### Séminaire de groupe

One-dimensional Bose-Fermi mixtures with strong repulsions |

Anna Minguzzi |

LPM2C |

mardi 07 juin 2011 , 10h25 |

Salle de séminaire du groupe de Physique Statistique |

Progress in trapping and cooling of ultracold atomic gases allows to produce quasi-onedimensional systems with tunable interaction strength. A peculiarity of such systems is the inhomogeneity of the external confining potential which has to be taken into account in the theory. In the limit of infinitely strong repulsions among bosons (Tonks-Girardeau regime) an exact solution for the many-body wavefunction of the inhomogeneous system is known and allows to extract several physical observables. We have recently generalized such a solution to the case of a trapped mixture of bosons (B) and fermions (F) with very strong repulsive BB an d BF repulsions. Such a model displays a large degeneracy of the ground state. I will report on the solution for the whole set of ground-state wavefunctions of the degenerate manifold and their characterization according to group-symmetry considerations. Calculation of some observables, such as the density profile and the momentum distribution, show that they depend on the symmetry of the solution. Finally, by combining the wavefunctions of the degenerate manifold with suitable symmetry and guided by the strong-coupling form of the Bethe-Ansatz solution for the homogeneous system I will present an analytic expression for the many-body wavefunction of the inhomogeneous system which well describes the ground state at finite, large and equal interactions strengths, as validated by numerical DMRG simulations. |