Misc,
Gravitational redshift in quantum-clock interferometry
(2018)cite arxiv:1810.06744Comment: 21 + 17 pages including appendices, 17 figures.
Abstract
The creation of delocalized coherent superpositions of quantum systems
experiencing different relativistic effects is an important milestone in future
research at the interface of gravity and quantum mechanics. This could be
achieved by generating a superposition of quantum clocks that follow paths with
different gravitational time dilation and investigating the consequences on the
interference signal when they are eventually recombined. Light-pulse atom
interferometry with elements employed in optical atomic clocks is a promising
candidate for that purpose, but suffers from major challenges including its
insensitivity to the gravitational redshift in a uniform field. All these
difficulties can be overcome with a novel scheme presented here which is based
on initializing the clock when the spatially separate superposition has already
been generated and performing a doubly differential measurement where the
differential phase shift between the two internal states is compared for
different initialization times. This can be exploited to test the universality
of the gravitational redshift with delocalized coherent superpositions of
quantum clocks and it is argued that its experimental implementation should be
feasible with a new generation of 10-meter atomic fountains that will soon
become available. Interestingly, the approach also offers significant
advantages for more compact set-ups based on guided interferometry or hybrid
configurations. Furthermore, in order to provide a solid foundation for the
analysis of the various interferometry schemes and the effects that can be
measured with them, a general formalism for a relativistic description of atom
interferometry in curved spacetime is developed. It can deal with freely
falling atoms, but also include the effects of external forces and guiding
potentials, and can be applied to a very wide range of situations.
