  We study the effects of rotation on one-dimensional ultra-cold bosons
confined to a ring lattice. For commensurate systems, at a critical value of
the rotation frequency, an infinitesimal interatomic interaction energy opens a
gap in the excitation spectrum, fragments the ground state into a macroscopic
superposition of two states with different circulation and generates a sudden
change in the topology of the momentum distribution. These features are
reminiscent of the topological changes in the Fermi surface that occurs in the
Lifshitz transition in fermionic systems. The entangled nature of the ground
state induces a strong enhancement of quantum correlations and decreases the
threshold for the Mott insulator transition. In contrast to the commensurate
case, the incommensurate lattice is rather insensitive to rotation. Our studies
demonstrate the utility of noise correlations as a tool for identifying new
physics in strongly correlated systems.
