  We study the effect of time-periodically varying the hopping amplitude in a
one-dimensional Bose-Hubbard model, such that its time-averaged value 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. 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.
