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arXiv:1009.3335 · Physical Review A

Correlated two-photon transport in a one-dimensional waveguide side-coupled to a nonlinear cavity

Jie‐Qiao Liao, C. K. Law

Published Nov 29, 2010• 173 citations
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Abstract

We investigate the transport properties of two photons inside a one-dimensional waveguide side-coupled to a single-mode nonlinear cavity. The cavity is filled with a nonlinear Kerr medium. Based on the Laplace transform method, we present an analytic solution for the quantum states of the two transmitted and reflected photons, which are initially prepared in a Lorentzian wave packet. The solution reveals how quantum correlation between the two photons emerges after the scattering by the nonlinear cavity. In particular, we show that the output wave function of the two photons in position space can be localized in relative coordinates, which is a feature that might be interpreted as a two-photon bound state in this waveguide-cavity system.

DOI
10.1103/physreva.82.053836

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We investigate the transport properties of two photons inside a one-dimensional waveguide side-coupled to a single-mode nonlinear cavity. The cavity is filled with a nonlinear Kerr medium. Based on the Laplace transform method, we present an analytic solution for the quantum states of the two transmitted and reflected photons, which are initially prepared in a Lorentzian wave packet. The solution reveals how quantum correlation between the two photons emerges after the scattering by the nonlinear cavity. In particular, we show that the output wave function of the two photons in position space can be localized in relative coordinates, which is a feature that might be interpreted as a two-photon bound state in this waveguide-cavity system.
We study the photon-photon correlation properties of two-photon transport in a one-dimensional waveguide coupled to a nonlinear cavity via a real-space approach. It is shown that the intrinsic dissipation of the nonlinear cavity has an important effect upon the correlation of the transported photons. More importantly, strongly correlated photons can be obtained in the transmitted photons even when the nonlinear interaction strength is weak in the cavity. The strong photon-photon correlation is induced by the Fano resonance involving destructive interference between the plane wave and bound state for two-photon transport.
We investigate the two-photon transport properties inside one-dimensional waveguide side coupled to a cavity. The cavity is doped with a four-level atom. By employing dressed state basis, we show that the atom-cavity molecule produces a nonlinear interaction. The bunching and antibunching of the transmitted and reflected photons can be observed due to the nonlinearity. By tuning the Rabi frequency of the classical field, the transmission and reflection of the correlated photons can be controlled.
We investigate few-photon scattering properties in two one-dimensional waveguides chirally coupled to a nonlinear cavity. The quantum states of scattered few photons are solved analytically via a real-space approach, and the solution indicates the few-photon reflection and transmission properties. When inputting two photons of equal energy to resonate with the cavity, the propagation characteristics of the two photons will be interesting, which is different from the previous anti-bunching effects with a quantum emitter. More importantly, when the total energy of the two incident photons equals the energy of a nonlinear cavity accommodating two photons, influence of the bound state will become larger to result in disappearance of antibunching effect. However, the bound state has no effect on probability of routing to another waveguide.
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 study the coherent transport of one or two photons in a one-dimensional waveguide chirally coupled to a nonlinear resonator. Analytic solutions of the one-photon and two-photon scattering is derived. Although the resonator acts as a non-reciprocal phase shifter, light transmission is reciprocal at one-photon level. However, the forward and reverse transmitted probabilities for two photons incident from either the left side or the right side of the nonlinear resonator are nonreciprocal due to the energy redistribution of the two-photon bound state. Hence, the nonlinear resonator acts as an optical diode at two-photon level.