Theory of interacting fermions in shaken square optical lattice

Abstract

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 circularly shaken square lattice with near resonance frequencies, i.e., tuned close to the energy separation between $s$-band and the $p$-bands. First, we derive a time-independent four-band effective Hamiltonian in the non-interacting limit. Diagonalization of the effective Hamiltonian yields a quasi-energy 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 non-trivial 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 contact-like. 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.

12 pages with 5 figures. Comments and reference suggestions are welcome

References in corpus (8)

• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Dynamical control of matter-wave tunneling in periodic potentials
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Coherent control of dressed matter waves
• Shaping topological properties of the band structures in a shaken optical lattice
• Floquet FFLO superfluids and Majorana fermions in a shaken fermionic optical lattice
• Quantum Phase Transition of Bosons in a Shaken Optical Lattice

Cited by in corpus (3)

• Floquet dynamics in driven Fermi-Hubbard systems
• Suppressing dissipation in a Floquet-Hubbard system
• Selective population of a large-angular-momentum state in an optical lattice