Theoretical tools for atom optics and interferometry

The development of high sensitivity and high accuracy atom interferometers requires new theoretical tools for their modelization: in this article we e mphasize specifically a generalized Fresnel-Kirchhoff formula for atom opti cs in the form of ABCD matrices and covariant wave equations in the form of a Dirac equation for atom optics in the presence of gravito-inertial field s. As examples, we derive the phase shift for the atom gravimeter and the o utput of an atom laser. Some of the physics of the beam splitters is descri bed. We present a second-quantized field theory of massive spin one-half pa rticles or antiparticles in the presence of a weak gravitational field trea ted as a spin two external field in a Rat Minkowski background. This theory is used to calculate and discuss relativistic phase shifts in the context of matter-wave interferometry (especially atom or antiatom interferometry). In this way, many effects are introduced in a unified relativistic framewo rk, including spin-gravitation terms: gravitational red shift, Thomas prece ssion, Sagnac effect, spin-rotation effect, orbital and spin Lense-Thirring effects, de Sitter geodetic precession and finally the effect of gravitati onal waves. (C) 2001 Academie des sciences/Editions scientifiques et medica les Elsevier SAS.