Effect of Interactions on Harmonically Confined Bose-Fermi Mixtures in Optical Lattices

We investigate a Bose-Fermi mixture in a three-dimensional optical lattice, trapped in a harmonic potential. Using generalized dynamical mean-field theory, which treats the Bose-Bose and Bose-Fermi interaction in a fully nonperturbative way, we show that for experimentally relevant parameters a peak in the condensate fraction close to the point of vanishing Bose-Fermi interaction is reproduced within a single-band framework. We identify two physical mechanisms contributing to this effect: the spatial redistribution of particles when the interspecies interaction is changed and the reduced phase space for strong interactions, which results in a higher temperature at fixed entropy.

Figure 1

Phase border between bosonic Mott insulator and superfluid with $n_b=1$ for fermionic filling $n_f=0.7$, hopping ratio $t_f/t_b=2.2$, temperature $T\to 0$, and various values of $U_{bf}$. The Hartree shift due to the Bose-Fermi interaction is subtracted from the bosonic chemical potential to facilitate an easy comparison.

Figure 2

(a) Total condensate fraction $N_c$, (e) temperature $T$, and (f) spatial overlap of the bosonic and fermionic clouds as a function of Bose-Fermi scattering length $a_{bf}$ for various values of the entropy per particle and $V_{\mathrm{OL}}^{\alpha }/E_R^{\alpha }=9$ ($U_b/t_f=5.2$, $V_f/t_f=0.0058$, $V_b/t_f=0.0064$). (b)–(d) Spatial profiles of the bosonic and fermonic density and the local condensate fraction $N_c(r)=|⟨\widehat{b}(r)⟩{|}^2/N_b(r)$ as a function of distance from the trap center for three values of the Bose-Fermi interaction.

Figure 3

Condensate fraction (top row), temperature (middle row), and overlap of the bosonic and fermionic clouds (bottom row) for $V_{\mathrm{OL}}^{\alpha }/E_R^{\alpha }=5$ (left column) and $V_{\mathrm{OL}}^{\alpha }/E_R^{\alpha }=12$ (right column). Specific parameters are $V_{\mathrm{OL}}^{\alpha }/E_R^{\alpha }=5$: $U_b/t_f=1.06$, $V_f/t_f=V_b/t_f=0.0024$; $V_{\mathrm{OL}}^{\alpha }/E_R^{\alpha }=12$: $U_b/t_f=13.4$, $V_f/t_f=0.0108$, $V_b/t_f=0.012$.