We study spatial coherence near a classical environment by loading a
Bose-Einstein condensate into a magnetic lattice potential and observing
diffraction. Even very close to a surface (5μm), and even when the
surface is at room temperature, spatial coherence persists for a relatively
long time (≥500ms). In addition, the observed spatial coherence extends
over several lattice sites, a significantly greater distance than the
atom-surface separation. This opens the door for atomic circuits, and may help
elucidate the interplay between spatial dephasing, inter-atomic interactions,
and external noise.Comment: 15 pages, 14 figures, revised for final publication. This manuscript
includes in-depth analysis of the data presented in arXiv:1502.0160