george r. welch marlan o. scully irina novikova andrey matsko m. suhail zubairy eugeniy mikhailov

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