  The recent developments in the theory of rapidly rotating Bose atoms have
been reviewed in this article. Rotation leads to the development of
quantized-vortices, that cluster into a vortex array, exactly to how superfluid
helium behaves. Theoretically, a number of strongly correlated phases are
projected to exist in this domain, which might be thought of as bosonic
counterparts of fractional quantum Hall effect (FQHE). It is now possible for
bosons associating with a short-range interaction to exhibit a FQHE, because
the system of neutral bosons in a fast rotating atomic trap is analogous to
charged bosons placed in a fictitious magnetic field. The neutral collective
spin-conserving and spin-flip excitation for the rotating ultra-cold dilute
Bose atoms in the FQHE domain are being discussed. We have introduced a
realistic interaction between the Bose particles together with long-range
interaction and presented a short review article about various fractional
quantum Hall states and their spin conserving and spin reversed collective
modes.
