Bragg scattering of optical pulses from localized atoms in one-dimensional optical lattices

We outline the theory of a practical Bragg scattering technique for studying the long-range spatial order of atoms localized in one-dimensional optical lattices and we demonstrate the technique using and F = 1 → 1 transitions with lin ⊤ lin laser cooling fields. The latter transition gives a dark optical lattice. We show that the scattering by a spin grating, which may also be present, can be completely or partially filtered out by varying the polarizations of the cooling fields while holding the polarization of the probe and the detector analyser fixed. This allows the fraction of atoms that are localized to be measured. The probe field is treated as a pulse and so the technique also allows time-resolved details of the spatial structure to be studied.