Coexistence and shell structures of several superfluids in trapped three-component Fermi mixtures

We study the properties of a trapped interacting three component Fermi gas. We assume that one of the components can have a different mass from the other two. We calculate the different phases of the three component mixture and find a rich variety of different phases corresponding to different pairing channels, and simple ways of tuning the system from one phase to another. In particular, we predict coexistence of several different superfluids in the trap, forming a shell structure, and phase transitions from this mixture of superfluids to a single superfluid when the system parameters or temperature is varied. Such shell structures realize superfluids with a nontrivial spatial topology and leave clear observable signatures in the density profile of the gas.

Figure 1

(a) Gaps as a function of position ($R_{\mathrm{TF}}$ is the ideal gas Thomas-Fermi radius of the second component). Solid, dashed, and dashed-dotted lines describe ${\Delta }_{23}$, ${\Delta }_{13}$, and ${\Delta }_{12}$, respectively. (b) Doubly integrated density differences. Solid, dashed, and dashed-dotted lines describe $\Delta n_{23}$, $\Delta n_{13}$, and $\Delta n_{12}$, respectively. We used the parameters $N_1=6\times {10}^4$, $N_2=5\times {10}^4$, and $N_3=2\times {10}^4$, $k_F{a}_{12}=-1.04$, $(1+1∕r_m)k_F{a}_{13}=-1.03$, $(1+1∕r_m)k_F{a}_{23}=-1.15$, where $r_m=m_{\mathrm{Li}}∕m_{\mathrm{K}}$ and ${\omega }_3∕{\omega }_1=0.4$.

Figure 2

(a) Zero temperature phase diagram as a function $r_{\omega }$ and $r∕R_{\mathrm{TF}}$ with particle numbers $N_{1,2,3}=5.5\times {10}^4$. (b) Zero temperature phase diagram as a function particle number ratio $N_3∕N_2$ and $r∕R_{\mathrm{TF}}$, with $N_1=N_2=5.5\times {10}^4$ and $r_{\omega }=1$. In both figures we used $k_F{a}_{12}=-1$, $(1+1∕r_m)k_F{a}_{23}=-1$, and $\mid a_{23}\mid >\mid a_{13}\mid$. $N$ indicates a normal gas or a vacuum at sufficiently large distances.

Figure 3

Phase diagrams in the trap as functions $-k_F{a}_{12}$ and $r∕R_{\mathrm{TF}}$ for two different relative trap frequencies, in (a) $r_{\omega }=1.0$ and (b) $r_{\omega }=2.67$. We used parameters $N_{1,2,3}=5.5\times {10}^4$, $(1+1∕r_m)k_F{a}_{23}=1$, and $\mid a_{23}\mid >\mid a_{13}\mid$.

Figure 4

Phase diagram as a function of the temperature $T$ and position. We used parameters $N_{1,2,3}=5.5\times {10}^4$, $r_{\omega }=1$, $k_F{a}_{12}=-1$, $(1+1∕r_m)k_F{a}_{23}=-1$, and $\mid a_{23}\mid >\mid a_{13}\mid$. With our parameters the Fermi temperature $T_F\approx 600\mathrm{nK}$ and $R_{\mathrm{TF}}\approx 50\mu \mathrm{m}$.