Generation of atypical hopping and interactions by kinetic driving

We study the effect of time-periodically varying the hopping amplitude in a one-dimensional Bose-Hubbard model, such that the time-averaged hopping is zero. Employing Floquet theory, we derive a static effective Hamiltonian in which nearest-neighbor single-particle hopping processes are suppressed, but all even higher-order processes are allowed. Unusual many-body features arise from the combined effect of nonlocal interactions and correlated tunneling. At a critical value of the driving, the system passes from a Mott insulator to a superfluid formed by two quasi-condensates with opposite nonzero momenta. Even with hard-wall boundary conditions, a many-body cat state emerges which involves the superposition of two configurations each macroscopically occupying one of the two momentum eigenstates. This work shows how driving of the hopping energy provides a novel form of Floquet engineering, which enables atypical Hamiltonians and exotic states of matter to be produced and controlled.