  We study nonlinear dynamics of Rydberg-dressed Bose-Einstein condensates
(BECs) trapped in a triple-well potential in the semiclassical limit. The
Rydberg-dressed BECs experience a long-range soft-core interaction, giving rise
to strong nearest and next-nearest neighbor interactions in the triple-well
system. Using mean-field Gross-Pitaevskii (GP) equations, we show that lower
branches of the eigenspectra exhibit loops and level-crossings when the
soft-core interaction is strong. The direct level-crossings eliminate the
possibility of adiabatic Landau-Zener transitions when tilting of the
triple-well potential. We demonstrate that the long-range interaction allows
for self-trapping in one, two, or three wells, in a far more controllable manor
than BECs with short-range or dipolar interactions. Exact quantum simulations
of the three-well Bose-Hubbard model indicate that self-trapping and
nonadiabatic transition can be observed with less than a dozen bosons. Our
study is relevant to current research into collective excitation and nonlinear
dynamics of Rydberg-dressed atoms.
