2. George R. Welch Marlan O. Scully Irina Novikova Andrey Matsko M. Suhail Zubairy Eugeniy Mikhailov M. Suhail Zubairy Irina Novikova Andrey Matsko Ellipticity-Dependent Magneto-Optical Polarization Rotation via Multi-Photon Coherence Office of Naval Research Air Force Research Lab Office of Naval Research Air Force Research Lab Texas A&M University Institute for Quantum Studies

3. George R. Welch Irina Novikova Andrey Matsko M. Suhail Zubairy Eugeniy Mikhailov M. Suhail Zubairy Irina Novikova Andrey Matsko Ellipticity-Dependent Magneto-Optical Polarization Rotation via Multi-Photon Coherence Texas A&M University Institute for Quantum Studies Office of Naval Research Air Force Research Lab Office of Naval Research Air Force Research Lab

4. Outline:  Atomic Coherence  Electromagnetically induced transparency (EIT)  Nonlinear Magneto Optic Polarization Rotation  Large rotation, near Earth’s field  NMOR for Elliptically Polarized Light  Higher order atomic coherence  +M Scheme  Experimental results

5. Atomic Coherence Effects Three (or more) Atomic Energy Levels a b Probe Laser: frequency  c Natural decay  Coupling Laser ‘‘Drive Laser’’ The combined action of the drive and probe lasers produces a quantum superposition of the two lower states: Then, the probe field interacts with this superposition state. Coherence Decay  bc

6. Three Level System a b c   bc  pp For:  Low density (single atom response)  Monochromatic probe  Weak probe  p Calculate susceptibility of homogeneously broadened 3-level system. See for example, Scully and Zubairy, Quantum Optics, Cambridge University Press, 1997. where

7. (  -  0 )/  absorption index of refraction n=1 Three Atomic Energy Levels Electromagnetically Induced Transparency a b c Non- Anomolous dispersion Transparency Transmission through 10,000 absorption lengths, Harris et al., 1998. Vg = 1 m/s (c/300,000,000) Ketterly et al., 2001. Ultra slow light

8. Ideal System for Studying EIT: Nonlinear Magneto-Optic Rotation M=1M=-1M=0 E+E+ E-E- B -BB-BB atomic medium Linearly polarized light

10. Measurements Rotation angle Transmission  S 1 +S 2 Recorded signals

12. High Optical Density: Large rotation angle Scaling to high density and laser power gives multiple oscillations as polarization rotation passes 2 

13. Corresponding Verde constant: V~7·10 3 min·oersted -1 ·cm -1 Magnetic TGG crystal: V ~0.4 min·oersted -1 ·cm -1

19. Self-rotation

22. Ries et al., http://xxx.lanl.gov/abs/quant-ph/0303109

23.  +M Scheme Magneto-optic rotation of elliptical polarization F'=1 F'=2 A.B. Matsko, I. Novikova, M. S. Zubairy, G.R. Welch, PRA 67, 043805 (2003).  -Scheme 87 Rb

24.   +M A.B. Matsko, I. Novikova, M. S. Zubairy, G.R. Welch, Optics Letters, January 15 (2003).

25. Ellipticity-dependent NMOR: experiment

26. Isolation of M-scheme enhancement

27. F'=2 F=3 6-photon coherence Higher-order chains 3  + M Scheme 85 Rb 4-photon coherence

28. NMOR for atoms with higher angular momentum M 3  +M

29. Conclusion:  Study of NMOR of elliptically polarized light  , M, and higher-chain schemes  Enhancement of rotation due to multiphoton coherence