George R. Welch Marlan O. Scully Irina Novikova Andrey Matsko M. Suhail Zubairy Eugeniy Mikhailov
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Transcript of 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
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