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arXiv:1208.1258 · Physical Review A

Two-photon transport through a waveguide coupling to a whispering-gallery resonator containing an atom and photon-blockade effect

Tao Shi, Shanhui Fan

Published Jun 13, 2013• 55 citations
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Abstract

We investigate the two-photon transport through a waveguide side coupling to a whispering-gallery-atom system. Using the Lehmann-Symanzik-Zimmermann reduction approach, we present the general formula for the two-photon processes including the two-photon scattering matrices, the wave functions, and the second order correlation functions of the outgoing photons. Based on the exact results of the second order correlation functions, we analyze the quantum statistics behaviors of the outgoing photons for two different cases: (a) the ideal case without the intermodal coupling in the whispering-gallery resonator; and (b) the case in the presence of the intermodal coupling which leads to more complex nonlinear behavior. In the ideal case, we show that the system consists of two independent scattering pathways, a free pathway by a cavity mode without atomic excitation, and a ``Jaynes-Cummings'' pathway described by the Jaynes-Cummings Hamiltonian of a single-mode cavity coupling to an atom. The presence of the free pathway leads to two-photon correlation properties that are distinctively different from the standard Jaynes-Cummings model, in both the strong and weak-coupling regime. In the presence of intermodal mixing, the system no longer exhibits a free resonant pathway. Instead, both the single-photon and the two-photon transport properties depend on the position of the atom. Thus, in the presence of intermodal mixing, one can in fact tune the photon correlation properties by changing the position of the atom. Our formalism can be used to treat resonator and cavity dissipation as well.

DOI
10.1103/physreva.87.063818

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We investigate the two-photon transport through a waveguide side coupling to a whispering-gallery-atom system. Using the Lehmann-Symanzik-Zimmermann reduction approach, we present the general formula for the two-photon processes including the two-photon scattering matrices, the wave functions, and the second order correlation functions of the outgoing photons. Based on the exact results of the second order correlation functions, we analyze the quantum statistics behaviors of the outgoing photons for two different cases: (a) the ideal case without the intermodal coupling in the whispering-gallery resonator; and (b) the case in the presence of the intermodal coupling which leads to more complex nonlinear behavior. In the ideal case, we show that the system consists of two independent scattering pathways, a free pathway by a cavity mode without atomic excitation, and a ``Jaynes-Cummings'' pathway described by the Jaynes-Cummings Hamiltonian of a single-mode cavity coupling to an atom. The presence of the free pathway leads to two-photon correlation properties that are distinctively different from the standard Jaynes-Cummings model, in both the strong and weak-coupling regime. In the presence of intermodal mixing, the system no longer exhibits a free resonant pathway. Instead, both the single-photon and the two-photon transport properties depend on the position of the atom. Thus, in the presence of intermodal mixing, one can in fact tune the photon correlation properties by changing the position of the atom. Our formalism can be used to treat resonator and cavity dissipation as well.
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Single-photon transport properties in a one-dimensional coupled resonator waveguide, coupled to a whispering-gallery resonator interacting with two separated two-level atoms, are theoretically investigated. Based on the real-space approach, the transmission and reflection amplitudes of the single photon are deduced. Numerical results demonstrate that the transmission and reflection depend on the resonator–atom coupling, the intermode backscattering, and especially the phase difference between these two separated atoms. Effects of dissipation on single-photon transport properties are also discussed.
We study single-photon transport properties in an array of coupled microcavities, coupled to a whispering-gallery-type resonator interacting with a two-level atom. The transmission and reflection coefficients for the single photon propagating in such a coupled system are deduced. We show that the coherent transport properties of the single photon can be well controlled by the intermode backscattering, the resonator–atom coupling and the detuning between the whispering-gallery resonator and the atom. In addition, the influence of the dissipation of the whispering-gallery resonator and the two-level atoms for the realistic physical system on the transport properties are also analysed.
We analyze the single-photon transport in a single-mode waveguide coupled to a whispering-gallery-type resonator interacting with a two-level atom. The single-photon transport properties such as the transmission and reflection amplitudes, as well as the resonator and the atom responses, are solved exactly via a real-space approach. The treatment includes the inter-mode backscattering between the two degenerate whispering gallery modes of the resonator, and the dissipations of the resonator and the atom. We also show that a generalized critical coupling condition, that the single-photon transmission at the output of the waveguide goes to zero on resonance for a matched system, holds for the full coupled waveguide-ring resonator-atom system.
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