Eur. Phys. J. Special Topics 163, 315-332 (2008)
https://doi.org/10.1140/epjst/e2008-00827-3

5D optics for atomic clocks and gravito-inertial sensors

¹ Laboratoire de Physique des Lasers, CNRS UMR 7538, Université Paris-Nord, 99 avenue J.-B. Clément, 93430 Villetaneuse, France
² SYRTE, CNRS UMR 8630, Observatoire de Paris, 61 avenue de l'Observatoire, 75014 Paris, France

Abstract

A new framework is proposed to compare and unify photon and atom optics, which rests on the quantization of proper time. A common wave equation written in five dimensions reduces both cases to 5D-optics of massless particles. The ordinary methods of optics (eikonal equation, Kirchhoff integral, Lagrange invariant, Fermat principle, symplectic algebra and ABCD matrices,...) are used to solve this equation in practical cases. The various phase shift cancellations, which occur in atom interferometers, and the quantum Langevin twin paradox for atoms, are then easily explained. A general phase-shift formula for interferometers is derived in five dimensions, which applies to clocks as well as to gravito-inertial sensors. The application of this formula is illustrated in the case of atomic fountain clocks.