Efficient averaging of vibration noise
This protocol is extracted from research article:
Interleaved atom interferometry for high-sensitivity inertial measurements
Sci Adv, Dec 21, 2018; DOI: 10.1126/sciadv.aau7948

Following Eq. 1 and assuming that the Raman lasers are oriented purely in the x direction, the four-light-pulse atom interferometer phase shift is given by (we neglect the duration of the Raman pulse)Embedded Image(4)with xb,t(t) as the position of the bottom and top retro-mirrors with respect to the free-falling atom cloud. The phase shift can be rewritten asEmbedded Image(5)with Embedded Image as the distance between the bottom and top mirrors and Embedded Image as the term associated to the linear acceleration of the top mirror. The second term represents pure rotation of the bottom mirror about the position of the top one. Recalling that Tc = 2T/3 and writing as Φi = Φ(iTc) the atom interferometer phase at cycle i, the mean phase after N measurement readsEmbedded Image(6)

The term Embedded Image encompasses contributions of detection noise, uncompensated linear acceleration noise, and laser phase noise. When expanding the sum in Eq. 6, most of the θb terms mutually cancel such that the mean phase readsEmbedded Image(7)

This equation shows that the random rotation noise averages as N−1 (first term). The second term represents the uncorrelated noise contributions of SD σδϕ. Their sum equals Embedded Image, which corresponds to a scaling of the phase sensitivity as N−1/2.

Besides rotation noise, uncompensated linear accelerations in the frequency range [0.1 − 1] Hz contribute, to a large part, to the interferometer phase noise (see section S3 for details). This contribution, estimated to typically about 500 mrad per shot, dominates the noise budget and may prevent from observing a clear τ−1 scaling of the gyroscope sensitivity. Interleaving, however, allows us to oversample these fluctuations, thus introducing correlations between successive measurements, which also contribute to the τ−1 dependence of the instrument sensitivity.

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