Floquet Engineered Quantum Many-Body State Simulation with Polar MgF Molecules.

Ultracold dipolar molecules in optical traps are emerging as a powerful platform for quantum simulation of strongly correlated many-body physics. We present Floquet engineering of ground state MgF molecules in an optical lattice under the influence of a dc magnetic field and resonantly driven by a circularly polarized microwave field. Electric dipole transitions between opposite parity rotational levels, specifically |N=0,F=1> and |N=1,F=2>, result in microwave dressed states that are coherent superpositions of the Zeeman shifted hyperfine energy levels. Since the dressed state quasienergies are of the order of the drive frequency (in GHz), they dominate over the dipole-dipole interaction strength (in KHz). But the dc magnetic field provides an additional knob to make the quasienergies in a given manifold (nearly) degenerate, wherein the quasienergy splitting between pairs of dressed states is much smaller compared to the dipole-dipole interaction strength. Thus, the molecules effectively simulate strongly interacting two-level and three-level systems in 1D and 2D arrays. We investigate the resultant quantum many-body phase diagram as a function of the filling fraction and dipole configuration.