Photonic band structure of the three-dimensional {sup 88}Sr atomic lattice
Based on the narrow linewidth {sup 1} S{sub 0}-{sup 3} P{sub 1} transition of the bosonic {sup 88}Sr atom, we investigate the dispersion relation for light propagating in a three-dimensional (3D) atomic dipolar lattice. Two factors determine the presence of the photonic band gap (PBG): lattice geometry and the atomic polarization. For a two-level atomic system, the former factor plays a major role. An omnidirectional PBG is predicted in the non-Bravais diamond lattice while no PBG exists in the Bravais lattices. However, since a PBG happens around the resonant {sup 1} S{sub 0}-{sup 3} P{sub 1} line, the probe beam suffers a significant atomic absorption, which is the major drawback in Bragg scattering. We propose applying an external field to couple the atomic {sup 3} P{sub 1}-{sup 3} D{sub 1} transition so as to modify the atomic polarization of the {sup 1} S{sub 0}-{sup 3} P{sub 1} transition. In the three level {sup 1} S{sub 0}-{sup 3} P{sub 1}-{sup 3} D{sub 1} atomic system, the atomic polarization strongly affects the band structure besides the lattice geometry. Dual PBGs can exist in simple cubic and face-centered cubic lattices, but the original PBG, in the diamond lattice composed of the two-level atoms, vanishes. Meanwhile, since two PBGs can be pushed far away from the atomic resonant {sup 1} S{sub 0}-{sup 3} P{sub 1} line, the atomic absorption is significantly suppressed, which enhances the reflection efficiency in Bragg scattering.