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Quantum Interference Effects in Horava-Lifshitz Gravity

The relativistic quantum interference effects in the spacetime of slowly rotating object in the Hořava-Lifshitz gravity as the Sagnac effect and phase shift of interfering particle in neutron interferometer are derived. We consider the extension of Kehagias-Sfetsos (KS) solution~\cite{ks09} in the Hořava-Lifshitz gravity for the slowly rotating gravitating object. Using the covariant Klein-Gordon equation in the nonrelativistic approximation, it is shown that the phase shift in the interference of particles includes the gravitational potential term with the KS parameter $ω$. It is found that in the case of the Sagnac effect, the influence of the KS parameter $ω$ is becoming important due to the fact that the angular velocity of the locally non rotating observer is increased in Hořava gravity. From the results of the recent experiments~\cite{holgeretal} we have obtained lower limit for the coupling KS constant as $ω\simeq 1.25 \cdot 10^{-25} \rm{cm}^{2}$. Finally, as an example, we apply the obtained results to the calculation of the UCN (ultra-cold neutrons) energy level modification in the gravitational field of slowly rotating gravitating object in the Hořava-Lifshitz gravity.