A momentum dependent 1D optical lattice potential induced by a periodically driven Raman process

We propose an experiment to create a one-dimensional optical lattice potential in an ultracold Bose gas system where the lattice potential depends on the transverse momentum of the Bose gas. The transverse momentum dependence of the optical lattice can be induced using an artificial gauge potential generated by a periodically driven, multi-laser Raman process. The momentum dependence of the lattice potential is caused by spin Hall effect. We construct a quasi-1D Bose--Hubbard model of the system by introducing a strong confinement potential in the transverse plane. Using the Gutzwiller mean-field theory, we explore the phase diagram and show that the superfluid-Mott-insulator transition in such a system can be driven by tuning the average transverse momentum of the Bose gas.