Project A05: Theory of LMT Atom Interferometers Involving Gravitational Fields

Results

In the previous funding period, we developed an analytical microscopic theory for high-order Bragg diffraction based on the adiabatic theorem. We presented a theoretical framework for analysing such pulses, grounded in the profound insight that the physics of Bragg pulses can be effectively described by the adiabatic theorem. Our research demonstrated that efficient Bragg diffraction can be achieved with any smoothly varying and adiabatic pulse shape, with high-fidelity Gaussian pulses being a prime example of such adiabatic pulses.

Another goal of the previous funding period was to set up a systematic mathematical scheme that would allow to compute in a systematic fashion all those additional terms in the Hamiltonian that result from the interaction of the system with an external gravitational field. Our approach was based on a well defined expansion scheme in terms of the inverse of the velocity of light (a so-called post-Newtonian approximation). This led to novel expansion techniques which we subsequently applied to a electromagnetically bound 2- body system (called “atom”), thereby giving the first complete and systematic derivation of all couplings such systems to the Eddington-Robertson class of spherically symmetric and static gravitational fields.