George R. WelchMarlan O. Scully

Irina NovikovaAndrey Matsko

M. Suhail Zubairy

Eugeniy MikhailovEugeniy Mikhailov

M. Suhail Zubairy

Irina NovikovaAndrey Matsko

Ellipticity-Dependent Magneto-Optical Polarization

Rotation via Multi-Photon Coherence

Office of Naval ResearchAir Force Research LabOffice of Naval ResearchAir Force Research Lab

Texas A&M University

Institute for Quantum Studies

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 EffectsThree (or more) Atomic Energy Levels

a

b

Probe Laser: frequency

c

Natural decay

Coupling Laser ‘‘Drive Laser’’

cb βαψ +=

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

Three Level System

a

b

c

b

c

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

(-0)/

abso

rptio

nin

dex

of r

efra

ctio

n

n=1

Three Atomic Energy Levels

Electromagnetically Induced Transparency

a

bc

Non-Anomolous dispersion

Non-Anomolous dispersion

cd

dn<<> gv0

ω

TransparencyTransparencyTransmission through 10,000 absorption lengths, Harris et al., 1998.

Vg = 1 m/s (c/300,000,000) Ketterly et al., 2001.

Ultra slow light

Ideal System for Studying EIT:Nonlinear Magneto-Optic Rotation

M=1M=-1 M=0

E+ E-

M=0

B

-BB

atomic medium

Linearly polarized light

Measurements

Rotation angle

Transmission S1+S2Recorded signals

√√↵

+−

=φ21

21

SS

SSarcsin

2

1

High Optical Density:Large rotation angle

Scaling to high density and laser power gives multiple oscillations as polarization rotation passes 2

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

+M Scheme

Magneto-optic rotation of elliptical polarization

F'=1

F'=2

√√↵

−=φ

in

outB

B I

Iln

dB

d

00

2

h ( ) ?

?

−

++√√

↵

−=

22

2

00 2

2

2

1ln

2

q

q

I

I

dB

d

in

outB

B γ

μφ

h

A.B. Matsko, I. Novikova, M. S. Zubairy, G.R. Welch, PRA 67, 043805 (2003).

-Scheme

2/)1(2

0

2 +=± qEE

87Rb

+M

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

( )22

2

2

2

2

1/q

q

dB

d

dB

d

M −

++=

Λ+Λ

φφ

Ellipticity-dependent NMOR: experiment

Isolation of M-scheme enhancement

F'=2

F=3

6-photon coherence

Higher-order chains

3 + M Scheme

85Rb

4-photon coherence

NMOR for atoms with higher angular momentum

M

3+M

( ) ( )22

42

22

2

3

34

368

2

1

4

4

q

qq

q

q

dBd

dBd

M

−

+−+

−

+=

φ

φ

Λ

+Λ↔

Conclusion: Study of NMOR of elliptically

polarized light

, M, and higher-chain schemes

Enhancement of rotation due to multiphoton coherence