EllipticityDependent MagnetoOptical Polarization Rotation via MultiPhoton Coherence George

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

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

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

Three Level System For: Low density (single atom response) Monochromatic probe Weak probe W > Wp a W g Wp c gbc b Calculate susceptibility of homogeneously broadened 3 -level system. See for example, Scully and Zubairy, Quantum Optics, Cambridge University Press, 1997. where

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

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

Measurements Recorded signals Transmission S 1+S 2 Rotation angle

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

Corresponding Verde constant: V~7· 103 min·oersted-1·cm-1 Magnetic TGG crystal: V ~0. 4 min·oersted-1·cm-1

Self-rotation

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

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

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

Ellipticity-dependent NMOR: experiment

Isolation of M-scheme enhancement

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

NMOR for atoms with higher angular momentum 3 +M M

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