Accueil > Événements > Actualités > Seminars

## Séminaire LPMMCNicola Lo Gullo ((thermodynamique))Ground-state and asymptotic dynamical properties of 1D ultracold gases in the presence of a mobility edge
Lieu : Salle de lecture 2, maison des Magistères, le lundi 26 juin 2017 à 13h30 Personne à contacter : Anna Minguzzi () In the first part of the talk we explore the ground-state properties of cold atomic gases focusing on the cases of noninteracting fermions and hard-core (Tonks-Girardeau) bosons, trapped by the combination of two potentials (bichromatic lattice) with incommensurate periods. In the tight-binding limit, the single-particle states in the lowest occupied band show a localization transition, as the strength of the second potential is increased above a certain threshold. In the continuum limit, when the tight-binding approximation does not hold, a mobility edge is found, instead, whose position in energy depends upon the strength of the second potential. Here, we study how the crossover from the discrete to the continuum behavior occurs, and prove that signatures of the localization transition and mobility edge clearly appear in the generic many-body properties of the systems. Specifically, we evaluate the momentum distribution, which is a routinely measured quantity in experiments with cold atoms, and demonstrate that, even in the presence of strong boson-boson interactions (infinite in the Tonks-Girardeau limit), the single-particle mobility edge can be observed in the ground-state properties. In the second part we study the dynamical many-body response of for a one-dimensional fermionic gas in a mono- and bi-chromatic optical potential following the sudden switching-on of a delta-like barrier at some at the center of the system. Specifically we look at the Loschmidt echo as a figure of merit to characterize the response of the system and its long time behavior. In order to evaluate the echo we employ two complementary approaches: (1) functional determinants (Levitov) which gives the exact numerical solution for time- and therefore frequency-resolved responses and (2) a perturbative approach (Linked Cluster Expansion) which provides an accurate evaluation of the contribution of different physical processes involved in the dynamics. Again we focus on the two limits of tight-binding and continuum showing that the phenomenon of the orthogonality catastrophe can be observed in such systems which, unlike their condensed matter counterpart, are nowadays created and controlled with a very high accuracy. |