Condensate in an optical lattice : from solid simulation to quantum information (I)

The fifth lesson dealt with the description of condensates in an optical lattice. We began by describing the properties of condensates trapped in a lattice with atoms in a single internal state. We recalled the definition of Bloch states to a particle in a grating and briefly described the band structure and the notion of Brillouin zone borrowed from solid state physics. We have described the images of the condensate obtained after its release from the trap and its expansion. The analogy between the structure of these images and the Bragg diffraction phenomenon in optics was recalled. The competition between inter-well tunneling and collisions within each well plays an essential role in the dynamics of the system. The Mott transition between a superfluid and an insulating phase reflects the effect of this competition. We have described recent experiments that have highlighted this transition, by studying the visibility of Bragg diffraction peaks in condensate images. We also analyzed an experiment that observed the collapse and periodic resurgence of the phase of a condensate suddenly carried into its insulating phase. In the second part of the lesson, we studied the manipulation of a two-state condensate of atoms trapped in a lattice. We showed how the insulating phase could be used to realize a two-level register of cold atoms. We described how the two optical sublattices trapping the two different spin states of the atoms could be moved independently. Finally, we showed how the device could be used to separate and recombine atomic wave functions and perform single-particle interference experiments "in parallel".