Robust cat state from kinetic driving of a boson gas

We investigate the behavior of a one-dimensional Bose-Hubbard gas 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. In some parameter range the system has similarities to the Richardson model, which permits a detailed understanding of its key features. The ground state is a cat-like superposition of two macroscopically occupied one-atom states of opposite momentum. Interactions give rise to a reduction (or modified depletion) cloud that is common to both macroscopic options. Symmetry arguments permit a precise identification of the two orthonormal, macroscopically distinguishable many-body states yielding the cat state, each involving a large number of momentum configurations. For a gas between hard walls, the cat correlations are fundamentally robust because the system cannot collapse into a nonzero current state.