Molecular superfluid phase in systems of one-dimensional multicomponent fermionic cold atoms

We study a simple model of $N$-component fermions with contact interactions which describes fermionic atoms with $N=2F+1$ hyperfine states loaded into a one-dimensional optical lattice. We show by means of analytical and numerical approaches that, for attractive interaction, a quasi-long-range molecular superfluid phase emerges at low density. In such a phase, the pairing instability is strongly suppressed and the leading instability is formed from bound states made of $N$ fermions. At small density, the molecular superfluid phase is generic and exists for a wide range of attractive contact interactions without an $\mathrm{SU}\left(N\right)$ symmetry between the hyperfine states.

Figure 1

(Color online) SU(3) model: triplet and density correlations vs distance obtained by DMRG with $L=153$, $n=1∕3$, and $U∕t=-4$. (a) Dominant triplet over CDW correlations can both be fitted with $K=2.7$. We also see the $k_F$ $\left(2k_F\right)$ oscillations of $M\left(x\right)$ $\left[N\left(x\right)\right]$. (b) One-particle Green function $G\left(x\right)$ and pairing correlations $P\left(x\right)$ vs distance. Both are short range and with the same correlation length $\xi =0.68$.

Figure 2

(Color online) SU(4) model: (a) quartet and density correlations vs distance obtained by DMRG with $L=128$ and $U∕t=-4$ at filling $n=0.25$. The same $K\simeq 2.7$ is used to give a rough estimate of the exponent. (b) One- and two-particle correlations vs distance. Both are short-range and the ratio of the two correlation lengths is ${\xi }_2∕{\xi }_1=0.68\simeq 1∕\sqrt{2}$.

Figure 3

SU(3) model. Phase diagram showing the Luttinger parameter $K$ vs filling $n$ and interaction $U$. The gray area is the superfluid triplet phase. Lines are guide for the eyes which behavior satisfies the perturbative limit close to the point ($U∕t=0$, $n=0$). We also plot the perturbative estimate separating both regions (see text), that agrees with our numerical finding at small $\mid U\mid$ but deviates for larger values.

Figure 4

Same as Fig. 3 for the SU(4) case.

Figure 5

(Color online) SO(5) model. (a) Quartet and density correlations for $U∕t=-4$ and $V∕t=-2$ at the density $n=0.5$. The value of the Luttinger parameter is $K=2.7$. (b) One- and two-particle correlations vs distance. Both are short range and the ratio of the two correlation lengths is ${\xi }_2∕{\xi }_1=0.72\simeq 1∕\sqrt{2}$.