Interband physics in an ultracold Fermi gas in an optical lattice

We study a gas of strongly polarized cold fermions in an optical lattice when the excited $p$ bands are populated. We derive the relevant Hamiltonian and discuss the expected phase diagram for both repulsive and attractive interactions. In the parameter regime covered here, checkerboard antiferromagnetic ordering is found to be possible for repulsive interactions, while for attractive interactions, transitions between different types of paired phases are predicted.

Figure 1

Magnitude of the antiferromagnetic order parameter $A_{x,\mathbf{Q},\uparrow }$ for the majority component in the checkerboard state, $\mathbf{Q}=(\pi ,\pi ,\pi )$, as a function of temperature and scattering length for a gas of ${}^{40}\mathrm{K}$ atoms in a lattice with strength $V_0=16E_R$, where $E_R$ is the recoil energy. The scattering length $a$ is given in units of the Bohr radius $a_B$.

Figure 2

Phase diagram with a fixed scattering length $a=-10a_B$ and the minority component chemical potential which corresponds to half filling for the ideal system at $T=0$. The $x$ axis shows the filling fraction of the ideal gas of majority atoms at $T=0$. Shading: symmetric state, light; on-axis state, gray; normal state, dark.