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Physical Review A

Utility of atomic kicked-rotor interferometers for precision measurements

R. A. Horne, Robert H. Leonard, Charles A. Sackett

Published Jun 13, 2011• 9 citations
Publisher

Abstract

We theoretically investigate a proposed scheme to use an atomic $\ensuremath{\delta}$-kicked rotor resonance for high-precision measurements of accelerations and the photon recoil frequency. Although the technique offers rapid scaling of the measurement sensitivity with pulse number, it also features a high sensitivity to initial atomic momentum. We find that for realistic atom sources, the momentum sensitivity significantly limits the achievable precision. We consider several different variations on the technique, but find similar limitations in all cases.

DOI
10.1103/physreva.83.063613

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We theoretically investigate a proposed scheme to use an atomic \ensuremathδ\ensuremath{\delta}\ensuremathδ-kicked rotor resonance for high-precision measurements of accelerations and the photon recoil frequency. Although the technique offers rapid scaling of the measurement sensitivity with pulse number, it also features a high sensitivity to initial atomic momentum. We find that for realistic atom sources, the momentum sensitivity significantly limits the achievable precision. We consider several different variations on the technique, but find similar limitations in all cases.
We investigate an atom interferometer in which large momentum differences between the arms are obtained by using quantum resonances in the atom-optics $\ensuremath{\delta}$-kicked rotor. The interferometer can potentially measure the Talbot time (from which h/mh/mh/m can be deduced) and the local gravitational field or can serve as a narrow velocity filter. We present an analytical analysis in the short pulse limit and a numerical investigation for finite pulse durations. The sensitivity of the interferometer is improved by a moderate violation of the short pulse limit. Remarkably simple relations predict the optimal pulse duration and the sensitivity of the interferometer.
We investigate the dynamics of the atom-optics δ-kicked rotor in the vicinity of quantum resonance. Although small deviations from resonant conditions lead to a negligible change in the momentum space probability density, they lead to a significant relative phase change between the different momentum states taking part in the dynamics. By adding a tailored pulse to the kicked rotor pulse sequence, one can measure the overlap between the resonant state and any other state, i.e. perform a fidelity measurement. Using this sequence, we predict a narrow peak around quantum resonance with a width that scales as 1/ N 3 with N being the number of pulses in the kicked rotor sequence. This method may be of interest to precision measurements, such as h / M .
Atom interferometers have been used to measure acceleration with at best a T2T^2T2 scaling in sensitivity as the interferometer time TTT is increased. This limits the sensitivity to acceleration which is theoretically achievable by these configurations for a given frequency of acceleration. We predict and experimentally measure the acceleration-sensitive phase shift of a large-momentum-transfer atom interferometer based upon Bloch oscillations. Using this novel interferometric scheme we demonstrate an improved scaling of sensitivity which will scale as T3T^3T3. This enhanced scaling will allow an increase in achievable sensitivity for any given frequency of an oscillatory acceleration signal, which will be of particular use for inertial and navigational sensors, and proposed gravitational wave detectors. A straight forward extension should allow a T4T^4T4 scaling in acceleration sensitivity.
Echo atom interferometers have emerged as interesting alternatives to Raman interferometers for the realization of precise measurements of the gravitational acceleration g and the determination of the atomic fine structure through measurements of the atomic recoil frequency ω q . Here we review the development of different configurations of echo interferometers that are best suited to achieve these goals. We describe experiments that utilize near-resonant excitation of laser-cooled rubidium atoms by a sequence of standing wave pulses to measure ω q with a statistical uncertainty of 37 parts per billion (ppb) on a time scale of ∼50 ms and g with a statistical precision of 75 ppb. Related coherent transient techniques that have achieved the most statistically precise measurements of atomic g-factor ratios are also outlined. We discuss the reduction of prominent systematic effects in these experiments using off-resonant excitation by low-cost, high-power lasers.
Quantum resonances in the kicked rotor are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances occur when the scaled Planck's constant Planck's [over ]=r/s 4pi, for any integers r and s. However, only the variant Planck's [over ]=r2pi resonances are easily observable. We have observed high-order quantum resonances (s>2) utilizing a sample of low energy, noncondensed atoms and a pulsed optical standing wave. Resonances are observed for variant Planck's [over ]=r/16 4pi for integers r=2-6. Quantum numerical simulations suggest that our observation of high-order resonances indicate a larger coherence length (i.e., coherence between different wells) than expected from an initially thermal atomic sample.