitations. Our analytical result is consistent with previous numerical calculations when there is only one atom. For an atomic chain, the collective interaction between the atoms mediated by the waveguide mode can significantly change the dynamics of the system. The reflectivity of a photon can be tuned by changing the ratio of coupling strength and the photon linewidth or by changing the number of atoms in the chain. The reflectivity of a single-photon pulse with finite bandwidth can even approach 100100%100. The spectrum of the reflected and transmitted photon can also be significantly different from the single-atom case. Many interesting physical phenomena can occur in this system such as the photonic band-gap effects, quantum entanglement generation, Fano-like interference, and superradiant effects. For engineering, this system may serve as a single-photon frequency filter, single-photon modulation, and may find important applications in quantum information.
The simulation codes for the figures (5,6,8,9,10,11,12,13) used in our article 'Single-photon frequency comb generation in a giant-atom cavity coupled to a one-dimensional waveguide' are available here. Fig. 5: Frequency spectra of a single photon Gaussian pulse initially outside the giant-atom cavity. Fig. 6: Cavity finesse as a function of the number of giant atoms and the number of coupling points per giant atom. Fig. 8: Frequency spectra of a single photon Gaussian pulse initially inside the giant-atom cavity. Fig. 9: Spectral enhancement as a function of the number of giant atoms and the number of coupling points per giant atom.Fig 10: Number of peaks, Peak location, Peak spacing as a function of the number of giant atoms and the number of coupling points per giant atom. Fig 11: Frequency spectra of a single photon Gaussian pulse initially inside the giant-atom cavity, with reduced coupling strength.Fig 12: Number of peaks, Peak location, Peak spacing as a function of the coupling strength. Fig 13: Cavity linewidth, Spectral enhancement as a function of the coupling strength.
We study the decay of a single-photon pulse inside a cavity consisting of two atomic mirrors coupled to a one-dimensional waveguide. The finesse of the cavity can be increased with proper choice of coupling strength, cavity length, spontaneous decay rate, and separation between atoms. The loss rate of a single-photon pulse inside the cavity can be decreased with narrower spectrum width and smaller detuning between the photon pulse and the atomic resonance. The decay of a single-photon pulse in the atomic cavity can be significantly slowed down with proper parameters and the increase of the number of atoms within the atomic mirrors.
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.