We develop a theory of weakly interacting fermionic atoms in shaken optical lattices based on the orbital mixing in the presence of time-periodic modulations. Specifically, we focus on fermionic atoms in a circularly shaken square lattice with near-resonance frequencies, i.e., tuned close to the energy separation between the $s$ band and the $p$ bands. First, we derive a time-independent four-band effective Hamiltonian in the noninteracting limit. Diagonalization of the effective Hamiltonian yields a quasienergy spectrum consistent with the full numerical Floquet solution that includes all higher bands. In particular, we find that the hybridized $s$ band develops multiple minima and therefore nontrivial Fermi surfaces at different fillings. We then obtain the effective interactions for atoms in the hybridized $s$ band analytically and show that they acquire momentum dependence on the Fermi surface even though the bare interaction is contactlike. We apply the theory to find the phase diagram of fermions with weak attractive interactions and demonstrate that the pairing symmetry is $s+d$ wave. Our theory is valid for a range of shaking frequencies near resonance, and it can be generalized to other phases of interacting fermions in shaken lattices.We develop a theory of weakly interacting fermionic atoms in shaken optical lattices based on the orbital mixing in the presence of time-periodic modulations. Specifically, we focus on fermionic atoms in a circularly shaken square lattice with near-resonance frequencies, i.e., tuned close to the energy separation between the $s$ band and the $p$ bands. First, we derive a time-independent four-band effective Hamiltonian in the noninteracting limit. Diagonalization of the effective Hamiltonian yields a quasienergy spectrum consistent with the full numerical Floquet solution that includes all higher bands. In particular, we find that the hybridized $s$ band develops multiple minima and therefore nontrivial Fermi surfaces at different fillings. We then obtain the effective interactions for atoms in the hybridized $s$ band analytically and show that they acquire momentum dependence on the Fermi surface even though the bare interaction is contactlike. We apply the theory to find the phase diagram of fermions with weak attractive interactions and demonstrate that the pairing symmetry is $s+d$ wave. Our theory is valid for a range of shaking frequencies near resonance, and it can be generalized to other phases of interacting fermions in shaken lattices.

arXiv:1703.04074Physical Review AJun 23, 201711 citations

A Closer Look at Fermions in Optical Lattices

Daniel Pertot, Luke Miller, Eugenio Cocchi +5 more

Bulletin of the American Physical SocietyJun 4, 20140 citations

Shaping topological properties of the band structures in a shaken optical lattice

Shaoliang Zhang, Qi Zhou

The realization of band structures with nontrivial topological properties in an optical lattice is an exciting topic in current studies of ultracold atoms. Here we point out that this lofty goal can be achieved by using a simple scheme of shaking an optical lattice, which is directly applicable in current experiments. The photon-assisted band hybridization leads to the production of an effective spin-orbit coupling, in which the band index represents the pseudospin. When this spin-orbit coupling has finite strengths in multiple directions, nontrivial topological structures emerge in the Brillouin zone, such as topological defects with a winding number of 1 or 2 in a shaken square lattice. The shaken lattice also allows one to study the transition between two band structures with distinct topological properties.The realization of band structures with nontrivial topological properties in an optical lattice is an exciting topic in current studies of ultracold atoms. Here we point out that this lofty goal can be achieved by using a simple scheme of shaking an optical lattice, which is directly applicable in current experiments. The photon-assisted band hybridization leads to the production of an effective spin-orbit coupling, in which the band index represents the pseudospin. When this spin-orbit coupling has finite strengths in multiple directions, nontrivial topological structures emerge in the Brillouin zone, such as topological defects with a winding number of 1 or 2 in a shaken square lattice. The shaken lattice also allows one to study the transition between two band structures with distinct topological properties.

arXiv:1403.0210Physical Review ANov 6, 201448 citations

Disordered fermions in optical lattices

Brian DeMarco

Bulletin of the American Physical SocietyMar 18, 20210 citations

s

band and the

p

bands. First, we derive a time-independent four-band effective Hamiltonian in the noninteracting limit. Diagonalization of the effective Hamiltonian yields a quasienergy spectrum consistent with the full numerical Floquet solution that includes all higher bands. In particular, we find that the hybridized

s

band develops multiple minima and therefore nontrivial Fermi surfaces at different fillings. We then obtain the effective interactions for atoms in the hybridized

s

band analytically and show that they acquire momentum dependence on the Fermi surface even though the bare interaction is contactlike. We apply the theory to find the phase diagram of fermions with weak attractive interactions and demonstrate that the pairing symmetry is

s+d

wave. Our theory is valid for a range of shaking frequencies near resonance, and it can be generalized to other phases of interacting fermions in shaken lattices.