Gravity gradiometry with Bose-Einstein condensates (BECs) has reached unprecedented precisions. The basis of this technique is the measurement of differential forces by interference of single-atom wave functions. In this article, we propose a gradiometry scheme where phonons, the collective oscillations of a trapped BEC's atoms are used instead. We show that our scheme could, in principle, enable high-precision measurements of gravity gradients of bodies such as the Earth or small spheres with masses down to the milligram scale. The fundamental error bound of our gravity gradiometry scheme corresponds to a differential force sensitivity in the nano-gal range per experimental realization on the length scale of the BEC.
A Bose-Einstein condensate is used as an atomic source for a high precision sensor. A $5\ifmmode\times\else\texttimes\fi{}1{0}^{6}\text{ }\text{ }\mathrm{atom}$
F=1 spinor condensate of
87Rb is released into free fall for up to 750 ms and probed with a
T=130 ms Mach-Zehnder atom interferometer based on Bragg transitions. The Bragg interferometer simultaneously addresses the three magnetic states $|{m}_{f}=1,0,\ensuremath{-}1⟩$, facilitating a simultaneous measurement of the acceleration due to gravity with a 1000 run precision of $\mathrm{\ensuremath{\Delta}}g/g=1.45\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ and the magnetic field gradient to a precision of
120 pT/m.