Long-wavelength optical lattices from optical beatnotes: Theory and applications

A central challenge in strongly interacting many-body systems is understanding the far-from-equilibrium dynamics. Here we study the many-body magnetic dynamics of the two-component Bose-Hubbard model by developing a two-component extension of nonequilibrium bosonic dynamical mean-field theory. Using this numerical method, we uncover rich quantum spin dynamics via interspecies interaction quenches. A sudden ramp up of interactions induces slow thermalization, leading to a long-lived metastable state, whereas quenching to weakinteractions results in rapid thermal equilibrium, featuring a two-step relaxation behavior through distinct exponential decays. Furthermore, under periodic modulation of the interspecies interactions, emergent Floquet dynamics drives a transition from a magnetic to an unordered phase.