2. Comparison of atom and photon interferometers using 5D optics Comparison of atom and photon interferometers using 5D optics Christian J. Bordé Académie des Sciences FLORENCE 2009

3. π/2 Pulses Atoms a b space time cτcτ Total phase=Action integral+End splitting+Beam splitters Laser beams

4. Total phase=Action integral+End splitting+Beam splitters Atoms BORDÉ-CHU INTERFEROMETER π/2 π

5. BORDÉ-RAMSEY INTERFEROMETERS

6. Multiple wave interferometer

10. FROM 3 TO 4 SPATIAL DIMENSIONS

11. E(p) p // a b Mac2Mac2 Mbc2Mbc2

12. p Mc E

13. x S =c  t

14. OPTICAL PATH & FERMAT’S PRINCIPLE IN (4+1)D

15. E(p) p BASICS OF ATOM /PHOTON OPTICS Parabolic approximation of slowly varying phase and amplitude

16. Schroedinger-like equation for the atom /photon field: BASICS OF ATOM /PHOTON OPTICS

17. ABCD  LAW OF ATOM/PHOTON OPTICS

18. Ehrenfest theorem + Hamilton equations

19. GENERAL FORMULA FOR THE PHASE SHIFT OF AN ATOM/PHOTON INTERFEROMETER

21. Exact phase shift for the atom gravimeter which can be written to first-order in  with T=T’  Reference: Ch. J. B., Theoretical tools for atom optics and interferometry, C.R. Acad. Sci. Paris, 2, Série IV, p. 509-530, 2001

22. ARBITRARY 3D TIME-DEPENDENT GRAVITO-INERTIAL FIELDS Example: Phase shift induced by a gravitational wave

23. Atomic phase shift induced by a gravitational wave Ch.J. Bordé, Gen. Rel. Grav. 36 (March 2004) Ch.J. Bordé, J. Sharma, Ph. Tourrenc and Th. Damour, Theoretical approaches to laser spectroscopy in the presence of gravitational fields, J. Physique Lettres 44 (1983) L983-990

26. Bordé-Ramsey interferometers Laser beams Atom beam