Raman-pulse-duration effect in gravity gradiometers composed of two atom interferometers

We investigated the Raman-pulse-duration effect in a gravity gradiometer with two atom interferometers. Since the two atom clouds in the gradiometer experience different gravitational fields, it is hard to compensate for the Doppler shifts of the two clouds simultaneously by chirping the frequency of a common Raman laser. This leads to an appreciable phase shift. The magnitude of the phase shift relative to the differential phase shift of the two interferometers is in an order of $\tau /T$, and cannot be neglected in the precision measurements such as measuring the gravity gradient and the Newtonian gravitational constant.

Figure 1

Diagram of the time sequence of a three-pulse Mach-Zehnder type interferometer.

Figure 2

Space-time diagram of an atom interferometer. $\mathrm{\Delta }z$ is the spacial distance between the two arms and it varies linearly with time.

Figure 3

Left and right: The gravitational field along the vertical symmetry axis of the far (left) and close (right) configuration (dotted line, with data from [23, 24, 25]). The solid lines on the plots indicate the gravitational field the atomic cloud experienced during the interference process. Middle: The schematic of two atom interferometers in a chamber.