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arXiv:0706.3799 · Physical Review A

Mott insulators and correlated superfluids in ultracold Bose-Fermi mixtures

F. Hébert, Florence Haudin, Lode Pollet, G. G. Batrouni

Published Oct 17, 2007• 25 citations
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Abstract

We study the effects of interaction between bosons and fermions in Bose-Fermi mixtures loaded in an optical lattice. We concentrate on the destruction of a bosonic Mott phase driven by repulsive interaction between bosons and fermions. Once the Mott phase is destroyed, the system enters a superfluid phase where the movements of bosons and fermions are correlated. We show that this phase has simultaneous correlations reminiscent of a conventional superfluid and of a pseudospin density wave order.

DOI
10.1103/physreva.76.043619

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We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.
We describe interacting mixtures of ultracold bosonic and fermionic atoms in harmonically confined optical lattices. For a suitable choice of parameters we study the emergence of superfluid and Fermi-liquid (noninsulating) regions out of Bose-Mott and Fermi-band insulators due to finite boson and fermion hoppings. We obtain the shell structure for the system and show that angular momentum can be transferred to the noninsulating regions from Laguerre-Gaussian beams, which combined with Bragg spectroscopy can reveal all superfluid and Fermi-liquid shells.
We obtain the phase diagram of a Bose-Fermi mixture of hardcore spinless bosons and spin-polarized fermions with nearest-neighbor intraspecies interaction and on-site interspecies repulsion in an optical lattice at half filling using a slave-boson mean-field theory. We show that such a system can have four possible phases which are (a) supersolid bosons coexisting with fermions in the Mott state, (b) Mott state of bosons coexisting with fermions in a metallic or charge-density wave state, (c) a metallic fermionic state coexisting with superfluid phase of bosons, and (d) Mott insulating state of fermions and bosons. We chart out the phase diagram of the system and provide analytical expressions for the phase boundaries within mean-field theory. We demonstrate that the transitions between these phases are generically first order with the exception of that between the supersolid and the Mott states which, within mean-field theory, is a continuous quantum phase transition. We also obtain the low-energy collective excitations of the system in these phases. Finally, we study the particle-hole excitations in the Mott insulating phase and use it to determine the dynamical critical exponent zzz for the supersolid-Mott insulator transition. We discuss experiments which can test our theory.
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We investigate the properties of trapped Bose-Fermi mixtures for experimentally relevant parameters in one dimension. The effect of the attractive Bose-Fermi interaction onto the bosons is to deepen the parabolic trapping potential, and to reduce the bosonic repulsion in higher order. This leads for many situations to an increase in bosonic coherence. The opposite effect was observed in 87Rb-40K^{87}\text{R}\text{b-}^{40}\text{K}87Rb-40K experiments, most likely due to a sharp rise in temperature. We also discuss low-temperature features, such as a bosonic Mott insulator transition driven by the fermion concentration, and the formation of composite particles such as polarons and molecules.