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

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 for both photonic and atomic states, a cubic-quintic complex nonlinear Schrödinger equation is derived for the dynamics of coupled atom-light states, wave function of low-branch polaritons, associated with PolC in the continuous limit. A 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 appearing due to a three-body polariton interaction. By studying the nonequilibrium (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.