Scattering and bound states of two polaritons in an array of coupled cavities

TL;DR

This paper presents an analytical method to study how two polaritons interact and form bound states in a 1D array of coupled cavities with two-level systems, revealing resonances and transport properties.

Contribution

The authors develop an analytical approach to calculate scattering and bound states of two polaritons in a 1D cavity array with nonlinearity-induced contact interactions.

Findings

Identification of 1D resonances for two polaritons

Analytical solutions for zero center-of-mass momentum states

Insights into polariton transport and many-body physics

Abstract

We develop an analytical approach for calculating the scattering and bound states of two polaritons in a one-dimensional (1D) infinite array of coupled cavities, with each cavity coupled to a two-level system (TLS). In particular, we find that in such a system a contact interaction between two polaritons is induced by the nonlinearity of the Jaynes-Cummigs Hamiltonian. Using our approach we solve the two-polariton problem with zero center-of-mass momentum, and find 1D resonances. Our results are relevant to the transport of two polaritons, and are helpful for the investigation of many-body physics in a dilute gas of polaritons in a 1D cavity array.