Theory of Atom Optics: Feynman’s Path Integral Approach

Abstract

The present theory of atom optics is established mainly on the Schrödinger equations or the matrix mechanics equation. The authors present a new theoretical formulation of atom optics: Feynman s path integral theory. Its advantage is that one can describe the diffraction and interference of atoms passing through slits (or grating), apertures, and standing wave laser field in Earth s gravitational field by using a type of wave function and calculation is simple. For this reason, we derive the wave functions of particles in the following configurations: single slit (and slit with the van der Waals interaction), double slit, N slit, rectangular aperture, circular aperture, the Mach Zehnder-type interferometer, the interferometer with the Raman beams, the Sagnac effect, the Aharonov Casher effect, the Kapitza Dirac diffraction effect, and the Aharonov Bohm effect. The authors give a wave function of the state of particles on the screen in abovementioned configurations. Our formulas show good agreement with present experimental measurements.