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 emphasize specifically a generalized Fresnel-Kirchhoff formula for atom optics 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 fields. As examples, we derive the phase shift for the atom gravimeter and the output of an atom laser. Some of the physics of the beam splitters is described. We present a second-quantized field theory of massive spin one-half particles or antiparticles in the presence of a weak gravitational field treated 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 framework, including spin-gravitation terms: gravitational red shift, Thomas precession, Sagnac effect, spin-rotation effect, orbital and spin Lense-Thirring effects, de Sitter geodetic precession and finally the effect of gravitational waves. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.