Twisted superfluids in moving frame

{Helical waveguide filled by superfluid is shown to transform the linear displacements of reference frame $\vec V$ into rotations of atomic ensemble and vise versa rotations of reference frame $\vec \Omega_{\oplus}$ are the cause of linear displacements of ensemble. In mean-field Gross-Pitaevskii equation with a weakly modulated gravitation the exact solutions for macroscopic wavefunction $\Psi$ demonstrate the emergence of $redshift$ phase factor being proportional to the population of condensate $N_a$. is shown to have}Comment: 6 pages, 2 figures , submitted to referred journa

Optical counterpart of the Foucault pendulum

The twin beam vortex interferometer with phase-conjugating mirror in rotating reference frame is analyzed. Using the concept of the $ideal$ phase-conjugating mirror it is shown that motion of helical interference pattern may be used for detection of the slow rotations. The pattern motion is due to exchange of angular momenta between photons and interferometer. The conditions of experimental realization of such rotation sensor are discussed and $scaling$ relations for geometric parameters, coherent backscattering and angular momenta transformations are obtained.Comment: 9 pages,3 figures, submitted to referred journa