Color Superfluidity and “Baryon” Formation in Ultracold Fermions

We study fermionic atoms of three different internal quantum states (colors) in an optical lattice, which are interacting through attractive on site interactions, $U<0$. Using a variational calculation for equal color densities and small couplings, $|U|<|U_C|$, a color superfluid state emerges with a tendency to domain formation. For $|U|>|U_C|$, triplets of atoms with different colors form singlet fermions (trions). These phases are the analogies of the color superconducting and baryonic phases in QCD. In ultracold fermions, this transition is found to be of second order. Our results demonstrate that quantum simulations with ultracold gases may shed light on outstanding problems in quantum field theory.

Figure 1

Upper panel: Condensation energy as a function of $|U|/t^{*}$ for filling $\varrho \equiv n/3=1/3$. Note that $t^{*}=t\sqrt{d}$ is the typical kinetic energy of the fermions and determines the Fermi temperature $T_F$. The inset shows how the superconducing order parameter, $\Delta$, the deviation from equal densities, $\delta n_3\equiv \varrho -n_3$, and $1/g$ scale to zero as one approaches the critical value $U_C/t^{*}\approx -1.774$. Lower panel: $U_C/t^{*}$ as a function of the filling factor $\varrho =n/3$. The phase diagram is symmetric to $\varrho =0.5$.