Photonic spectrum of bichromatic optical lattices

We study the photonic spectrum of a one-dimensional optical lattice possessing a double primitive cell, when the atoms are well localized at the lattice minima. While a one-dimensional lattice with a simple Wigner-Seitz cell always possesses a photonic band gap at the atomic resonance, in this configuration the photonic transmission spectrum may exhibit no, double, or multiple photonic band gaps depending on the ratio between the interparticle distance ϱ inside the cell and the cell size a. The transmission spectra of a weak incident probe are evaluated when the atoms are trapped in free space and inside an optical resonator for realistic experimental parameters.