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Journal of Optics B Quantum and Semiclassical Optics

Quantum theory of atomic clocks and gravito-inertial sensors: an update

Ch. Antoine, Ch J Bord

Published Apr 1, 2003• 84 citations
Publisher

Abstract

In the framework of the ABCD ξ formulation of atom optics and with an adequate modelization of the beam splitters, we establish an exact analytical phase shift expression for atom interferometers. This result is valid for a time-dependent external Hamiltonian at most quadratic in position and momentum operators and is expressed in terms of coordinates and momenta of the wave packet centres at the interaction vertices only. As a specific application, the case of atom gyrometers and accelerometers is presented in detail.

DOI
10.1088/1464-4266/5/2/380

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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.
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The effect of a rotation on a matter-wave-laser beam splitter is studied and modeled. This modeling is shown to give important nontrivial corrections to the Sagnac phase shift of matter-wave gyrometers when the duration of the laser action cannot be neglected with respect to the propagation time between beam splitters. This result is illustrated on a Mach-Zehnder atom gyrometer (rate gyroscope) with running laser beam splitters. A quasiclassical description of the interferometer arms inside the beam splitters is proposed to interpret the corrected Sagnac phase shift in terms of an effective interferometer area.