Bragg spectroscopy of ultracold atoms in optical lattices

The interplay between ultracold atoms and laser light open wide sceneries: it allows creating different kinds of potentials, periodic (optical lattices) or disordered; in addition, it permits to control the system dimensionality. The same interplay also provides convenient probes to study these kinds of systems, e.g. absorption imaging technique, or Bragg and Raman spectroscopy. The work I will present is focused on the Bragg spectroscopy [1] of a Bose Einstein condensate (BEC) loaded in optical lattices: in particular, we investigated an elongated 3D BEC and a set of 1D uncoupled tubes, in the presence of an optical lattice in the same longitudinal direction. We employed two counter-propagating laser beams (Bragg beams) with opportune wavelength, along the longitudinal direction of the system. Thus, we induced a large energy and momentum transfer, and we measured single-particle excitation spectrum and dynamical structure factor [2]. The experimental results demonstrate that the resonance frequency and the transition strength in the presence of the longitudinal optical lattice are well described by a mean-field theory both in 1D and in 3D case [3]. While the resonance width can be connected with the coherence properties of the system. As it is known, in 1D systems correlations can play a role even in a mean-field regime [4]: for this reason, we also investigated the 3D-1D cross-over by varying the optical confinement of each 1D tube, without superimposing a longitudinal lattice. -- References: [1] J. Stenger et al., Physical Review Letters 82, 4569 (1999). [2] F. Zambelli et al., Physical Review A 61, 063608 (2000). [3] C. Menotti et al., Physical Review A 67, 053609 (2003). [4] B. Laburthe Tolra et al., Physical Review Letters 92, 190401 (2004).