Atomic clocks and inertial sensors

We show that the language of atom interferometry provides a unified picture for microwave and optical atomic clocks as well as for gravito-inertial sensors. The sensitivity and accuracy of these devices is now such that a new theoretical framework common to all these interferometers is required that includes: (a) a fully quantum mechanical treatment of the atomic motion in free space and in the presence of a gravitational field (most cold-atom interferometric devices use atoms in "free fall" in a fountain geometry); (b) an account of simultaneous actions of gravitational and electromagnetic fields in the interaction zones; (c) a second quantization of the matter fields to take into account their fermionic or bosonic character in order to discuss the role of coherent sources and their noise properties; (d) a covariant treatment including spin to evaluate general relativistic effects. A theoretical description of atomic clocks revisited along these lines is presented, using both an exact propagator of atom waves in gravito-inertial fields and a covariant Dirac equation in the presence of weak gravitational fields. Using this framework, recoil effects, spin-related effects, beam curvature effects, the sensitivity to gravito-inertial fields and the influence of the coherence of the atom source are discussed in the context of present and future atomic clocks and gravito-inertial sensors.