Transcript Nonlinear Magneto-Optical Rotation with Frequency

Nonlinear Magneto-Optical Rotation
with
Frequency-Modulated Light
Derek Kimball
Dmitry Budker
Simon Rochester
Valeriy Yashchuk
Max Zolotorev
and many others...
Some of the many others:
Budker Group:
Non-Berkeley Folks:
D. English
K. Kerner
C.-H. Li
T. Millet
A.-T. Nguyen
J. Stalnaker
A. Sushkov
Technical Support:
M. Solarz
A. Vaynberg
G. Weber
J. Davis
E. B. Alexandrov
M. V. Balabas
W. Gawlik
Yu. P. Malakyan
A. B. Matsko
I. Novikova
A. I. Okunevich
H. G. Robinson
A. Weis
G. R. Welch
Funding: ONR
Plan:
• Linear Magneto-Optical (Faraday) Rotation
• Nonlinear Magneto-Optical Rotation (NMOR)
– Coherence effects
– Paraffin-coated cells
– Experiments
Review: Budker, Gawlik, Kimball, Rochester, Yashchuk,
Weis (2002). Rev. Mod. Phys. 74(4), 1153-1201.
• NMOR with Frequency-Modulated light (FM NMOR)
– Motivation
– Experimental setup
– Data: B-field dependence, spectrum, etc.
• A little mystery...
• Applications
– Sensitive magnetometry
– EDM search?
Linear Magneto-Optical (Faraday) Rotation
1846-1855: Faraday discovers magneto-optical rotation
1898,1899: Macaluso and Corbino discover resonant character
of Faraday rotation
Linear Polarization
Medium
0l
 = (n+-n-)
= (n+-n-) l
2c


Circular
Components
Magnetic
Field
Linear Magneto-Optical (Faraday) Rotation
1898: Voigt connects Faraday rotation to the Zeeman effect
Linear Magneto-Optical (Faraday) Rotation
Linear Magneto-Optical (Faraday) Rotation
0.6
0.5
0.4
Rotation angle  (rad)
0.3
0.2
0.1
-0.0
-0.1
B ~ 400 G
-0.2
-0.3
-0.4
-0.5
-0.6
-5
-4
-3
-2
-1
0
1
2
3
Normalized magnetic field (b = 2gF0B / )
2 g F 0 B / 
l

2
2l0 1  2 g F 0 B / 
4
5
Nonlinear Magneto-Optical Rotation
• Faraday rotation is a linear effect because rotation is independent
of light intensity.
• Nonlinear magneto-optical rotation possible when light modifies
the properties of the medium:
Number of atoms
1
0.8
0.5
Index of refraction
 Spectral hole-burning:
B0
0
B=0
-0.5
0.6
-1
0.4
Re[n+-n-]
0.2
-2
-2
-1
0
1
Atomic velocity
2
-1
0
1
Light detuning
2
3
Small field NMOR enhanced!
3
Coherence Effects in NMOR
x-polarized light interacts
with coherent superposition
of ground state Zeeman sublevels
1
 M  1  M  1 
2
Three-stage process:
1.
Resonant light polarizes atomic sample via optical pumping.
2. Polarized atoms precess in the magnetic field.
3. This changes the optical properties of the medium
 rotation of light polarization.
Coherence Effects in NMOR
Optical pumping:
 Polarizes atoms
 Aligns magnetic dipole moments
 Creates optical anisotropy (linear dichroism)
Coherence Effects in NMOR
Visualization of atomic polarization:
Draw 3D surface where distance from origin equals the probability
to be found in a stretched state (M=F) along this direction.
Rochester and Budker (2001). Am. J. Phys. 69, 450-4.
Coherence Effects in NMOR

  B torque causes atomic polarization to precess:

B
.
Coherence Effects in NMOR

  B torque causes atomic polarization to precess:

Coherence Effects in NMOR
(polarized atoms only)
• Relaxation of atomic polarization:
• Equilibrium conditions result in net atomic
polarization at an angle to initial light polarization.
• Plane of light polarization is rotated,
just as if light had propagated through
a set of “polaroid” films.
Coherence Effects in NMOR
Magnetic-field dependence of NMOR due to coherence effects
can be described by the same formula we used for linear Faraday
rotation, but   rel :

2 g F 0 B /  rel
l
l
 rel t

dt e
sin 2 g F 0 Bt  

2l0 t 0
2l0 1  2 g F 0 B /  rel 2
How can we get slowest possible rel?
Paraffin-coated cells
Academician Alexandrov has
brought us some beautiful
“holiday ornaments”...
Magical!
Paraffin-coated cells
F=3
Alkali atoms work best with
paraffin coating...
F=2
F=1
5 2 P3/2
D2 (780.0 nm)
F=0
Most of our work involves Rb:
~
~
F=2
D1 (794.8 nm)
5 2 P1/2
87Rb
496 MHz
(I = 3/2)
812 MHz
F=1
~
~
F=2
5 2S1/2
F=1
6835 MHz
Paraffin-coated cells
Polarized atoms can bounce off the walls of a paraffin-coated
cell ~10,000 times before depolarizing!
This can be seen using the method of “relaxation in the dark.”

4

B
Paraffin-coated cells
Probe transmission (arb. units)
0.26
0.25
Bx = 100 G
rel = 2  1.004(2) Hz
0.24
0.23
0.22
0.0
0.2
0.4
0.6
0.8
1.0
Time (s)
1.2
1.4
1.6
1.8
2.0
Experimental Setup
lock-in
magnetic
coil
reference
DC
polarimeter
calibration
magnetic
shield
Rb-cell
pre-amplifier
polarizer
analyzer
polarizationmodulator
PD1
PD2
magnetic
field
current
absorption
first harmonic
attenuator
light-pipe
PD
control
and data
acquisition
spectrum analyzer
fluorescence
laser frequency control
feedback
differential
amplifier
polarizationrotator
Dichroic Atomic Vapor Laser Lock
PD
BS
PD
/4
uncoated Rb cell
in magnetic field
P
diode laser
Magnetic Shielding
ø 18"
ø 21"
16"
20"
25"
ø 24.5"
12"
Four-layer ferromagnetic magnetic shielding with nearly
spherical geometry reduces fields in all directions
by a factor of 106!
Magnetic Shielding
3-D coils allow control
and cancellation of fields
and gradients inside shields.
NMOR Coherence Effect in Paraffin-coated Cell
85Rb
D2 Line, I = 50 W/cm2,
F=3  F’=4 component
10
8
Rotation Angle (mrad)
6
4
2
0
-2
-4
-6
-8
-10
-10
-8
-6
-4
-2
0
2
4
Magnetic Field (G)
Kanorsky, Weis, Skalla (1995). Appl. Phys. B
60, 165.
Budker, Yashchuk, Zolotorev (1998). PRL
rel
81, 5788.
Budker, Kimball, Rochester, Yashchuk, Zolotorev (2000). PRA 62, 043403.

= 2  0.9 Hz
6
8
10
Sensitive measurement of magnetic fields
85Rb
D2 line, F=3  F’ component,
I = 4.5 mW/cm2
Bz) (10-12 G/Hz1/2)
50
40
30
3 1012 G/ Hz
20
10
Transmission
0
1.0
0.9
0.8
0.7
-1.2
-0.8
-0.4
-0.0
0.4
Relative Frequency (GHz)
0.8
1.2
The dynamic range of an NMOR-based magnetometer is
limited by the width of the resonance:
10
8
Rotation Angle (mrad)
6
4
2
0
-2
B ~ 2 G
-4
-6
-8
-10
-10
-8
-6
-4
-2
0
2
4
6
8
10
Magnetic Field (G)
How can we increase the dynamic range?
NMOR with Frequency-Modulated Light
• Magnetic field modulates optical properties of medium at 2L.
• There should be a resonance when the frequency of light is
modulated at the same rate!
Experimental
Setup:
Inspired by:
Barkov, Zolotorev (1978).
JETP Lett. 28, 503.
Barkov, Zolotorev, Melik-Pashaev (1988).
JETP Lett. 48, 134.
NMOR with Frequency-Modulated Light
1.00
In-phase component
0.75
87Rb
D1 Line
F=21
0.50
First Harmonic Amplitude (mrad)
0.25
0.00
-0.25
-0.50
m = 21 kHz
-0.75
-1.00
1.00
Out-of-phase (quadrature) component
0.75
 = 2220 MHz
0.50
P  15 W
0.25
0.00
-0.25
Budker, Kimball,
Yashchuk, Zolotorev (2002).
PRA 65, 055403.
-0.50
-0.75
-1.00
-1600
-1200
-800
-400
0
400
Longitudinal Magnetic Field (G)
800
1200
1600
NMOR with Frequency-Modulated Light
Low field resonance:
L  rel
Low-field FM NMOR resonance is analogous
to that seen in conventional NMOR.
NMOR with Frequency-Modulated Light
High field resonances:
L >> rel
• Laser frequency modulation  modulation of optical pumping.
• If periodicity of pumping is synchronized with Larmor precession,
atoms are pumped into aligned states rotating at L.
NMOR with Frequency-Modulated Light
• Optical properties of the atomic medium are modulated at 2L.
• Resonances occur for n m = 2L. Largest amplitude for n = 1.
NMOR with Frequency-Modulated Light
• Quadrature signals arise due to
difference in phase between
rotating medium and probe light.
• Second harmonic signals appear for
m = L.
First Harmonic Amplitude (mrad)
NMOR with Frequency-Modulated Light
(a)
2
Low field resonance
1
0
-1
-2
(b)
2
High field resonance
1

f 

0
-1
Transmission
Rotation (mrad)
-2
(c)
12
8
4
0
1.0
87
87
Rb, F=2
0.9
85
Rb
Rb, F=1
,
F =1
0.8
0.7
Note that spectrum of
FM NMOR First Harmonic
is related to NMOR spectrum:
,
F =1
,
F =2
,
F =2
Laser Frequency Detuning (GHz)
(d)
For 2nd harmonic (not shown):
 2
s
 2
NMOR with Frequency-Modulated Light
Measurement of magnetic field with FM NMOR
1.0
First Harmonic (mrad)
0.9
0.8
0.7
0.6
1 G
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
0
20
40
60
80
100
120
140
160
180
200
Time (s)
Demonstrated sensitivity ~ 10-9 G / Hz
A mystery...
Quadrature Signal
(arb. un.)
In-phase Signal
(arb. un.)
In-phase Signal
(arb. un.)
Larmor Frequency (Hz)
400
200
0
-200
-400
400
200
0
-200
-400
800
P = 210 W
(a)
m = 200 Hz
P = 800 W
(b)
m = 4 L
for high light power!
x5
P = 800 W
(c)
400
0
-400
See new resonances at
x5
-800
Longitudinal Magnetic Fied (G)
Hexadecapole Resonance
Arises due to creation and probing of
hexadecapole moment ( = 4).
Yashchuk, Budker, Gawlik, Kimball,
Malakyan, Rochester (2003). PRL 90,
253001.
Hexadecapole Resonance
Highest moment possible:
 = 2F
No resonance
for F=1
Hexadecapole Resonance
At low light powers:
Quadrupole signal  I2
Hexadecapole signal  I4
Applications
Measurement of decay
of hyperpolarized Xe:
(In collaboration with Pines Group)
EDM search?
s
d
d
T
P
s
d
s
Permanent EDM violates
parity and time-reversal
invariance!
Best limit on electron EDM:
Regan, Commins, Schmidt, DeMille (2002). PRL 88, 071805.
EDM search?
E = 5 kV/cm
 60 ms
EDM search?
Use nonlinear induced ellipticity to measure electric field:
my= 0
+

F= 1
my= -1
my= 0
my= + 1
y
Electric field plates
x
Laser beam
z
Initial
polarization
Output
polarization
Enhanced by Bennett structures in the atomic velocity distribution!
EDM search?
Ellipticity Hmrad L
1
0
- 1
- 2
- 3
1.1
Transmission
85
85
RbFg = 3
Fe = 2, 3, 4
1
RbFg = 2
Fe = 1, 2, 3
0.9
0.8
D2
0.7
0.6
- 2
- 1
0
LaserDetuning HGHz L
1
2
Comparison of experiment to density matrix calculation indicates
atoms see full 5 kV/cm electric field!
EDM search?
Cs Density during Electric Field Reversal
T = 21.7 oC
Cs Density (109 atoms/cm3)
15
10
5
Applied Voltage (kV)
0
6
4
2
0
-2
-4
-6
0
10
20
30
Time (min)
40
50
60
70
Future directions...
• Reduce technical sources of noise in system.
• Demonstrate projected sensitivity at Earth field.
• Investigate application of electric field to cells.
• Investigate causes of spin-relaxation in paraffin-coated
cells.
• Apply FM NMOR to magnetic field measurements!
• Apply FM NMOR to fundamental symmetry tests?