Quantum Theory of a Resonant Photonic Crystal

Abstract

We present a quantum model of two-level atoms localized in a 3D lattice, based on the Hopfield theory of exciton polaritons. In addition to a polaritonic gap at the exciton energy, a photonic bandgap opens up at the Brillouin zone boundary. Upon tuning the lattice period or angle of incidence to match the photonic gap with the exciton energy, one obtains a combined polaritonic and photonic gap as a generalization of Rabi splitting. For typical experimental parameters, the size of the combined gap is on the order of 25 cm^{-1}, up to 10^5 times the detuned gap size. The dispersion curve contains a branch supporting slow-light modes with vanishing exciton probability density.

arXiv comment4 pages, 3 figures

References in corpus (1)

• Polariton Dispersion Law in Periodic Bragg and Near-Bragg Multiple Quantum Well Structures

Cited by in corpus (6)

• Optical properties of atomic Mott insulators: from slow light to dynamical Casimir effects
• Light scattering by ultracold atoms in an optical lattice
• Light-mass Bragg cavity polaritons in planar quantum dot lattices
• Photonic spectrum of bichromatic optical lattices
• Microcavity polaritons in disordered exciton lattices
• Light propagation in atomic Mott Insulators