The Feynman path integral approach to atomic interferometry. A tutorial

Abstract

Many problems of current interest in interferometry lend themselves to a path integral treatment. We present a practical guide to solving such problems, taking as examples the gravitational experiments of Kasevich and Chu, and the equivalents of the Sagnac and Aharonov-Bohm effects. Atomic interferometry is a new and rapidly-developing field of research, concerned with physical phenomena in which the wave-nature of neutral atoms plays an important role ill. The wide variety of internal degrees of freedom of an atom opens up new possibilities for investigation which do not exist in the more traditional types of interferometry using photons, electrons and neutrons. The development of interferometry has been aided by recent technical advances, particularly in the manipulation of atoms. New mechanisms for slowing, deflecting, cooling and trapping atoms allow control of both their position and momentum. Also important has been the birth of atomic optics, a range of mechanisms providing the equivalent of mirrors, beamsplitters and lenses for atoms. Recently it has been pointed out that certain high-resolution spectroscopy techniques which avoid the Doppler effect amount to realizing an interferometer (2). These methods have since been adapted to measure inertial fields (due to rotation and gravitation) by interferometry. The situation encountered in interferometry experiments is often close to the classical limit. When this is the case a path integral approach to the analysis is very appropriate since it reduces to a calculation of integrals along classical paths. Further simplifications can be made if the Lagrangian is quadratic, as is true for a particle in a gravitational field or a rotating (*) The Laboratoire Kastler Brossel is associated with the CNRS and the Universit4 Pierre et Marie