14 December 2019

### Ultrasensitive atom gradiometry

The context of this project is the utilization of atom interferometry techniques for the measurement of the Earth gravity field in satellites. Operating such sensors in space will allow to increase drastically the duration of the interferometer with respect to operation on Earth. Extending this duration in the range of seconds will allow to obtain intrinsic sensitivities well beyond what can be reached on the ground, and offers the possibility of realizing gravity measurements with a resolution better than previous missions of space gravity field mapping.

In particular, atomic gradiometers with sensitivities in the mE/Hz^{1/2} range (1E=10^{-9}s^{-2}) are envisioned, based on relatively classical architectures, which performances in terms of cycling time and ultracold atoms preparation rate are extremely demanding. Such sensitivities would allow to reach a better resolution in the determination of the Earth gravity field than the GOCE mission, which used electrostatic gradiometers.

### Development of a laboratory setup for gradiometry

The gradiometer being developed at SYRTE will combine 1) ultracold atomic sources prepared on atom chips and 2) the use of large momentum beamsplitters. These two key elements will be combined to realize interferometers based on beamsplitters of several tens or hundreds of ħk in a fountain geometry. For an interferometer duration of 2T = 500 ms, a separation of 100 ħk, a cycle time of 2 s and a number of atoms of 10^{5} per source, the differential accelerometric sensitivity will be of 1.3 10^{-11}g at 1 s. For a distance between sources of one meter, the sensitivity on the gravity gradient will be of 126 mE at 1 s.

### Differential phase extraction

We have recently demonstrated a new method for the extraction of the differential phase [M. Langlois et al., Phys. Rev. A 96, 053624 (2017)], which exploits correlations between the phases of the two interferometers and an estimation of the seismic phase, determined thanks to the simultaneous measurements of ground vibrations with a seismometer. This method, which we had proposed a few years ago [F. Pereira Dos Santos, Phys. Rev. A 91, 063615 (2015)], allows to reject vibration noise with an efficiency limited by the detection noise, and allows retrieving the differential phase without bias, by contrast with the methods used so far.

### Simultaneous accurate determination of *g* and its vertical gradient

We have recently implemented a method for the accurate measurements of both the gravity *g* and its vertical gradient. Two atomic samples are prepared at different heights and released. During their free fall, two simultaneous interferometers are performed with the same Raman beam. Using a frequency chirp and a frequency jump on this Raman beam frequency, we realize a dual lock which stirs simustaneously the chirp to compensate for *g* and the jump to compensate for the vertical gravity gradient. We then determine these two quantities in terms of frequencies. Moreover, this technique does not require the precise knowledge of the « gradiometer baseline », i.e. the distance between the two sources, which is difficult to determine precisely. The following figure displays the evolution of *g* and its gradient obtained with the implemented dual lock method. One clearly sees the rejection of the common mode vibration noise in the gradient measurement.

**Results of the dual lock measurement.**- Top: Gravity acceleration measurement fluctuation. Bottom: Gravity gradient measurement fluctuation.

### Status of the project

The vacuum chamber is completely assembled today. We have installed in the top trap zone a first generation atom chip, which will be used for the production of ultracold atoms. Next steps will be the validation of this key-subsystem and the implementation of large momentum transfer beamsplitters.

### Publications

- R. Caldani, S. Merlet, F. Pereira dos Santos, G. Stern, A.-S. Martin, B. Desruelle, V. Ménoret

*“A prototype industrial laser system for cold atom inertial sensing in space”*

Eur. Phys. J. D 73, 248 (2019)

- A. Trimeche, B. Battelier, D. Becker, A. Bertoldi, P. Bouyer, C. Braxmaier, E. Charron, R. Corgier, M. Cornelius, K. Douch, N. Gaaloul, S. Herrmann, J. Müller, E. Rasel, C. Schubert, H. Wu, F. Pereira dos Santos

*“Concept study and preliminary design of a cold atom interferometer for space gravity gradiometry”*

Classical and Quantum Gravity 36, 215004 (2019)

- T. Lévèque, C. Fallet, M. Mandea, R. Biancale, J. M. Lemoine, S. Tardivel, M. Delpech, G. Ramillien, I. Panet, S. Bourgogne, F. Pereira Dos Santos, Ph. Bouyer

*"Correlated atom accelerometers for mapping the Earth gravity field from Space*

Proceedings Volume 11180, International Conference on Space Optics-ICSO 2018, 111800W (2019)

- R. Caldani, K. Weng, S. Merlet, Franck Pereira dos Santos

*“Simultaneous accurate determination of both gravity and its vertical gradient”*

Phys. Rev. A 99, 033601 (2019)

- K. Douch, H. Wu, C. Schubert, J. Müller, F. Pereira dos Santos

*“Simulation-based evaluation of a cold atom interferometry gradiometer concept for gravity field recovery”*

Advances in Space Research 61, 1307-1323 (2018)

- M. Langlois, R. Caldani, A. Trimeche, S. Merlet, and F. Pereira Dos Santos

*“Differential phase extraction in dual interferometers exploiting the correlation between classical and quantum sensors”*

Phys. Rev. A 96, 053624 (2017)

*Copyright 2017 by the American Physical Society*

- F. Pereira Dos Santos

*“Differential phase extraction in an atom gradiometer”*

Phys. Rev. A 91, 063615 (2015)

*Copyright 2015 by the American Physical Society*

- A. Landragin, and F. Pereira Dos Santos

“Accelerometer using atomic waves for space applications”

In Atom Optics and Space Physics, Proceedings of the Enrico Fermi International School of Physics “Enrico Fermi,” Course CLXVIII, Varenna, 2007, edited by E. Arimondo, W. Ertmer, E. M. Rasel, and W. P. Schleich (IOS press) p337-350, arXiv:0808.3837v1 (2009)

- P. Bouyer, F. Pereira Dos Santos, A. Landragin et Ch. J. Bordé

“Atom Interferometric Inertial Sensors for Space Applications”

In “Lasers, Clocks, and Drag Free: Exploration of Relativistic Gravity in Space”, ed. by H. Dittus, C. Lämmerrzahl and S. Turyshev, Springer 2007, 297. (2007)