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Ellipticity-Dependent Magneto-Optical Polarization Rotation via Multi-Photon Coherence. George R. Welch Marlan O. Scully Irina Novikova Andrey Matsko M. Suhail Zubairy Eugeniy Mikhailov. Texas A&M University Institute for Quantum Studies. Irina Novikova Andrey Matsko. M. Suhail Zubairy. - PowerPoint PPT Presentation
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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
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