Abstract
We develop a unified theory for clocks and gravimeters using the interferences of multiple atomic waves put in levitation by traveling light pulses. Inspired by optical methods, we identify a propagation invariant, which enables us to analytically derive the wave function of the sample scattering on the light pulse sequence. A complete characterization of the device sensitivity with respect to frequency or acceleration measurements is obtained. These results agree with previous numerical simulations and confirm the conjecture of sensitivity improvement through multiple atomic wave interferences. A realistic experimental implementation for such a clock architecture is discussed.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Controlling the atomic motion, and in particular the gravitational acceleration, is a major issue in cold atom precision experiments. In contrast to setups using atomic traps (such as optical network clocks) or simply letting the sample fall down (such as atomic fountain gravimeters/clocks), the following strategy has been explored recently: the use of a single laser field which simultaneously interrogates and levitates the atomic sample. The levitation method considered uses quantum interferences between multiple atomic waves in order to maintain the sample within a network of suspended paths. Numerical simulations suggest that multiple-wave interferences yield a quick improvement in the accuracy of clocks and gravimeters using this levitation scheme.
Main results. We develop a unified theory for clocks and gravimeters involving the multiple-wave atomic levitation with traveling light pulses. Inspired by optical methods, we identify a propagation invariant, which enables one to analytically derive the wave function of the sample scattering on the light pulse sequence. We characterize the setup sensitivity exactly, in the regime of clock and gravimeter operation. These results agree with previous simulations and confirm the conjecture of accuracy improvement with the atomic interrogation time. We also discuss a realistic implementation for such a clock architecture and estimate the corresponding frequency shifts.
Wider implications. The method of analysing levitation experiments developed here can also provide new insights into general multiple-wave atom interferometers. These results pave the way for the realization of atomic clocks using such a quantum levitation.
Figure. Network of atomic trajectories in a quantum levitator.