Macroscopic superpositions and gravimetry with quantum magnetomechanics.

Mattias T Johnsson,Gavin K Brennen,Jason Twamley

doi:10.1038/srep37495

Abstract

Precision measurements of gravity can provide tests of fundamental physics and are of broad practical interest for metrology. We propose a scheme for absolute gravimetry using a quantum magnetomechanical system consisting of a magnetically trapped superconducting resonator whose motion is controlled and measured by a nearby RF-SQUID or flux qubit. By driving the mechanical massive resonator to be in a macroscopic superposition of two different heights our we predict that our interferometry protocol could, subject to systematic errors, achieve a gravimetric sensitivity of Δg/g ~ 2.2 × 10−10 Hz−1/2, with a spatial resolution of a few nanometres. This sensitivity and spatial resolution exceeds the precision of current state of the art atom-interferometric and corner-cube gravimeters by more than an order of magnitude, and unlike classical superconducting interferometers produces an absolute rather than relative measurement of gravity. In addition, our scheme takes measurements at ~10 kHz, a region where the ambient vibrational noise spectrum is heavily suppressed compared the ~10 Hz region relevant for current cold atom gravimeters.

Highlights

Gravimetry is the measurement of the local acceleration due to gravity on a test body
We show our scheme has the potential to achieve a gravimetry sensitivity of ~2.2 × 10−9 ms−2 Hz−1/2, which is over an order of magnitude better than the precision offered by the current state of the art absolute gravimeters
This sensitivity is over an order of magnitude better than the Δg/g = 4.2 × 10−9 Hz−1/2 achieved by current state-of-the-art absolute gravimeters which rely on atom interferometry[23]

Summary

Expected Sensitivity

Using Eqs (15) and (19) the gravimeter sensitivity obtained after one full cycle of the phase estimation scheme is. As we execute a complete N-measurement estimation cycle we only alter the double well displacements via λk but each of the N interferometry-measurement runs take the same duration of time This permits us to quote an effective per-root-Hertz sensitivity if we repeat the entire estimation cycle many times. This sensitivity compares favourably with the best free-fall corner cube measurements (Δg/g = 1.5 × 10−8 Hz−1/2 16) and cold atom interferometers (Δg/g = 4.2 × 10−9 Hz−1/2 23). In order to obtain a precise estimate of g, we must know the parameters m, ω, ωq and λ to the same level of precision These quantities can be measured offline with any additional resources, and will not affect the time taken for the phase estimation protocol. We consider possible ways of accomplishing this in Supp Material C

Effect of Decoherence on Sensitivity

Conclusion

Author Contributions

Additional Information