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arXiv:1005.4784 · Physical Review A

Zero-temperature phase diagram of Bose-Fermi gaseous mixtures in optical lattices

T. P. Polak, T. K. Kopeć

Published Apr 14, 2010• 25 citations
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Abstract

We study the ground-state phase diagram of a mixture of bosonic and fermionic cold atoms confined on two- and three-dimensional optical lattices. The coupling between bosonic fluctuations and fermionic atoms can be attractive or repulsive and has similarities with electron-phonon coupling in crystals. We investigate behavior of the mixtures in the limit, where the Bogoliubov sound velocity that dictates bosonic dynamics is comparable to the Fermi velocity, hence the retardation effects are an important part of the physics. The dynamic Lindhard response function of the fermionic density to changes in the bosonic number of particles above some critical frequency can alter the sign, and consequently the interspecies interaction between particles becomes repulsive in contrast to the static limit (instantaneous and always attractive). Considering the above, we show that the structure of the phase diagrams crucially depends on the difference in masses of the bosons and fermions. We discuss the situations where integrating out the fermionic field provides an additional interaction that can decrease or increase bosonic coherence.

DOI
10.1103/physreva.81.043612

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We study a mixture of fermionic and bosonic cold atoms on a two-dimensional optical lattice, where the fermions are prepared in two isospin states and the bosons have Bose-Einstein condensed. Number density fluctuations of the condensate form delocalized bosonic modes which couple to the fermionic atoms similarly to the electron-phonon coupling in crystals. We study the phase diagram for this system at fixed fermion density of one per site. We find that tuning of the lattice parameters and interaction strengths drives the system to undergo antiferromagnetic ordering, s-wave and d-wave pairing superconductivity, or a charge density-wave phase. We use functional renormalization group analysis where retardation effects are fully taken into account. We calculate response functions and also provide estimates of the energy gap associated with the dominant order, and how it depends on different parameters of the problem.
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With the objective of simulating the physical behavior of electrons in a dynamic background, we investigate a cold atomic Bose-Fermi mixture confined in an optical lattice potential solely affecting the bosons. The bosons, residing in the deep superfluid regime, inherit the periodicity of the optical lattice, subsequently serving as a dynamic potential for the polarized fermions. Owing to the atom-phonon interaction between the fermions and the condensate, the coupled system exhibits a Berezinskii-Kosterlitz-Thouless transition from a Luttinger liquid to a Peierls phase. However, under sufficiently strong Bose-Fermi interaction, the Peierls phase loses stability, leading to either a collapsed or a separated phase. We find that the primary function of the optical lattice is to stabilize the Peierls phase. Furthermore, the presence of a confining harmonic trap induces a diverse physical behavior, surpassing what is observed for either bosons or fermions individually trapped. Notably, under attractive Bose-Fermi interaction, the insulating phase may adopt a fermionic wedding-cake-like configuration, reflecting the dynamic nature of the underlying lattice potential. Conversely, for repulsive interaction, the trap destabilizes the Peierls phase, causing the two species to separate. Published by the American Physical Society 2024
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 consider a mixture of interacting bosons and fermions in optical lattices described by the Bose–Fermi Hubbard Hamiltonian. To treat bosonic degrees of freedom, we use a generalized dynamical mean field theory (GDMFT). By combining the GDMFT with the numerical renormalization group method, we revisit the zero-temperature phase diagram with particular emphasis on many-body effects in a supersolid state and discuss the origin of an anomalous peak structure emerging in the density of states for fermions.
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.