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