Abtract: Within the last decade, artificially engineered Bose Einstein
Condensation has been achieved in atomic systems. Bose Einstein
Condensates are superfluids just like bosonic Helium is and all
interacting bosonic fluids are expected to be at low enough temperatures.
One difference between the two systems is that superfluid Helium exhibits
roton excitations while Bose Einstein Condensates have never been observed
to have such excitations. The reason for the roton minimum in Helium is
its proximity to a solid phase. The roton minimum is a consequence of
enhanced density fluctuations at the reciprocal lattice vector of the
stillborn solid. Bose Einstein Condensates in atomic traps are not near a
solid phase and therefore do not exhibit roton minimum. We conclude that
if Bose Einstein Condensates in an optical lattice are tuned near a
transition to a Mott insulating phase, a roton minimum will develop at a
reciprocal lattice vector of the lattice. Equivalently, a peak in the
structure factor will appear at such a wavevector. The smallness of the
roton gap or the largeness of the structure factor peak are experimental
signatures of the proximity to the Mott transition.