Josephson frequency shift near magnetized objects in slowly rotating spacetime

Abstract

We investigate the influence of the gravitational fields of slowly rotating magnetized celestial objects on the AC Josephson effect in superconductivity on the objects. Starting from the covariant phase evolution equation in a stationary and rotating spacetime in the slow rotation approximation, we derive a unified expression for the leading general relativistic and rotation corrections to the Josephson frequency. It is observed that the frequency shift is proportional to the vertical separation between the junctions and comprises two contributions: a gravitoelectric term associated with the Newtonian potential, and a rotational kinetic term proportional to the objects’ angular momentum and radii. We then apply our results to laboratory-scale experiments on Earth and to a formal extrapolation to neutron-star conditions, thereby illustrating the parametric amplification of relativistic effects in the gravitational compact objects. Our results demonstrate that Josephson junctions are theoretically dependent on surface gravity and rotation of the magnetized objects.