1. Measuring the Earth’s gravity field with cold atom interferometers Olivier Carraz, Christian Siemes, Luca Massotti, Roger Haagmans, Pierluigi Silvestrin Paris, France 28/11/2014

2. Earth Gravity Field

3. What is needed in the near future? Future Concepts?

4. Cold Atom Physics 1.Why cold atoms? a.Study/observe internal structure of free atoms (≠ solid state physics) b.Atom waves potentially more interesting than electron or neutron waves (neutral + rich internal structure) c.Interaction with external electric fields and gravity 2.BUT: RT atom speeds ~ 300 m/s a.Atom beams have low coherence  difficult to handle as waves b.Limited observation time (few ms) on a table-top experiment 3.Low temperature physics a.4K (LHe) He thermal velocity ~ 90 m/s b.Cryopump effect: condensation  no gas phase 4.Laser cooling techniques: a.Magneto Optical Traps (MOT) < 10µK ~ cm/s b.Adiabatic Expansion c.Raman Cooling d.Velocity Selective Coherent Population Trapping e.Evaporative cooling in magnetic or optical traps ~ 100nK f.Sympathetic cooling (involving more than one species) Velocity-distribution data of a gas of rubidium atoms, confirming the discovery of a new phase of matter, the Bose–Einstein condensate.

5. AI Gravimeter : How does it work ? Free fall of an object - Inertial reference : Earth - Free fall of an object in the inertial reference - ‘Measurement’ of the free falling... z g EARTH Here - Object : Cold atoms in the vacuum - Measurement of the free falling by atomic interferometry...

6. Principle of an AI gravimeter Atoms are cooled down (4  K ~ 2 cm/s) Long time of interaction

7. Laser cooling LASER z E 0   m f =0 m f =+1 m f Trapping by Zeeman effect Cooling by Doppler effect              

8. Bose Einstein Condensate

10. Atom interferometry Matter wave Louis De Broglie (1924) a.Waves phenomena for matter: –Diffraction –Interferences b.Interferences : Atoms have different paths to follow Louis de Broglie Nobel Price 1929 Young experiment realised with cold atoms at NIST

11. t 0 1 Temps Probability a b  -pulse Stimulated Raman transition Coherent transfert of population a b i Energy Rabi Oscillation Control the transfert from state a to state b a  /2-pulse Coherent superposition

12. Stimulated Raman transition Coherent transfert of population a b i Energy Give an important and directive recoil pulse Contrapropagating Lasers For Rb, 2.v rec ~ 12 mm.s -1

13. Principle of an AI gravimeter 1.Chu-Bordé Configuration : 2.Interferometric signal : The phase of the laser is printed on the phase of the atoms during Raman transitions : Stationary wave referenced to the mirror

14. AI Performances

15. Gyroscope – Gradiometer : Raman in common mode Gyroscope : 2 accelerometers with physical surface rejecting acceleration in differential mode Gradiometer : 2 gravimeters rejecting common vibrations of the miror.  /2   g    g    /2   g1  g2 x t z z

16. Concept of an AI inertial sensor for space : 1D  /2  y z  g1  g2 -v v  g3  g4 -v v

17. CAI GG Concept – design for one axis Gravity gradiometer (V zz – w x 2 – w y 2 ), gyroscope (w x ), accelerometer (a z )

18. CAI GG Concept – design for three axes Gravity gradiometer (V zz – w x 2 – w y 2 ), gyroscope (w x ), accelerometer (a z ) Theoretical performance: (V+Ω 2 )  4.7 mE / sqrt(Hz) Ω  35 prad/s / sqrt(Hz) a  2 pm/s 2 / sqrt(Hz) Ambiguity due to phase jumps: (V+Ω 2 )  16 E Ω  160 nrad/s a  7.8 nm/s 2

19. CAI GG Concept – simulations by Christian Siemes (email: christian.siemes@esa.int) christian.siemes@esa.int Earth System Model http://www.gfz-potsdam.de/en/research/organizational-units/departments-of- the-gfz/department-1/earth-system-modelling/services/esaesm/ Instrument noise 4.7 mE/sqrt(Hz) GG 2 cm orbit 100 nrad attitude (STR and CAI GG) Background model errors 10% AO … time-variable gravity field 10% AOHIS … mean gravity field EOT11a – GOT4.7 (8 major tidal constituents) GRACE Science Team Meeting 2014, Potsdam (Germany)

20. CAI GG Concept – simulations by Christian Siemes (email: christian.siemes@esa.int) christian.siemes@esa.int Time variable gravity field Orbit: 31 day repeat, a = 400 km, e = 0.001, i = 89 o  Mean  Omission Modelling error … relevant GRACE Science Team Meeting 2014, Potsdam (Germany)

21. CAI GG Concept – simulations by Christian Siemes (email: christian.siemes@esa.int) christian.siemes@esa.int Time variable gravity field Orbit: 31 day repeat, a = 400 km, e = 0.001, i = 89 o Modelling error … relevant Position noise … negligible GRACE Science Team Meeting 2014, Potsdam (Germany)

22. CAI GG Concept – simulations by Christian Siemes (email: christian.siemes@esa.int) christian.siemes@esa.int Time variable gravity field Orbit: 31 day repeat, a = 400 km, e = 0.001, i = 89 o Modelling error … relevant Position noise … negligible Attitude noise … negligible GRACE Science Team Meeting 2014, Potsdam (Germany)

23. CAI GG Concept – simulations by Christian Siemes (email: christian.siemes@esa.int) christian.siemes@esa.int Time variable gravity field Orbit: 31 day repeat, a = 400 km, e = 0.001, i = 89 o Modelling error … relevant Position noise … negligible Attitude noise … negligible AO error … relevant GRACE Science Team Meeting 2014, Potsdam (Germany)

24. CAI GG Concept – simulations by Christian Siemes (email: christian.siemes@esa.int) christian.siemes@esa.int Time variable gravity field Orbit: 31 day repeat, a = 400 km, e = 0.001, i = 89 o Modelling error … relevant Position noise … negligible Attitude noise … negligible AO error … relevant OT error … relevant GRACE Science Team Meeting 2014, Potsdam (Germany)

25. CAI GG Concept – simulations by Christian Siemes (email: christian.siemes@esa.int) christian.siemes@esa.int Time variable gravity field Orbit: 31 day repeat, a = 400 km, e = 0.001, i = 89 o Modelling error … relevant Position noise … negligible Attitude noise … negligible AO error … relevant OT error … relevant GG noise … bottle neck GRACE Science Team Meeting 2014, Potsdam (Germany)

26. CAI GG Concept – simulations by Christian Siemes (email: christian.siemes@esa.int) christian.siemes@esa.int Mean gravity field Orbit: 61 day repeat, a = 250 km, e = 0.001, i = 89 o GRACE Science Team Meeting 2014, Potsdam (Germany)

27. CAI GG Concept – simulations by Christian Siemes (email: christian.siemes@esa.int) christian.siemes@esa.int Mean gravity field Orbit: 61 day repeat, a = 250 km, e = 0.001, i = 89 o GRACE Science Team Meeting 2014, Potsdam (Germany)

28. Hybridization Classical/Quantum sensors

29. Electro-static Accelerometer

30. Hybridization Classical/Quantum sensors Benefits of the performance of electro static accelerometers at high frequency. Calibration for long term measurements. Compacity

31. Hybridization Classical/Quantum sensors J. Lautier, L. Volodimer, T. Hardin, S. Merlet, M. Lours, F. Pereira Dos Santos, and A. Landragin "Hybridizing matter-wave and classical accelerometers” Appl. Phys. Lett. 105, 144102 (2014)

32. CAI GG Concept – studies Running studies: -Compact Vacuum chamber for an Earth Gravity Gradiometer based on Laser-Cooled Atom Interferometry (2014) Planned studies -Study of a Cold-Atom interferometry gravity gradiometer sensor and mission concept (KO ~ 2014) -Development of Cooling/Raman Laser source with enhanced operational features (KO ~ 2015) -Development of phase and frequency modulators for atom sensor systems -Hybrid Atom Electrostatic System for Satellite Geodesy (KO ~ 2015)

33. Conclusion & Outlook 1.Future challenging gravity mission (Mass distribution and mass transport) a.Explore deeper the Earth b.Comprehension of other planets 2.Different concepts for measuring Geoid a.Satellite ranging b.Gravity gradiometer 3.Atom interferometry can improve both techniques a.Hybridization classical accelerometers/AI b.Cold atom gradiometer

34. Improvements in Optical Frequency Standards Essen’s Cs clock Cs redefinition of the second Cs fountain clocks Hg + Al + Sr Hg + Sr Yb Hg +, Yb +, Ca H H H Ca Iodine-stabilised HeNe Femtosecond combs (Margolis, 2008) 10 -17 =10 cm in height

35. Relativistic Geodesy: unify geometry (GNSS) & gravitational positioning geoid ellipsoid B’’ B’ B A C D E Geometry measured with GPS Gravitational potential measured with optical clocks & satellite two-way links Satellite link 50 m clock frequency B / A = T A /T B = 1 + (V B - V A )/c 2 Gravitational potential (x,y,z)