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## Quantum atomic gases

^{^9}times less than air) and reach temperatures of a few hundreds of nanoKelvins. In this regime the DeBroglie wavelength of the atoms is comparable with the inter-particle distance, and quantum mechanical aspects become evident. For bosonic isotopes, Bose Einstein condensation has been observed in 1995. For fermionic isotopes, a pairing analogous to the formation of Cooper pairs in superconductors has been realized in 2003. The large tunability of the geometry, confining potential and interaction strength in these systems allows nowadays for the exploration of correlated quantum phases, out-of-equilibrium phenomena, superfluidity, the effects of disorder and of artificial gauge fields. Quantum gases are hence an important example of a quantum simulator, capable to bring insight into several condensed-matter-physics models under controlled conditions.

At LPMMC we study several aspects of quantum gases with a broad range of techniques, from analytical classical and quantum field-theoretical methods, mathematical methods and exact solutions, to numerical Quantum Monte Carlo simulations. We detail here some examples of our recent results :

## Anderson localization of matter waves

We describe the dynamics of the expansion of an atomic cloud in the presence of a random potential by means of a self-consistent theory for the enegy-dependent diffusion coefficient. Anderson localization occurs when the diffusion coefficient vanishes. Within this model we can predict the details of the expanding density profiles, the build-up of correlations and take into account realistic features of the experimental disorder.

## Kosterlitz-Thouless transition of two-dimensional trapped Bose gases

Using Quantum Monte Carlo calculations we have studied the phase diagram of quasi-two-dimensional bosons in harmonic traps and the cross-over from a Kosterlitz-Thouless transition to Bose condensation for finite and small systems. Our simulations turned out to be important for the qualitative and quantitative understanding of quasi-two-dimensional experiments. Without relying on finite-size scaling, they provide rather unique, parameter free comparisons between theory and experiments for a interacting many-body system in a correlation dominated regime.

## Atoms on a tight ring trap

It is nowadays possible to realize ring-shaped traps for ultracold atoms. In this geometry we study metastable current flows and superfluidity for interacting bosons. We also consider the possibility of generating macroscopic superpositions of current states by a moving barrier potential. Our results provide a contribution to the study of novel nonclassical states with strongly correlated gases.

## Vortices in rotating Bose-Einstein condensates

A striking manifestation of quantum mechanics on a macroscopic scale is the superfluidity of Bose-Einstein condensates. It has been spectacularly confirmed in recent years by the observation of quantized vortices in ultracold rotating bosons clouds. At LPMMC we study this phenomenon via a rigorous mathematical analysis of a nonlinear Schroedinger equation, the Gross-Pitaevskii equation, which well describes Bose-Einstein condensates. More specifically we study within this framework the occurrence, distribution and properties of quantized vortices, characterizing some phase transitions in terms of the number of vortices, their multiplicity (i.e. the quantum of phase circulation they carry) and the patterns they form in the gas, such as the famous Abrikosov lattices akin to those occurring in type II superconductors.

## Fermi gases and Bose-Fermi mixtures with attractive interactions : superfluidity, pairing and quartet formation

With our collaborators, cited in the references given below, we treat several aspects of cold atomic gases, mostly fermions or Fermi-Bose mixtures. We are recently actively working on the latter case pointing out the formal similarity between strongly polarised two component Fermi systems and Bose-Fermi mixtures. The point of investigation is to formulate a theory which fullfills Luttinger theorem. It seems that this basic theorem is violated in several recents works leading to strange results (e.g. Negative susceptibility). We show that a correct application of the Nozieres Schmitt-Rink approach has the appreciable property to fullfill Luttinger theorem and thus also particle number conservation.

## Quasi-one dimensional gases : properties of the strongly correlated Tonks-Girardeau regime of impenetrable bosons

A Tonks-Girardeau gas corresponds to infinitely strong repulsive interactions between 1D bosons. Quite noticeably, for this strongly correlated regime an exact solution was found for the many-body wave function. The solution is based on a mapping onto a Fermi gas, since interactions play the same role of the Pauli exclusion principle. We have studied several properties of this gas, in particular the momentum distribution at large momenta, its exact dynamical evolution, its finite-temperature coherence properties. We have also explored generalizations of the exact solution to multi-component and fermionic systems.

## Low-dimensional lattice models : interplay of interactions and pseudo-disorder effects, effects of long-range interactions and exotic quantum phases

Low-dimensional lattice models are realized experimentally by loading atoms onto an optical lattice. If a second incommensurate lattice is applied, it plays the role of a pseudo-disorder for the atoms, allowing for studying the interplay of disorder and repulsive interaction effects. We have studied the phase diagram of the system both in the case of atoms with on-site interactions and in the case of atoms with dipolar interactions.

## Selected publications

*Physics*

**5**, 123 (2012)