Polarized Fermi Condensates with Unequal Masses: Tuning the Tricritical Point

We consider a two-component atomic Fermi gas within a mean-field, single-channel model, where both the mass and population of each component are unequal. We show that the tricritical point at zero temperature evolves smoothly from the BEC to BCS side of the resonance as a function of mass ratio $r$. We find that the interior gap state proposed by Liu and Wilczek is always unstable to phase separation, while the breached pair state with one Fermi surface for the excess fermions exhibits differences in its density of states and pair correlation functions depending on which side of the resonance it lies. Finally, we show that, when $r\gtrsim 3.95$, the finite-temperature phase diagram of trapped gases at unitarity becomes topologically distinct from the equal mass system.

Figure 1

Zero temperature phase diagrams for different mass ratios $r=m_{\downarrow }/m_{\uparrow }$, where a positive polarization $m$ corresponds to an excess of particles with spin $\uparrow$. All mass ratios exhibit the same three phases: the normal state (N), the spatially homogeneous superfluid (${\mathrm{SF}}_{\mathrm{M}}$), and phase separation (PS) between normal and superfluid states in real space. The region of ${\mathrm{SF}}_{\mathrm{M}}$ expands with increasing $r$. The boundaries enclosing the PS region are all first order, while the tricritical point is represented by a circle. The line defined by $m/n=0$ corresponds to the usual BCS-BEC crossover.

Figure 2

Evolution of the tricritical point $(1/k_{F}a,h/{\epsilon }_F{)}_{\mathrm{tric}}$ as a function of mass ratio $r$ with $h>0$. The values of $r=1$, the equal mass case, and $r=3$, where the chemical potential $\mu$ changes sign, are explicitly marked.

Figure 3

Quasiparticle dispersions $E_{\mathbf{k}\uparrow }$, $E_{\mathbf{k}\downarrow }$ together with the majority species ($\uparrow$) projection of the $\mathrm{DOS}(\omega )=-\frac{1}{\pi }\sum _{\mathbf{k}}\Im [G_{11}(\mathbf{k},i{ϵ}_n=\omega +i\eta )]$ for mass ratios $r=0.5$ (upper panels) ($\Delta /|\mu |=0.25$, $h/|\mu |=1.06$, $1/k_{F}a=2.93$, $m/n=0.12$) and $r=10.0$ (lower panels) ($\Delta /\mu =0.85$, $h/|\mu |=1.44$, $1/k_{F}a=-0.07$, $m/n=0.16$).

Figure 4

Averaged momentum distribution for each spin state $n_{\mathbf{k}\uparrow ,\downarrow }$ and correlation function $C_{\uparrow \downarrow }$ for $r=0.5$ (left panels) and $r=10.0$ (right panels) and the same parameter values used in Fig. 3.

Figure 5

Phase diagrams in the ($T/\mu$, $h/\mu$) plane for different mass ratios $r$ at unitarity $1/k_{F}a=0$. Mass ratio $r=6.7$ corresponds to the case of ${}^6\mathrm{Li}\mathrm{\text{−}}{}^{40}\mathrm{K}$ mixtures. The transition between the N and SF phase can be first (red line) or second order (black solid line), separated by the tricritical point. The dashed black line describes the second-order transition in the region where the true transition is first order. Lines of constant gradient $T/h$ represent the trajectory traveled from the center to the edges of the trap, examples of which are shown by the arrows (a)–(e). The starting points on these lines are the values of ($T/\mu$, $h/\mu$) at the trap center.