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

Abstract

We study the ground-state phase diagram of a mixture of bosonic and fermionic cold atoms confined on twoand 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.

Sign reversal of the boson-boson interaction potential in planar Bose-Fermi mixtures under a synthetic magnetic field

“…With these concerns in mind we do not restrict our calculations to the static limit but consider also the local dynamical response function; hence, the retardation effects are an important part of the physics. Moreover, we see [14] from the U bf (m b /m f ) dependence that even if the fermion mass is very large, the system has a finite value of the interaction strength. On the other hand, slow bosonic atoms would affect the system, providing strong interspecies coupling considerably faster.…”

“…These observations are supported by a theoretical description that includes the multiband virtual transitions [13], different masses of strongly interacting particles [14], and numerical calculations [15]. The density-density (DD) interaction between different species can be repulsive or attractive and is produced by changes of one species density that induce a modulation of another.…”

“…Using the bosonic (fermionic) path integral over the complex fields depending on the "imaginary time" 0 τ β ≡ 1/k B T with T being the temperature we can easily integrate over the fermionic fields [14] because spins are frozen due to influence of the magnetic trap and there is no direct interaction between fermions. After that, we obtain the partition func-…”

“…The critical line equation that separates the Mott insulatorsuperfluid transition ( Fig. 3; details of similar derivation of the critical line equation are described in [14]) takes the simple form…”

“…Because the higher values of the normalized chemical potential for the fermions µ f /t f decreases χ (ω) and χ (ω) [14], consequently terms containing explicitly the average density of fermions N F will acquire more significance than these with exclusively the interspecies interaction U bf . The periodicity of the phase diagram can be easily characterized by its evolution with changing the α parameter and applied magnetic field (see Fig.…”