# Laboratoire de Physique ThéoriqueToulouse - UMR 5152

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Mardi 31 mars 2015-14:00

## Diptyque LPT

Medha SONI et François DAMON (doctorants LPT)

par - 31 mars 2015

### François DAMON Matter Waves in Optical Lattices

Spatial gaps correspond to the projection in position space of the gaps of a periodic structure when its envelope is inhomogeneous. Such a situation is common in cold atoms manipulation with finite size optical lattice. Spatial gaps provide a new kind of tunnel barriers whose specific properties are investigated. We detail different methods to characterize quantitatively the evanescent matter waves that take place in those tunnel barriers. We discuss their use to realize 1D matter wave Fabry-Perot cavities and the generalization in 2D to design multiply connected 2D cavities or in 3D to generate a quantum dot structure for atoms. Modulating in time the amplitude of a finite size optical lattice offers a wide variety of possible atom manipulations including the control of the scattering of an incoming wave packet, the feeding of cavities delimited by spatial gaps, their coupling by multiphonon processes, the realization of a tunable source of atoms or the propagation in curved wave guides. This large range of possibilities offered by space and time engineering of optical lattices demonstrates the concept of optical metamaterials for atoms.

### Medha SONI Itinerant Fibonacci anyons in two-dimesnions

Fibonacci anyons are non-Abelian anyons described by $SU(2)_3$ theories, which are quantum deformations of the SU(2) algebra. We study ladders composed of coupled chains of interacting itinerant Fibonacci anyons. In the strong antiferromagnetic rung limit, the low-energy effective model is that of a t—J model of Fibonacci anyons. The spectra of the t—J anyonic chains are known to exhibit a fractionalisation into charge and anyon degrees of freedom. We show that indeed the doped ladders show exactly the same behaviour as that of t—J chains. Thus, this suggests that, in contrast to SU(2) spins, itinerant interacting anyons might exhibit the phenomenon of spin-charge separation in the limit of two-dimensions. In the strong ferromagnetic rung limit, we obtain a new model that hosts two different kinds of Fibonacci particles - which we denote as the heavy and light $\tau$’s. These two particle types carry the same (non-Abelian) topological charge but different (Abelian) electric charges. We find the appearance of gapless modes for certain particle densities whereas a topological gapped phase is suggested for another density regime.

Post-scriptum :

contact : G. Lemarié