Protected cat states from kinetic driving of a boson gas

Fast driving of the hopping energy with zero time-average of bosons in an optical lattice results in an effective time-independent Hamiltonian, whose ground state is a protected cat state. The two cat branches preferentially occupy modes with momenta ±π/2, while sharing a small reduction cloud of unusually paired momenta, which contributes to the protection. The resulting system is superfluid despite the absence of first-order single-particle hopping.