Ellipticity-Dependent Magneto-Optical Polarization
Rotation via Multi-Photon Coherence
George R. Welch
Marlan O. Scully
Texas A&M
University
Irina
Irina Novikova
Novikova
Andrey
Andrey Matsko
Matsko
Institute for
Quantum
Studies
M.
M. Suhail
Suhail Zubairy
Zubairy
Eugeniy
Mikhailov
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
 L+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
  b   c
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
c
NonAnomolous
dispersion
dn
> 0 vg  c
dw
n=1
Ultra slow
light
Transmission through
10,000 absorption lengths,
Harris et al., 1998.
Vg = 1 m/s (c/300,000,000)
Ketterly et al., 2001.
absorption
b
Transparency
(w-w0)/g
Refractive
Refractive index
index
Ideal System for Studying EIT:
Nonlinear Magneto-Optic Rotation
M=0
E-
-BB
M=-1
M=0
Transmission
Linearly polarized
light
M=1
Laserfrequency
frequency
Laser
B
atomic medium
Magnetic field
Rotation angle
E+
Magnetic field
S1, arb.units
Transmission,
arb.units
Measurements
-15
-5
5
-15
15
Magnetic field, mG
Rotation angle f ,
rad
5
Magnetic field, mG
15
Transmission  S1+S2
S2, arb.units
-5
5
Magnetic field, mG
Recorded signals
-15
-5
15
0.5
0.25
0
-15
-5
-0.25
5
15
-0.5
Magnetic field, mG
 S1  S2 
1

Rotation angle f  arcsin 
2
 S1  S2 
High Optical Density:
Photodetector signals
Large rotation angle
-600
-400
-200
0
200
400
600
Magnetic field, mG
Scaling to high density and laser power
gives multiple oscillations as polarization
rotation passes 2p
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
L-Scheme
L+M
Scheme
87Rb
F'=2
2 


2 BB  IIout

ddff
2
1
2

q


ln out  
 
ln
2

2
dB

g
I
dB BB
g 00  Iinin 
00
2 2  q 



2
2
E  E0 (q  1) / 2
A.B. Matsko, I. Novikova, M. S. Zubairy, G.R. Welch, PRA 67, 043805 (2003).
df
dB L  M
Relative rotation rate
4
/
df
1
2  q2
 
dB L 2 2  q 2 2

3

L+M
2
1
L
0
0
0.5
1
Ellipticity parameter q
A.B. Matsko, I. Novikova, M. S. Zubairy, G.R. Welch, Optics Letters, January 15 (2003).
Ellipticity-dependent NMOR: experiment
2
Relative rotation rate
1.5
1.5
1.5
111
1.8
T=32
T=55
T=70.5
T=85
T-90
1.6
1.4
1.2
1
0.8
0
0.5
1
Ellipticity parameter q
0.5
0.5
0.5
0.8
Output ellipticity e out
Relative
Relative rotation
rotation rate
rate
222
0.6
000
000
0.5
0.5
0.5
0.4
11
Ellipticity
parameterqqq
0.2
Ellipticity
parameter
Ellipticity
parameter
0
0
0.2
0.4
T=30
T=70.5
T=85
T=90
0.6
Input ellipticity e in
0.8
Trans. 1-1
Trans. 1-1
P=2mW
Trans.
1-1
P=2mW
P=1mW
Trans. 2-1
P=1mW
wide beam
Isolation of M-scheme enhancement
Higher-order chains
F'=2
85Rb
F=3
4-photon coherence
6-photon coherence
3L + M Scheme
NMOR for atoms with higher angular
momentum
2
Relative rotation rate
Relative rotation rate
10
8
6
3L+M
4
2
M
1.5
1
0.5
0
0
0
0
0.5
df
dB L

4  q2
4  q 
2 2
0.4
0.6
0.8
1
Ellipticity parameter q
df
dB 3L M
0.2
F=2->F'=1 transition 87Rb
Ellipticity parameter q
F=3->F'=2 transition 85Rb
1 8  6q2  3q4

2 4  3q2 2


1
Conclusion:
 Study of NMOR of elliptically
polarized light
 L, M, and higher-chain
schemes
 Enhancement of rotation due
to multiphoton coherence