  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.

Quantum Physics