Gravitational and relativistic deflection of X-ray superradiance

Einstein predicted that clocks at different altitudes tick at various rates under the influence of gravity. This effect has been observed using Fe-57 Mossbauer spectroscopy over an elevation of 22.5 m (ref. 1) or by comparing accurate optical clocks at different heights on a submetre scale(2). However, challenges remain in finding novel methods for the detection of gravitational and relativistic effects on more compact scales. Here, we investigate a scheme that potentially allows for millimetre- to submillimetre-scale studies of the gravitational redshift by probing a nuclear crystal with X-rays. Also, a rotating crystal can force interacting X-rays to experience inhomogeneous clock tick rates within it. We find that an association of gravitational redshift and special-relativistic time dilation with quantum interference is manifested by a time-dependent deflection of X-rays. The scheme suggests a table-top solution for probing gravitational and special-relativistic effects, which should be within the reach of current experimental technology(3-5).