Chandrasekhar-Clogston limit and critical polarization in a Fermi-Bose superfluid mixture

We study mixtures of a population-imbalanced, strongly interacting Fermi gas and of a Bose-Einstein condensed gas at zero temperature. In the homogeneous case, we find that the Chandrasekhar-Clogston critical polarization for the onset of instability of Fermi superfluidity is enhanced due to the interaction with the bosons. Predictions for the critical polarization are also given in the trapped case, with a special focus on the situation of equal Fermi-Bose and Bose-Bose coupling constants, where the density of fermions becomes flat in the center of the trap. This regime can be realized experimentally using Feshbach resonances and is well suited to investigate the emergence of exotic configurations, such as the occurrence of spin domains or the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase.

Figure 1

Critical ratios $x\equiv n_{\downarrow }/n_{\uparrow }$ (solid blue line with left axis) and $y\equiv n_s/n_{\uparrow }$ (dotted green line with right axis) as a function of $G\equiv n_{\uparrow }{g}_{bf}^2/{\epsilon }_{F\uparrow }{g}_{bb}$.

Figure 2

Local 3D density profile of the two opposite limits where the inhomogeneous phase in the core is about to appear. We fix $N_b={10}^5$ and $N_{\uparrow }=1.5\times {10}^5$. The solid (blue) lines are spin-up fermions, the dotted (green) lines are spin-down fermions, and the dash-dotted (red) lines are bosons. The left axis is for the fermion densities and the right axis is for the boson density. The number of spin-down fermions is (a) $N_{\downarrow }=0.22\times {10}^5$ and (b) $N_{\downarrow }=0.33\times {10}^5$. The length is in units of $l_{\mathrm{ho}}$, and the density of particles is in units of $1/l_{\mathrm{ho}}^3$.

Figure 3

Critical polarizations for entering the inhomogeneous core as a function of $N_f/N_b$ for $N_b={10}^5$ (solid blue lines) and $N_b={10}^4$ (dashed red lines). The cross corresponds to the situation of Fig. 4.

Figure 4

Local 3D density and doubly integrated density profiles for two different configurations for the core, corresponding to the S-N and N-S-N scenarios in the text. We have chosen $N_b={10}^5$ and $N_{\uparrow }=1.5\times {10}^5$ as in Fig. 2. The value of $N_{\downarrow }$ is instead $0.28\times {10}^5$, corresponding to $P=0.69$ and $N_f/N_b=1.78$, i.e., to the inhomogeneous core region of Fig. 3. The solid (blue) lines are for spin-up fermions and the dotted (green) lines are for spin-down fermions. The dash-dotted (red) lines are for bosons for the local density, and the dash-dotted (black) lines are the difference ${\overline{n}}_{\uparrow }-{\overline{n}}_{\downarrow }$ for the doubly integrated density. For the local density, the left axis is for fermions and the right axis is for bosons. Lengths are in units of $l_{\mathrm{ho}}$.