Photon correlations in a two-site non-linear cavity system under coherent drive and dissipation

TL;DR

This paper investigates photon correlations in a two-site nonlinear cavity system with coherent drive and dissipation, revealing a crossover between delocalized coherent states and photon blockade-induced antibunching.

Contribution

It provides an analytical steady-state solution for the second-order correlation function in a coupled cavity system with Kerr nonlinearity, including dissipation effects.

Findings

Photon correlations range from 0 to 1, indicating antibunching and coherence.

System behavior transitions from delocalized to localized states based on tunneling and nonlinearity.

Photon blockade occurs in the regime of dominant nonlinear interaction.

Abstract

We calculate the normalized second-order correlation function for a system of two tunnel-coupled photonic resonators, each one exhibiting a single-photon nonlinearity of the Kerr type. We employ a full quantum formulation: the master equation for the model, which takes into account both a coherent continuous drive and radiative as well as non-radiative dissipation channels, is solved analytically in steady state through a perturbative approach, and the results are compared to exact numerical simulations. The degree of second-order coherence displays values between 0 and 1, and divides the diagram identified by the two energy scales of the system - the tunneling and the nonlinear Kerr interaction - into two distinct regions separated by a crossover. When the tunneling term dominates over the nonlinear one, the system state is delocalized over both cavities and the emitted light is coherent. In the opposite limit, photon blockade sets in and the system shows an insulator-like state with photons locked on each cavity, identified by antibunching of emitted light.