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

TL;DR

This paper develops an exact theoretical framework for analyzing two-photon transport and photon blockade effects in a waveguide coupled to a whispering-gallery resonator with an atom, revealing how intermodal coupling and atom position influence photon correlations.

Contribution

The authors present a general formula for two-photon scattering in a waveguide-resonator-atom system, including effects of intermodal coupling and atom position, advancing understanding of photon blockade phenomena.

Findings

Exact two-photon scattering matrices derived.

Photon correlations can be tuned by atom position in intermodal coupling.

Intermodal mixing eliminates free resonant pathways, affecting photon statistics.

Abstract

We investigate the two-photon transport through a waveguide side-coupling to a whispering-gallery-atom system. Using the Lehmann-Symanzik-Zimmermann (LSZ) reduction approach, we present the general formula for the two-photon processes including the two-photon scattering matrices, the wavefunctions and the second order correlation functions of the out-going photons. Based on the exact results of the second order correlation functions, we analyze the quantum statistics behaviors of the out-going photons for two different cases: (a) the ideal case without the inter-modal coupling in the whispering gallery resonator; (b) the case in the presence of the inter-modal 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 free pathway does not contribution to correlated two-photon processes. In the presence of intermodal mixing, the system no longer exhibit 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.