Atom interferometers’ phases at the presence of heavy masses; their use to measure Newtonian gravitational constant; optimization, error model, perspectives

The contribution to the phase of the atom interferometer caused by the gravity field of a massive test mass is considered. This contribution can be extracted by applying the double difference technique to measure the Newtonian gravitational constant G. Estimates and further calculations showed that after choosing the largest (given the current state of the art) multiphoton wave vector, the time delay between pulses, the mass of the test body and the signal optimization in respect to atomic positions and velocities, one should be able to obtain an accurate G measurement of 200 ppb, which is 2-3 orders of magnitude more accurate than what can currently be obtained. Calculated variations of the phases under the small deviations of atomic variables made it clear that atom clouds’ radii and temperatures have to be as small as 100 micron and 100 pK, which has also been achieved already.