Phase Separation in a Polarized Fermi Gas at Zero Temperature

We investigate the phase diagram of asymmetric two-component Fermi gases at zero temperature as a function of polarization and interaction strength. The equations of state of the uniform superfluid and normal phase are determined using quantum Monte Carlo simulations. We find three different mixed states, where the superfluid and the normal phase coexist in equilibrium, corresponding to phase separation between (a) the polarized superfluid and the fully polarized normal gas, (b) the polarized superfluid and the partially polarized normal gas, and (c) the unpolarized superfluid and the partially polarized normal gas.

Figure 1

Binding energy $A$ of a single spin-down impurity in a Fermi sea of spin-up particles. The dashed line is the molecular binding energy ${ϵ}_b$ for our short-range square well potential (with $2n_{\uparrow }{R}_0^3={10}^{-6}$ as in Ref. 12). In the inset we show the equation of state of the unpolarized superfluid ${\mathrm{SF}}_0$. The solid lines correspond to best fits to the FN-DMC results.

Figure 2

Equation of state of the normal partially polarized phase ${\mathrm{N}}_{\mathrm{PP}}$ as a function of the concentration $x$ for different values of the interaction strength. The solid lines correspond to best fits of the energy functional (3) with the values of $A$ and $m^{*}$ obtained from the single-impurity calculations.

Figure 3

Equation of state of the superfluid polarized phase $\mathrm{S}{\mathrm{F}}_{\mathrm{P}}$ as a function of the concentration $y$ for different values of the interaction strength. The solid lines correspond to the energy functional (4).

Figure 4

Phase diagram as a function of polarization and interaction strength. In terms of the Fermi wave vector $k_F=(3{\pi }^{2}n{)}^{1/3}$ fixed by the total density $n=N/V$ one has $1/k_{F}a=1/k_{F\uparrow }a$ at $P=0$ and $1/k_{F}a=2^{1/3}/k_{F\uparrow }a$ at $P=1$. On the BCS side of the resonance our determination of the critical polarization is not reliable. For $-1/k_{F\uparrow }a\gtrsim 1$ we obtain $P_c$ using the BCS theory (see the text).