Canceling the Gravity Gradient Phase Shift in Atom Interferometry

Gravity gradients represent a major obstacle in high-precision measurements by atom interferometry. Controlling their effects to the required stability and accuracy imposes very stringent requirements on the relative positioning of freely falling atomic clouds, as in the case of precise tests of Einstein’s equivalence principle. We demonstrate a new method to exactly compensate the effects introduced by gravity gradients in a Raman-pulse atom interferometer. By shifting the frequency of the Raman lasers during the central $\pi$ pulse, it is possible to cancel the initial position- and velocity-dependent phase shift produced by gravity gradients. We apply this technique to simultaneous interferometers positioned along the vertical direction and demonstrate a new method for measuring local gravity gradients that does not require precise knowledge of the relative position between the atomic clouds. Based on this method, we also propose an improved scheme to determine the Newtonian gravitational constant $G$ towards the 10 ppm relative uncertainty.

Figure 1

(a) Space time trajectories in a freely falling Mach-Zehnder AI operated with Raman transitions in the absence of GGs (straight thin lines) and with GGs, when the compensation scheme is not applied (dashed line) and after readapting the effective wave vector during the central $\pi$ pulse (thick curved lines). (b) Scheme of the experimental apparatus. By varying the position of the external source masses, it is possible to generate the two different vertical acceleration profiles.

Figure 2

Gravity gradiometer phase angle as a function of the applied $\mathrm{\Delta }\nu$ for the three simultaneous gradiometers: results for the gradiometer 2-3, 1-2, and 1-3 are in red (triangles), black (squares), and blue (circles), respectively. The source masses are positioned in the far configuration [see Fig. 1].

Figure 3

As in Fig. 2, but with the source masses in the close configuration.

Figure 4

GG obtained with both the method of the ellipse fitting (black circles) and the new technique based on the determination of the zero-crossing frequency (red squares) from five measurements taken over five days. Residual instabilities are due to the systematics affecting our measurements.

Figure 5

GG obtained with both the method of the ellipse fitting (in black) and the new technique based on the zero-crossing frequency measurement (in red) when changing the position of the higher atomic cloud by $\pm 1\mathrm{cm}$ (circle and square data).