  Application of hybrid atom-mechanical oscillator for absolute rotation
detection is studied. The hybrid atom-mechanical oscillator consists of an
atomic cell, filled with three level atoms, which is fixed on a mechanical
oscillator. The atom-mechanical oscillator is placed on a rotating table such
that the Coriolis force moves the atomic cell with respect to the incoming
laser field. Thus the atomic resonance frequencies are Doppler shifted, and the
phase of the laser field interacting with the atomic medium changes. Absolute
rotation parameters are estimated by measuring the phase change in the laser
field at the output of the atomic cell. Large dispersion is created in the
atomic medium, using electromagnetically induced transparency, to enhance the
phase change in the laser field interacting with the atomic medium.
Contribution of the shot noise, the atomic noise and the noise due to the
mechanical oscillation of the atomic cell are studied. We show that, under
certain conditions, noise due to the mechanical oscillation of the atomic cell
is on the same order of magnitude as the shot noise. The quantum limit of
detectable rotation rate is estimated as $8.1\times10^{-19}$\,rad/s.
