Magnetic tensor gradiometry using Ramsey interferometry of spinor condensates

TL;DR

This paper demonstrates a magnetic tensor gradiometer using Ramsey interferometry of spatially separated Bose-Einstein condensates, achieving high precision in measuring magnetic field gradients with noise suppression and potential quantum-limited sensitivity.

Contribution

The authors develop a novel interferometric scheme with BECs to measure magnetic field gradients, surpassing traditional methods in noise suppression and approaching quantum-limited sensitivity.

Findings

Achieved differential magnetic field measurement with >50 dB phase noise suppression.

Measured magnetic field gradient tensor with 30 μG/cm precision.

Predicted quantum-limited magnetic energy resolution of order ħ.

Abstract

We have realized a magnetic tensor gradiometer by interferometrically measuring the relative phase between two spatially separated Bose-Einstein condensates (BECs). We perform simultaneous Ramsey interferometry of the proximate $^{87}$Rb spin-1 condensates in freefall and infer their relative Larmor phase -- and thus the differential magnetic field strength -- with a common-mode phase noise suppression exceeding $50\,\mathrm{dB}$. By appropriately biasing the magnetic field and separating the BECs along orthogonal directions, we measure the magnetic field gradient tensor of ambient and applied magnetic fields with a nominal precision of $30\,\mathrm{\mu G\,cm^{-1}}$ and a sensor volume of $2\times10^{-5}\,\mathrm{mm}^3$. We predict a spin-projection noise limited magnetic energy resolution of order $\hbar$ for typical Zeeman coherence times of trapped condensates with this scheme, even with the low measurement duty cycle inherent to BEC experiments.