Introduction to HYPER Measuring Lense-Thirring with Atom Interferometry

1. Introduction to HYPERMeasuring Lense-Thirring with Atom Interferometry P. BOUYERLaboratoire Charles Fabry de l’Institut d’OptiqueOrsay, France

2. Agenda Introduction to Lense-Thirring Effect Key requirements for the HYPER mission The Payload : Atomic Sagnac Unit Atom Inertial sensors : How does-it work ? HYPER and future space missions Early earth-based Atom Inertial sensors Ongoing earth based projects

3. General relativistic effect Gravitomagnetism Curvature of space-time around massive rotating bodies The Lense-Thirring Effect Courtesy of Astrium

4. General relativistic effect gravitomagnetism Curvature of space-time around massive rotating bodies Strong effect near black holes Precession and twist of acretion disks The Lense-Thirring Effect Images from Center for Theoretical Astrophysics University of Illinois at Urbana-Champaign

5. General relativistic effect gravitomagnetism Curvature of space-time around massive rotating bodies Strong effect near black holes Precession and twist of acretion disks Small effect close to earth Possible to measure average frame dragging LAGEOS GP-B The Lense-Thirring Effect

6. General relativistic effect gravitomagnetism Curvature of space-time around massive rotating bodies Strong effect near black holes Precession and twist of acretion disks Small effect close to earth Possible to measure average frame dragging LAGEOS GP-B Mapping Lense-Thirring HYPER The Lense-Thirring Effect

7. Agenda Introduction to Lense-Thirring Effect Key requirements for the HYPER mission The Payload : Atomic Sagnac Unit Atom Inertial sensors : How does-it work ? HYPER and future space missions Early earth-based Atom Inertial sensors Ongoing earth based projects

8. The Lense-Thirring effect The periodic cycle is half the orbit period 2 ASU in quadrature Geodetic de Sitter 40 to 80 times bigger Constant for circular orbit The HYPER mission configuration 3x10-14 rad/s -3x10-14 rad/s

9. MISSION DRIVERS & CONSTRAINTS Low-Earth Orbit (for mapping the Lense-Thirring effect) Extremely demanding pointing accuracy Relative Pointing Error: 10-8 radians (2 marcsec) over 3 sec Stable relative pointing between PST and ASU Drag-free environment 10 -9 g residual accelerations Precise control of gravity gradients The HYPER mission configuration • The Lense-Thirring effect • Maximum about 10-14 rad/s • 1 year integration • High accuracy of rotation measurement

10. Agenda Introduction to Lense-Thirring Effect Key requirements for the HYPER mission The Payload : Atomic Sagnac Unit Atom Inertial sensors : How does-it work ? HYPER and future space missions Early earth-based Atom Inertial sensors Ongoing earth based projects

11. The HYPER Payload ASU1 Cold Atom Source Precision Star Tracker Pointing ASU2 ASU Reference (connected to the Raman Lasers & to the Star Tracker)

12. Payload components ASU Resolution: 3x10-11rad/s/Hz ASU2 Precision Star Tracker ASU1 • Expected Overall Performance: • 3x10-15rad/s over one year of integration i.e. a S/N~10 at twice the orbital frequency Raman Lasers Module Laser Cooling Module

13. Agenda Introduction to Lense-Thirring Effect Key requirements for the HYPER mission The Payload : Atomic Sagnac Unit Atom Inertial sensors : How does-it work ? HYPER and future space missions Early earth-based Atom Inertial sensors Ongoing earth based projects

14. Manipulating atoms with light • Atom Interferometry uses laser induced resonance oscillation • Atoms with 2 different states (red/blue) with different energy • Laser with frequency equal to energy difference Time

15. Manipulating atoms with light • Controlling the interfaction time controls the result of the oscillation • Half way between red and blue • P/2 pulse Time

16. Manipulating atoms with light • Controlling the interfaction time controls the result of the oscillation • Half way between red and blue • P/2 pulse • Another half : all the way from red to blue • P pulse Time

17. Manipulating atoms with light • Controlling the interfaction time controls the result of the oscillation • Half way between red and blue • P/2 pulse • Another half : all the way from red to blue • P pulse • The other way : from blue to red • P pulse Time

18. Manipulating atoms with light • The p/2 pulse is a beam splitter • Half way between red and blue • Coherent superposition of red and blue

19. Manipulating atoms with light • The p/2 pulse is a beam splitter • Half way between red and blue • Coherent superposition of red and blue • The red and blue states correspond to different kinetic energies • Velocities along laser direction • Blue : excited state • Photon absorbed from laser • Photon momenum transferred to atom • Recoil velocity ≈1cm/s • Red : «ground» state • No photon absorbed • No velocity

20. The Atom Interferometer • The first p/2 pulse - beam splitter • Creates the coherent superposition

21. The Atom Interferometer • The first p/2 pulse - beam splitter • Creates the coherent superposition • The two parts of the atom separate • Splitting between the two parts

22. The Atom Interferometer • The first p/2 pulse - beam splitter • Creates the coherent superposition • The two parts of the atom separate • Splitting between the two parts • Apply the p pulse - mirror • Changes blue to red • Velocity from 0 to recoil • Changes red to blue • Velocity from recoil to 0

23. The Atom Interferometer • The first p/2 pulse - beam splitter • Creates the coherent superposition • The two parts of the atom separate • Splitting between the two parts • Apply the p pulse - mirror • Changes blue to red • Velocity from 0 to recoil • Changes red to blue • Velocity from recoil to 0 • Apply last p/2 pulse when the two parts overlap again

24. The Atom Interferometer • The first p/2 pulse - beam splitter • Creates the coherent superposition • The two parts of the atom separate • Splitting between the two parts • Apply the p pulse - mirror • Changes blue to red • Velocity from 0 to recoil • Changes red to blue • Velocity from recoil to 0 • Apply last p/2 pulse when the two parts overlap again • Red or Blue output depend of phase difference between two path Atomic State phase difference Df

25. The atom «reads» the phase of the laser • Each time the atom changes state, the laser imprints its phase on the atom «Stationary» Laser Phase eikx «Stationary» Laser Phase eikx «Stationary» Laser Phase eikx «Stationary» Laser Phase eikx «Stationary» Laser Phase eikx

26. 0 f1 The atom «reads» the phase of the laser • Each time the atom changes state, the laser imprints its phase on the atom

27. 0 f1 The atom «reads» the phase of the laser • Each time the atom changes state, the laser imprints its phase on the atom

28. 0 f1 f2l -f2r The atom «reads» the phase of the laser • Each time the atom changes state, the laser imprints its phase on the atom

29. 0 f1 f2l -f2r The atom «reads» the phase of the laser • Each time the atom changes state, the laser imprints its phase on the atom

30. 0 f1 f2l -f2r -f3 0 The atom «reads» the phase of the laser • Each time the atom changes state, the laser imprints its phase on the atom Final phase difference (f1 -f2r)-(f2l -f3)

31. 0 f1 f2l -f2r -f3 0 Phase shift comes from acceleration Final phase difference (f1 -f2r)-(f2l -f3)0

32. The atomic sagnac unit • 3 separated diffraction zones • Corriolis acceleration comes from rotating laser

33. a a The atomic sagnac unit • 3 separated diffraction zones • Corriolis acceleration comes from rotating laser • Rotation and acceleration signal are mixed • Need dual ASU for real rotation measurement

34. The atomic sagnac unit Interferometer length 60 cm Atom velocity 20 cm/s Drift time 3 s 109atoms/shot Sensitivity 3x10-11 rad/s

35. MISSION DRIVERS & CONSTRAINTS • Typical measurement time : 3 sec • Typical rotation sensitivity of ASU : 10-11 rad/s (1 sec) • Signal detection : 2.2x10-15 rad/s rms @ half orbit • ASU measures lasers rotations/vibrations • Low-Earth Orbit (for mapping the Lense-Thirring effect) • Extremely demanding pointing accuracy • Relative Pointing Error: 10-8 radians (2 marcsec) over 3 sec • Stable relative pointing between PST and ASU about 1 arcsec • Drag-free environment • 10-9 g residual accelerations • Precise control of gravity gradients • Knowledge and/or control to better than 10-10 g/m

36. Agenda Introduction to Lense-Thirring Effect Key requirements for the HYPER mission The Payload : Atomic Sagnac Unit Atom Inertial sensors : How does-it work ? HYPER and future space missions Early earth-based Atom Inertial sensors Ongoing earth based projects

37. HYPER and future space missions • HYPER can benefit from TD of other missions • PHARAO/ACES • Laser Cooling Benches • Radiofrequency chains • LISA/SMART-2/GOCE/MICROSCOPE • Drag Free • Accelerometers • LAGEOS/GOCE/MICROSCOPE • AOCS (low orbit) • GP-B • Precision Star Tracker (HYPER more demanding) • Also from LISA

38. Agenda Introduction to Lense-Thirring Effect Key requirements for the HYPER mission The Payload : Atomic Sagnac Unit Atom Inertial sensors : How does-it work ? HYPER and future space missions Early earth-based Atom Inertial sensors Ongoing earth based projects

39. Stanford laboratory gravimeter Courtesy of S. Chu, Stanford 10-8 g

40. Atoms L a s e r B e a m 1.4 m Atoms Stanford/Yale laboratory gravity gradiometer Courtesy of M. Kasevich, Stanford Demonstrated diffential acceleration sensitivity: 4x10-9 g/Hz1/2 (2.8x10-9 g/Hz1/2 per accelerometer) Distinguish gravity induced accelerations from those due to platform motion with differential acceleration measurements.

41. Stanford/Yale laboratory gyroscope Rotation signal Courtesy of M. Kasevich, Stanford Bias stability AI gyroscope, demonstrated laboratory performance: 2x10-6 deg/hr1/2 ARW < 10-4 deg/hr bias stability Compact, fieldable (navigation) and dedicated very high-sensitivity (Earth rotation dynamics, tests of GR) geometries possible.

42. Agenda Introduction to Lense-Thirring Effect Key requirements for the HYPER mission The Payload : Atomic Sagnac Unit Atom Inertial sensors : How does-it work ? Early earth-based Atom Inertial sensors HYPER and future space missions Ongoing earth based projects

43. Cold Atom Inertial Base (Paris) Courtesy of A. Landragin (Paris) Theoretical model (include. relativity) by C. Bordé

44. CASI : Cold Atom Sagnac Interferometer (Hannover) Courtesy of E. Rasel (Hannover)) Rubidium-87 launch velocities:  1 m/s enclosed area A  0.2 cm2 expected sensitivity: DW 10-8-10-9 rad/sHz-1

45. Courtesy of G. Tino (Fireze)

46. Interferometry with Coherent Ensemble (Paris) Courtesy of P. Bouyer (Paris) • ONERA-SYRTE-IOTA-CNES project • Explore Best coherent source configuration for space • Study coherence properties of degenerate source of atoms • Interferometry with coherent sources