Bragg spectroscopy of cold atom gases in optical lattices

The dynamic structure factor S(q, ?) provides an important characterization of the dynamic behavior of quantum many-body systems. In the case of gaseous Bose-Einstein condensates, it provides information both on collective excitations (at low momentum transfer q) and on the momentum distribution (at high momentum transfer q) where the response is single-particle like, thus fully characterizing the excitations of the system. Bragg spectroscopy of cold atomic gases, which consists in coupling two momentum states of the same ground state by a stimulated two-photons transition, gives such a measurement of S(q, ?). The use of optical lattices with cold atomic gases has proven to be a very useful tool in the past years. It allows to change the dimensionality of these systems and study the transition from a superfluid in the presence of a lattice, where the Bloch band picture applies, to a strongly-correlated insulating state, the Mott phase. We are interested in characterizing Bose-Einstein condensates loaded in optical lattices via the measurement of their dynamic structure factor by means of Bragg spectroscopy. We first have studied the Bragg spectra of 3D and 1D Bose-Einstein condensates in the presence of an optical lattice along the direction of the counter-propagating Bragg beams. From the measurements, we extract the resonance frequency, the width and the transition strength of the transitions to different Bloch bands of the optical lattice. We have also measured the spectra of 1D gases for different trap anisotropies, i.e. different Luttinger parameters. In particular, we observe an enlargement of the width of those spectra when the anisotropy increases which could be a signature of the presence of correlations.