1. Applications of Atom Interferometry to Fundamental Physics on Earth and in Space Applications of Atom Interferometry to Fundamental Physics on Earth and in Space Atomic clocks Christian J. Bordé Gyros, accelerometers, gravimeters General Relativity - Measurement of the fine structure constant - Test of the equivalence principle - Lense-Thirring effect ERICE 2001

3. MOMENTUM E(p) p atom slope=v photon slope=c rest mass ENERGY ERICE 2001

4. E(p) p // Recoil energy ERICE 2001

5. E(p) pp ERICE 2001

6. FIRST-ORDER EXCITED STATE AMPLITUDE

7. REINTERPRETATION OF RAMSEY FRINGES

8. RAMSEY FRINGES WITH TWO SPATIALLY SEPARATED FIELD ZONES b ab a a b ERICE 2001

9. FOUNTAIN CLOCK a a b b ERICE 2001

10. Atom Interferometer Laser beams Atom beam ERICE 2001

11. Laser Cooling of Atoms  reduction of systematic errors  higher interaction times: T drift  µs... ms towards 1-10 s  new atom sources such as atom lasers (Bose-Einstein condensates) “working horse“ of laser cooling: Magneto-optical trap (MOT) MOT density n 10 11 cm -3 temperature T 100  K size  x 1mm BEC 10 14 cm -3 10 nK 10-100  m

12. Optical clocks with cold atoms use the “working horse” of laser cooling: Magneto-optical trap (MOT)  In the future new atom sources such as atom lasers ERICE 2001

13. Time-domain Ramsey-Bordé interferences with cold Ca atoms ERICE 2001

14. Femtosecond lasers as frequency comb generators Time domain: Frequency domain: ceo measurement e.g.: ceo = 2 (m) - (2m) ERICE 2001

15. Experimental Setup J. Stenger, T. Binnewies, G. Wilpers, F. Riehle, H.R. Telle, J.K. Ranka, R.S. Windeler, A.J. Stentz, private communication J. Stenger, T. Binnewies, G. Wilpers, F. Riehle, H.R. Telle, J.K. Ranka, R.S. Windeler, A.J. Stentz, private communication f Ca -Servo & Counting f rep -Servo PLL Counter FVC CEO -Counting Ti:Sa LBO 100 MHz ( H - maser / Cs-clock controlled) 455 986 240 MHz from Ca-Standard (via fiber) MS Fiber Frequency Comb Generator PLL Counter PM PD OC PZTs SESAM - PZT Method:  Count Ca beat  Count ceo  phase-lock f rep ERICE 2001

16. 

17. Interféromètres atomiques Jets atomiques Faisceaux laser

18. E(p) p p RECOIL DOUBLING ERICE 2001

21. 21 HYPER Measurements of  with Atom Interferometers frequency shift due to the photon recoil in a Ramsey-Bordé interferometer HYPER determined by HYPER measured in ground-based experiments, e.g. ion traps accuracy 2  10 -10 2  10 -10 5  10 -9

22. HYPER-precision cold atom interferometry in space

23. BNM-LPTF ( A. Clairon, P. Wolf, Paris) ENS-LKB (C. Salomon, Paris) IAMP (K. Danzmann, Hanover) IQO (W. Ertmer & E.M. Rasel, C.Jentsch, Hanover) IOTA (P. Bouyer, Paris) LHA (N. Dimarcq, A. Landragin, Paris) LGCR (P. Tourrenc, Paris) LPL (C. Bordé, Paris & Hanover) PTB (J. Helmcke, Braunschweig) RAL (M.K. Sandford, R. Bingham, M. Caldwell, B.Kent, Chilton, Didcot) Queen Mary and Westfield College (I. Percival, London) University Trento (S. Vitale, Trento) University Ulm (W. Schleich, Ulm) University Konstanz (C.Lämmerzahl, Konstanz) HYPER The HYPER Core Team:

28. GRAVITOELECTRIC AND GRAVITOMAGNETIC INTERACTIONS: THE USUAL PICTURE Two entries: 1 - Field equations - R.L. Forward, General Relativity for the Experimentalist (1961) - Braginsky, Caves & Thorne, Laboratory experiments to test relativistic gravity (1977) 2 - Motion equation and Schroedinger equation - DeWitt, Superconductors and gravitational drag (1966) - G. Papini, Particle wave functions in weak gravitational fields (1967)

29. Atom Interferometers as Gravito-Inertial Sensors:Analogy between gravitation and electromagnetism 1 00 hg   g  TT ’T Laser beams Atoms Metric tensor Newtonian potential Gravitoelectricfield ERICE 2001

30. Atom Interferometers as Gravito-Inertial Sensors: I - Gravitoelectric field case Laser beams Atoms Gravitational phase shift: TT ’T with light: Einstein red shift with neutrons: COW experiment (1975) with atoms: Kasevich and Chu (1991) Phase shift Circulation of potential Ratio of gravitoelectric flux to quantum of flux Mass independent  (time) 2 ERICE 2001

32. 32 Atom Interferometric Gravimeter Performances : –Resolution: 3x10 -9 g after 1 minute –Absolute accuracy:  g/g<3x10 -9 From A. Peters, K.Y. Chung and S. Chu ERICE 2001

35. 35 ERICE 2001 Gradiometer with cold atomic clouds Yale university  Sensitivity: 3.10 -8 s -2 /  Hz 30 E/  Hz  Potential on earth: 1E/  Hz

37. Laser beams Atoms Atom Interferometers as Gravito-Inertial Sensors: Analogy between gravitation and electromagnetism Metric tensor Gravitomagnetic field Pure inertial rotation ERICE 2001

38. Laser beams Atoms with light: Sagnac (1913) with neutrons: Werner et al.(1979) with atoms: Riehle et al. (1991) Atom Interferometers as Gravito-Inertial Sensors: II - Gravitomagnetic field case Phase shift Circulation of potential Ratio of gravitomagnetic flux to quantum of flux Sagnac phase shift: ERICE 2001

44. 44 Atomic Beam Gyroscope Sensitivity: 6.10 -10 rad.s -1 /  Hz (Yale University) Magnetic shield Cs oven Wave packet manipulation Atomic beams State preparation Laser cooling Detection Rotation rate (x10 -5 ) rad/s -10-50510 15 20 Normalized signal 0 1 Interference fringes ERICE 2001

45. 45 ERICE 2001

46. HYPER HYPER -precision cold atom interferometry in space

47. 47 HYPER Atomic Sagnac Unit Interferometer length 60 cm Atom velocity 20 cm/s Drift time 3 s 10 9 atoms/shot Sensitivity 2x10 -12 rad/s 125th Anniversary of the Metre Convention Area 54 cm 2

48. LENSE-THIRRING FIELD Gravitomagnetic field lines Gravitomagnetic field generated by a massive rotating body: Field lines ~ to magnetic dipole:

49. 49 HYPER HYPER Lense-Thirring measurement Signal vs time Hyper carries two atomic Sagnac interferometers, each of them is sensitive to rotations around one particular axis. The two units will measure the vector components of the gravitomagnetic rotation along the two axes perpendicular to the telescope pointing to a guide star. 125th Anniversary of the Metre Convention

50. 50 HYPER HYPER The HYPER Satellite ASU1 ASU2 Star Tracker Pointing Cold Atom Source ASU Reference (connected to the Raman Lasers & to the Star Tracker) ONERA 2001

51. Atomic Sagnac Unit 1 Atomic Sagnac Unit 2 Star Tracker Raman Lasers Module Laser Cooling Module Conclusion Expected Overall Performance: 3x10 -16 rad/s over one year of integration i.e. a S/N~100 at twice the orbital frequency Resolution : 3x10 -12 rad/s /  Hz Lense-Thirring Measurement

52. 52 HYPER measurement of the fine-structure constant improved by one or even two orders of magnitude to test QED latitudinal mapping of the general relativistic gravito-magnetic effect of the Earth (Lense-Thirring-effect) HYPER The HYPER Mission Goals (1) 

53. 53 HYPER investigation of decoherence of matter-waves for the first time cold-atom gyroscopes control a spacecraft HYPER The HYPER Mission Goals (2)

54. HYPER HYPER Summary HYPER HYPER will investigate precision measurement of  (h/m at ) gravito-inertial effects (Lense-Thirring-Effect) decoherence (effects of quantum gravity) navigation by atom interferometric sensors

55. ABCD  PROPAGATOR

57. GRAVITOELECTRIC AND GRAVITOMAGNETIC INTERACTIONS: THE USUAL PICTURE Two entries: 1 - Field equations - R.L. Forward, General Relativity for the Experimentalist (1961) - Braginsky, Caves & Thorne, Laboratory experiments to test relativistic gravity (1977) 2 - Motion equation and Schroedinger equation - DeWitt, Superconductors and gravitational drag (1966) - G. Papini, Particle wave functions in weak gravitational fields (1967)

58. A new analogy between electromagnetic and gravitational interactions

59. RELATIVISTIC PHASE SHIFTS