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arXiv:1009.2828 · Physical Review A

Two-photon transport in a waveguide coupled to a cavity in a two-level system

Tao Shi, Shanhui Fan, C. P. Sun

Published Dec 1, 2011• 164 citations
arXivHTMLPDF

Abstract

We study two-photon effects for a cavity quantum electrodynamics system where a waveguide is coupled to a cavity embedded in a two-level system. The wave function of two-photon scattering is exactly solved by using the Lehmann-Symanzik-Zimmermann reduction. Our results about quantum statistical properties of the outgoing photons explicitly exhibit the photon blockade effects in the strong-coupling regime. These results agree with the observations of recent experiments.

DOI
10.1103/physreva.84.063803

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We study two-photon effects for a cavity quantum electrodynamics system where a waveguide is coupled to a cavity embedded in a two-level system. The wave function of two-photon scattering is exactly solved by using the Lehmann-Symanzik-Zimmermann reduction. Our results about quantum statistical properties of the outgoing photons explicitly exhibit the photon blockade effects in the strong-coupling regime. These results agree with the observations of recent experiments.
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.
We investigate theoretically the model of a cavity-quantum-electrodynamics (QED) system that consists of two two-level atoms coupled to a single-mode cavity in the weak coupling regime, where the system is driven by quantum light. The dynamics behavior of the entire system is tackled in the framework of a cascaded quantum system. We find that the two-photon blockade with two-photon bunching and three-photon antibunching can be obtained even when the strong system dissipation is included. This result shows that our work has potential for realizing entangled photon pairs in a weakly coupled cavity. Moreover, we also analyze the photon statistics of the system in the case of out-of-resonance coupling between cavity and two nonidentical atoms. Here, an unconventional photon blockade effect with suppression of two-photon correlation and enhancement of three-photon correlation can be realized, which shows many quantum statistical characteristics of a cavity QED system in weak coupling.
Waveguide cavity quantum electrodynamics (QED) with atomic mirrors is a growing research area of quantum optics and can be applied to quantum information processing. We here study the photon statistics of output fields from a waveguide cavity QED system, in which the waveguide is coupled to quantized mirror atoms and one driven medium atom. Our results show that the photon blockade can occur even for a bad atom cavity with large dissipation and small coupling between the medium atom and the cavity, in contrast to the small dissipation and the strong coupling of the medium atom to the cavity field for the conventional photon blockade or the quantum interference for the unconventional photon blockade in the cavity QED system. Utilizing both the master equation and scattering theories, we derive the condition under which the photon blockade occurs in weakly driven systems. We find that such photon anomalous blockade is due to the quantum Zeno effect and is robust against variations of the medium atom's position within the cavity. Our study paves a way to exploit the photon blockade and single-photon devices via the waveguide cavity QED.
The single-photon transport in a single-mode waveguide, coupled to a cavity embedded with a two-level atom, is analyzed. The single-photon transmission and reflection amplitudes, as well as the cavity and the atom excitation amplitudes, are solved exactly via a real-space approach. It is shown that the dissipations of the cavity and of the atom, respectively, affect distinctively on the transport properties of the photons and on the relative phase between the excitation amplitudes of the cavity mode and the atom.
Abstract We investigate the single-photon transport properties in a hybrid waveguide quantum electrodynamics system, in which a one-dimensional waveguide is simultaneously coupled to a cavity and a driven Λ-type three-level atom. The cavity and the atom are also coupled to each other. We show that when the waveguide is coupled to the cavity and the atom at the same point, double electromagnetically induced transparency (EIT) can be observed from the system. The physical mechanism of the double EIT effect has been given by setting up the eigenstate structure for the whole system. When the waveguide is coupled to the cavity and the atom at different points, we demonstrate that the single-photon transmission spectra can be effectively controlled by adjusting the relative separation between the cavity and the atom. Moreover, this non-zero relative separation can lead to the occurrence of the controllable nonreciprocal scattering effect. These results have potential applications in realization of photonic coherent control.
We give exact solutions for correlated two-photon transport in one-dimensional waveguide coupled to a two-level system, using a Bethe-Ansatz-like approach. The S-matrix is explicitly constructed to account for the transport properties of the photons. We show that the scattering eigenstates of this system include a two-photon bound state that passes through the two-level system as a composite single particle. Also, the two-level system can induce effective attractive or repulsive interactions in space for photons. This general procedure can be applied to the Anderson model as well.