  We investigate the behavior of a one-dimensional Bose-Hubbard model whose
kinetic energy is made to oscillate with zero time-average. The effective
dynamics is governed by an atypical many-body Hamiltonian where only even-order
hopping processes are allowed. At a critical value of the driving, the system
passes from a Mott insulator to a superfluid formed by a cat-like superposition
of two quasi-condensates with opposite non-zero momenta. We analyze the
robustness of this unconventional ground state against variations of a number
of system parameters. In particular we study the effect of the waveform and the
switching protocol of the driving signal. Knowledge of the sensitivity of the
system to these parameter variations allows us to gauge the robustness of the
exotic physical behavior.
