Gravity-gradient suppression in spaceborne atomic tests of the equivalence principle

The gravity gradient is one of the most serious systematic effects in atomic tests of the equivalence principle (EP). While differential acceleration measurements performed with different atomic species under free fall test the validity of the EP, minute displacements between the test masses in a gravity gradient produce a false EP-violating signal that limits the precision of the test. We show that gravity inversion and modulation using a gimbal mount can suppress the systematics due to gravity gradients caused by both moving and stationary parts of the instrument as well as the environment, strongly reducing the need to overlap two species.

Figure 1

Illustration of the gravity modulation scheme in the context of the QTEST concept [1]. The center figure is the atom interferometer EP experimental setup on a turntable that is modulated between 0 and $\pi$ along the nadir direction ($r$). In the reference frame of the turntable (experiment), the projection of the earth's gravitational acceleration along $z$ ($g_z$), and therefore the EP signal ($\eta k_{\mathrm{eff}}g{T}^2$), changes sign as the turntable is modulated from $\theta =0$ (left) to $\theta =\pi$ (right). On the other hand, the gravity gradient from the earth, ${\gamma }_{zz}$, remains the same under the modulation (by definition, the gravity and the gravity gradient of the instrument remain constant in the experiment reference frame). Therefore, the gravity gradient effects can be effectively suppressed in differential measurements. The insets zoom to the apparatus size, emphasizing that the modulation changes the relative sign between the gravitational acceleration $g_z$ and the gravity gradient ${\gamma }_{zz}$ seen by the experiment.