Photonic bands and normal mode splitting in optical lattices interacting with cavities

TL;DR

This paper investigates how collective atom-cavity interactions lead to normal mode splitting and photonic band gaps, using models suited for different density regimes, and explores their implications for atomic lattice dynamics.

Contribution

It applies the open Dicke model and transfer matrix model to analyze normal mode splitting and photonic band gaps in ordered atomic clouds within optical cavities, highlighting their regimes of validity.

Findings

Normal mode splitting is observed in low-density regimes.

Photonic band gaps form at high optical densities.

Models' limitations and pathways for generalized theories are discussed.

Abstract

Strong collective interaction of atoms with an optical cavity causes normal mode splitting of the cavity's resonances, whose width is given by the collective coupling strength. At low optical density of the atomic cloud the intensity distribution of light in the cavity is ruled by the cavity's mode function, which is solely determined by its geometry. In this regime the dynamics of the coupled atom-cavity system is conveniently described by the open Dicke model, which we apply to calculating normal mode splitting generated by periodically ordered clouds in linear and ring cavities. We also show how to use normal mode splitting as witness for Wannier-Bloch oscillations in the tight-binding limit. At high optical density the atomic distribution contributes to shaping the mode function. This regime escapes the open Dicke model, but can be treated by a transfer matrix model provided the saturation parameter is low. Applying this latter model to an atomic cloud periodically ordered into a one-dimensional lattice, we observe the formation of photonic bands gaps competing with the normal mode splitting. We discuss the limitations of both models and point out possible pathways to generalized theories.