Phase-slips control dissipation in many bosonic systems, determining the critical velocity of superfluid helium and the generation of resistance in thin superconducting wires. Technological interest has been largely motivated by applications involving nanoscale superconducting circuit elements, such as standards based on quantum phase-slip junctions. Although phase slips caused by thermal fluctuations at high temperatures are well understood, controversy remains over the role of phase slips in small-scale superconductors - in solids, problems such as uncontrolled noise sources and disorder complicate their study and application. Here we show that phase slips can lead to dissipation in a clean and well-characterized Bose-Hubbard system, by experimentally studying the transport of ultracold atoms trapped in an optical lattice. In contrast to previous work, we explore a low-velocity regime described by the three-dimensional Bose-Hubbard model that is unaffected by instabilities, and we measure the effect of temperature on the dissipation strength. The damping rate of atomic motion (the analogue of electrical resistance in a solid) in the confining parabolic potential is well fitted by a model that includes finite damping at zero temperature. The low-temperature behaviour is consistent with the theory of quantum tunnelling of phase slips, whereas at higher temperatures a crossover consistent with a transition to thermal activation of phase slips is evident. Motion-induced features reminiscent of vortices and vortex rings associated with phase slips are also observed in time-of-flight imaging. These results clarify the role of phase slips in superfluid systems. They may also be of relevance in understanding the source of metallic phases observed in thin films, or serve as a test bed for theories of bosonic dissipation based upon variants of the Bose-Hubbard model.
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