Instability and Momentum Bifurcation of molecular BEC in Exotic Dispersion with Shaken Lattice

We place a molecular Bose-Einstein condensate in a 1D shaken lattice with a Floquet-engineered dispersion, and observe the dynamics in both position and momentum space. At the initial condition of zero momentum, our engineered dispersion is inverted, and therefore unstable. We observe that the condensate is destabilized by the lattice shaking as expected, but rather than decaying incoherently or producing jets, as in other unstable condensates, under our conditions the condensate bifurcates into two portions in momentum space, with each portion subsequently following semi-classical trajectories that suffer minimal spreading in momentum space as they evolve. We can model the evolution with a Gross-Pitaevskii equation, which suggests the initial bifurcation is facilitate by a nearly linear "inverted V"-shaped dispersion at the zone center, while the lack of spreading in momentum space is facilitated by interactions, as in a soliton. We propose that this relatively clean bifurcation in momentum space has applications for counter-diabatic preparation of exotic ground states in many-body quantum simulation schemes.