# Hybrid Electrostatic-Atomic Accelerometer for Future Space Gravity Missions
## 3 Results and Discussions
### Proof-Mass Rotation  
The proof-mass of the EA, acting as the reference mirror for the CAI, was excited in rotation during CAI measurement cycles. The method of rotation excitation follows a sine function, as described in Section of Rotation Issues for the CAI. We consider here the specific case of an excitation frequency of \(\
u_{exc}=1/2T\approx 10.87\) Hz and study the effect on atomic fringe contrast for different excitation phases. Here, the impact causing the contrast drop comes mainly from the Coriolis acceleration and angular acceleration of the proof-mass, which act with different weights depending on the phase and frequency of the excitation. We can see in Figure 18a the variation of the \(\Psi\) angle of the proof-mass around the \(Z\) axis for a specific phase excitation of 0 rad and \(\pi/2\) rad. The angle of the proof-mass is monitored in real time during the interferometer sequence by capacitive detection of the EA. These two phase values correspond to excitation configurations where the atomic contrast is at its extrema (see Figure 18b). The excitations represented here correspond to peak-to-peak amplitudes of around 106 \(\upmu\)rad, 7.2 mrad/s, and 494 mrad/s\({}^{2}\). For an excitation frequency of 10.87 Hz and a 0 rad phase, we can see on the black curve of Figure 18a that, during the three laser pulses, the mirror of the CAI (the EA's proof-mass) is at the same angular position. Therefore, for this phase configuration of excitation, the atomic contrast has no reason to be affected by rotation effects. The black dashed line in Figure 18b results from calculations (see Section of Rotation Issues for the CAI) of the contrast loss using the expected experimental parameters as the inputs. The input parameters for the calculated curve are a transverse atomic temperature of 1.6 \(\upmu\)K and an atomic source of 0.8 mm diameter (corresponding to 4\(\sigma\) with \(\approx\)87% of the atoms) with the assumption of a Gaussian position and velocity distribution. We can see that the calculations are in very good agreement with the experimental data. Figure 17: ASD acceleration noise for the EA (black curve), the cold atom gravimeter (blue curve), and the EA corrected by the CAI through a hybridization algorithm (red curve). The interrogation time of the CAI was set to \(T=20\) ms to highlight the interest of hybridization and reproducing qualitatively the noise assumptions treated in the numerical gravity simulations. Note that, at a high frequency (1 Hz), the red curve is completely superimposed on the black one. Note that the ability to control the CAI mirror as has been done offers the possibility to characterize the atomic source in terms of position and velocity dispersion. Indeed, by analyzing quantitatively the loss of contrast due to rotation due to the Coriolis effect or angular acceleration, we should be able to determine precisely these characteristics. The estimation of the transverse mean position and velocity of the atomic cloud relative to the mirror is also achievable by analyzing the variation of the measured acceleration for different rotation excitations. This could be of prime interest for space in-flight characterizations of the CAI. We show now the impact of the excitation of the whole setup by rotating the platform supporting all the hybrid instrument consisting mainly of the cold atom gravimeter and the electrostatic accelerometer. The excitation in rotation is much less accurate than the one that can be performed with the proof-mass. In Figure 19, we report the atomic contrast loss due to platform rotation following a sine function. The angular velocity of the table is measured with a gyroscope. This amplitude of excitation allows fully reducing the atomic contrast. In the next paragraph, we present a way to compensate the table rotation by actuating the PM of the EA. This section is devoted to presenting a very preliminary demonstration of rotation compensation with the hybrid prototype.