We introduce and investigate a system that uses temporal resonance-induced phase space pathways to create strong coupling between an atomic Bose-Einstein condensate and a traveling optical lattice potential. We show that these pathways thread both the classical and quantum phase space of the atom cloud, even when the optical lattice potential is arbitrarily weak. The topology of the pathways, which form web-like patterns, can by controled by changing the amplitude and period of the optical lattice. In turn, this control can be used to increase and limit the BECs center-of-mass kinetic energy to pre-specified values. Surprisingly, the strength of the atom-lattice interaction and resulting BEC heating of the center-of-mass motion is enhanced by the repulsive inter-atomic interactions.
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