  The twin beam vortex interferometer with phase-conjugating mirror is analyzed
in rotating reference frame.Circular motion of the interference pattern occurs
due to exchange of the angular momenta between photons and interferometer.
Using the concept of the $ideal$ phase-conjugating mirror it is shown that
motion of the helical interference pattern of the interacting vortex photons
with topological charge $\ell$ may be used for the detection of the slow
rotations. The higher density of interference fringes may improve the
sensitivity by factor containing $2 \ell$ compared to the conventional
Michelson interferometry.
