Spin-1 quantum magnetism in Floquet engineered dipolar MgF molecules

Ultracold dipolar molecules in optical traps are emerging as a powerful platform for quantum simulation of strongly correlated many-body physics. Here we discuss Floquet engineering of MgF molecules in an optical lattice under the influence of a dc magnetic field and driven by a circularly polarized microwave field near resonance. The microwave field causes electric dipole transitions between opposite parity rotational levels, specifically |N=0,F=1〉and |N=1,F=2〉, resulting 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). However, by adding a dc magnetic field, the three lowest dressed energy levels in the ground state manifold can be energetically isolated, thus effectively simulating a pseudospin-1 particle. Using this technology, we propose the quantum simulation of an effective spin-1 XXZ Heisenberg model with a transverse Zeeman term in the Hamiltonian. We study the rich phase diagram using density-matrix renormalization group and show the emergence of the topological Haldane phase in one dimension. We also discuss deviations from the theoretically established phase diagram due to the transverse Zeeman term, and conclude by identifying experimentally accessible regions in the phase diagram.