Evidence for Metallic Behavior in the Bose-Hubbard Model

We report measurements on transport of a $^{87}$Rb Bose-Einstein Condensate loaded into a 3D optical lattice well-characterized by the Bose-Hubbard model. We have measured temperature-dependent dissipation of center-of-mass oscillations in the low-velocity limit. The observed damping rate levels out as the system is cooled, which is the signature of a metallic phase. This behavior is consistent with the cross-over between quantum tunneling and thermal activation of phase slips. We find excellent agreement with this model and our measurements of the damping rate as a function of the Bose-Hubbard parameters. We have also observed vortices nucleated by center-of-mass motion, providing further evidence for quantum phase slips.