PHOTONIC BAND-GAPS IN OPTICAL LATTICES

We study photonic band gaps in a one-dimensional optical lattice of la ser-cooled trapped atoms. We solve for the self-consistent equilibrium positions of the atoms, accounting for the backaction of the atoms on the trapping beams. This solution depends strongly on the sign of the trapping laser detuning. For red-detuned trapping lasers, the resulti ng lattice exhibits a one-dimensional photonic band gap for frequencie s between the trapping laser frequency and the atomic resonance. For b lue detuning the stop band extends symmetrically about resonance, typi cally for hundreds of atomic linewidths, except for the small region b etween atomic resonance and the lattice frequency, which is excluded. We calculate the reflection spectrum for a lattice of Cs atoms for var ious trapping laser detunings and interpret its behavior as a function of the lattice size and density. For a mean density of 10(11) cm(-3), and 1000 planes, 55% reflection of a weak probe beam should be observ ed. We also consider Bragg scattering in a three-dimensional optical l attice as a means of probing the long-range order in the atomic densit y correlation function.