Gravitational redshift in quantum-clock interferometry

The creation of delocalized coherent superpositions of quantum systems experiencing di erent
relativistic e ects 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 di erent 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 su ers from major
challenges including its insensitivity to the gravitational redshift in a uniform eld. All these di-
culties 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 di erential phase shift between the two internal states is compared
for di erent initialization times. This can be exploited to test the universality of the gravitational
redshift (UGR) 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 o ers signi cant advantages for
more compact set-ups based on guided interferometry or hybrid con gurations. Furthermore, in
order to provide a solid foundation for the analysis of the various interferometry schemes and the
e ects 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 e ects of external forces and guiding potentials, and can be applied to a very wide range
of situations. As an important ingredient for quantum-clock interferometry, suitable difraction
mechanisms for atoms in internal-state superpositions are investigated too. Finally, the relation of
the proposed doubly-di erential measurement scheme to other experimental approaches and to tests
of the universality of free fall (UFF) is discussed in detail.