Three-component Fermi gas in a one-dimensional optical lattice

We investigate the effect of the anisotropy between the $s$-wave scattering lengths of a three-component atomic Fermi gas loaded into a one-dimensional optical lattice. We find four different phases which support trionic instabilities made of bound states of three fermions. These phases distinguish themselves by the relative phases between the $2k_F$ atomic density wave fluctuations of the three species. At small enough densities and strong anisotropies we give further evidences for a decoupling and the stabilization of more conventional BCS phases. Finally, our results are discussed in light of a recent experiment on ${}^6\text{L}\text{i}$ atoms.

Figure 1

(Color online) DMRG results for $\left(U/t,V/t\right)=\left(-4,-2\right)$ and $\overline{\rho }=5/12$ in the ${\mathcal{A}}_0$ phase. Both one-particle Green’s functions $G_n$ and BCS pairing correlations $P_{12}$ are short range, while trionic correlations decay algebraically. Note that symmetric trions dominate with $\left|T_0\right|>\left|T_{\pi }\right|$ and local densities of all species $n_i\left(x\right)$ are in phase.

Figure 2

(Color online) Same as Fig. 1 for $\left(U/t,V/t\right)=\left(-4,2\right)$ and $\overline{\rho }=5/12$ in the ${\mathcal{A}}_{\pi }$ phase. The only difference in that case is that antisymmetric trions dominate with $\left|T_{\pi }\right|>\left|T_0\right|$ and local densities $n_1$ and $n_2$ are out of phase with $n_3$.

Figure 3

(Color online) Effective Hubbard parameters $U_{nm}$ as a function of magnetic field. The cross indicates the critical field $B_c$ between ${\mathcal{A}}_0$ and ${\mathcal{A}}_{\pi }$ (or BCS) phases.