Nonlinear properties and stabilities of polaritonic crystals beyond the low-excitation-density limit

TL;DR

This paper investigates the nonlinear properties and stability of polaritonic crystals formed by trapped atoms in optical cavities, deriving a complex nonlinear Schrödinger equation and analyzing conditions for stable states beyond low-excitation densities.

Contribution

It introduces a cubic-quintic nonlinear Schrödinger equation model for polaritonic crystals and studies their stability and collapse behavior beyond the low-excitation-density limit.

Findings

Stable ground state wave function exists with oscillating width.

Collapse occurs with negative scattering length and small quintic nonlinearity.

Collapse can be prevented even with polariton decay.

Abstract

Coherent properties of a two dimensional spatially periodic structure - polaritonic crystal (PolC) formed by trapped two-level atoms in an optical cavity array interacting with a light field, are analyzed. By considering the wave function overlapping both for photonic and atomic states, a cubic-quintic complex nonlinear Schrodinger equation (CNLSE) is derived for the dynamics of coupled atom-light states - wave function of low branch (LB) polaritons, associated with PolC in the continuous limit. The variational approach predicts that a stable ground state wave function of PolC exists but is accompanied by an oscillating width. For a negative scattering length, the wave function collapses in the presence of a small quintic nonlinearity appear due to a three body polariton interaction. Studying non-equilibrium (dissipative) dynamics of polaritons with adiabatic approximation we have shown that the collapse of PolC wave function can be prevented even in the presence of small decaying of a number of polariton particles.