  We study first-order spatial coherence for interacting polar bosons trapped
in triple-well potentials. It is argued that besides the well-known coherence
produced by couplings related to tunneling between the sites, there exists a
nonlocal coherence predominantly determined by intersite interactions, which
prevails between the outer sites of the triple well when their total filling is
odd. We find that the nonlocal interaction-induced coherence originates from
the superposition of degenerate many-body states in symmetric triple wells, and
demonstrate its robustness against perturbations due to various tunneling
mechanisms and thermal fluctuations.
