Probing phase separation in Bose-Fermi mixtures by the critical superfluid velocity

We investigate the effect exerted by spin-polarized fermions on the interaction between superfluid bosons for a Bose-Fermi mixture residing on an optical lattice, with particular emphasis on the possibility of an induced phase separation. Using a set of microscopic parameters relevant to a ${}^{40}\mathrm{K}-{}^{87}\mathrm{Rb}$ mixture, we show how the phase-separation criterion may be directly probed by means of the critical superfluid velocity of the bosonic condensate. We report quantitative results for the magnitude of the superfluid velocity and its dependence on the trap depth, the boson-fermion interaction, and the fermionic filling fraction. All of these parameters can be controlled experimentally in a well-defined manner. We propose an experimental setup for probing the critical superfluid velocity.

Figure 1

Fermionic density of states on a square lattice, featuring a van Hove singularity at $\varepsilon =0$. We consider two filling fractions characterized by $\mu /t_f=0.5$ and $\mu /t_f=3.5$, respectively. Here, $N_0=1/(2{\pi }^2{t}_f)$.

Figure 2

Plot of the critical superfluid velocity $v_c$ for the bosons and its dependence on the trap depth for several values of the boson-fermion scattering length $a=a_{\mathit{bf}}$. Here, we have set (a) $\mu /t_f=0.5$ and (b) $\mu /t_f=3.5$. All other parameter values are given as follows: $T_{\mathrm{BEC}}=100$ nK, $m_f=6.64\times {10}^{-26}$ kg, $m_b=1.44\times {10}^{-25}$ kg, $a_b=98a_0$, $\lambda =755$ nm, and $T/T_{\mathrm{BEC}}=0.6$.

Figure 3

Plot of the critical superfluid velocity $v_c$ for the bosons and its dependence on the fermion-boson interaction for several values of the trap depth $s$. Here, we have set (a) $\mu /t_f=0.5$ and (b) $\mu /t_f=3.5$. All other parameter values are given as follows: $T_{\mathrm{BEC}}=100$ nK, $m_f=6.64\times {10}^{-26}$ kg, $m_b=1.44\times {10}^{-25}$ kg, $a_b=98a_0$, $\lambda =755$ nm, and $T/T_{\mathrm{BEC}}=0.6$.

Figure 4

Plot of the critical superfluid velocity as a function of the intrinsic boson-boson scattering length $a_b$ and the boson-fermion interaction $a_{\mathit{bf}}$. We have set $\mu /t_f=0.5$ and considered a trap depth $s=5$. All other parameter values are given as follows: $T_{\mathrm{BEC}}=100$ nK, $m_f=6.64\times {10}^{-26}$ kg, $m_b=1.44\times {10}^{-25}$ kg, $\lambda =755$ nm, and $T/T_{\mathrm{BEC}}=0.6$.

Figure 5

Proposed experimental setup for probing the critical superfluid velocity in a Bose-Fermi mixture. A laser beam serves as a macroscopic object flowing through the condensate, thereby creating a moving boundary condition for the quasiparticle excitations.