nonlinear magneto-optical rotation with frequency-modulated light
DESCRIPTION
Nonlinear Magneto-Optical Rotation with Frequency-Modulated Light. Derek Kimball Dmitry Budker Simon Rochester Valeriy Yashchuk Max Zolotorev and many others. D. English K. Kerner C.-H. Li T. Millet A.-T. Nguyen J. Stalnaker A. Sushkov. E. B. Alexandrov M. V. Balabas W. Gawlik - PowerPoint PPT PresentationTRANSCRIPT
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Nonlinear Magneto-Optical Nonlinear Magneto-Optical RotationRotation
with with Frequency-Modulated LightFrequency-Modulated Light
Derek KimballDmitry Budker
Simon RochesterValeriy Yashchuk
Max Zolotorevand many others...
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Some of the many others:
D. EnglishK. KernerC.-H. LiT. MilletA.-T. NguyenJ. StalnakerA. Sushkov
E. B. AlexandrovM. V. BalabasW. GawlikYu. P. MalakyanA. B. MatskoI. Novikova A. I. OkunevichS. PustelnyA. WeisG. R. Welch
Budker Group:Non-Berkeley Folks:
Technical Support:M. SolarzA. VaynbergG. WeberJ. Davis Funding: ONR, NSF
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Plan:Plan:
• Linear Magneto-Optical (Faraday) Rotation• Nonlinear Magneto-Optical Rotation (NMOR)
– Polarized atoms– Paraffin-coated cells– Experiments
• NMOR with Frequency-Modulated light (FM NMOR)– Motivation– Experimental setup– Data: B-field dependence, spectrum, etc.
• A little mystery...• Magnetometry
Review: Budker, Gawlik, Kimball, Rochester, Yashchuk, Weis (2002). Rev. Mod. Phys. 74(4), 1153-1201.
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Linear Magneto-Optical (Faraday) Linear Magneto-Optical (Faraday) RotationRotation
Medium
Linear Polarization
Circular Components
MagneticField
= (n+-n-)0l2c
= (n+-n-) l
1846-1855: Faraday discovers magneto-optical rotation
1898,1899: Macaluso and Corbino discover resonant character of Faraday rotation
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Linear Magneto-Optical (Faraday) Linear Magneto-Optical (Faraday) RotationRotation
1898: Voigt connects Faraday rotation to the Zeeman effect
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Linear Magneto-Optical (Faraday) Linear Magneto-Optical (Faraday) RotationRotation
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Linear Magneto-Optical (Faraday) Linear Magneto-Optical (Faraday) RotationRotation
-5 -4 -3 -2 -1 0 1 2 3 4 5
Normalized magnetic field (b = 2gF0B / )
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
-0.0
0.1
0.2
0.3
0.4
0.5
0.6
Rot
atio
n an
gle
(rad
)
20
0
0 /21
/2
2
Bg
Bg
l
l
F
F
B ~ 400 G
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Nonlinear Magneto-Optical RotationNonlinear 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:
-2 -1 0 1 2 3
0.2
0.4
0.6
0.8
1
B = 0
Spectral hole-burning:
-2 -1 0 1 2 3
-1
-0.5
0
0.5
Num
ber
of a
tom
s
Atomic velocity
Light detuning
Inde
x of
ref
ract
ion
Re[n+-n-]
B 0
Small field NMOR enhanced!
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Nonlinear Magneto-optical Nonlinear Magneto-optical RotationRotation
due to atomic polarizationdue to atomic polarizationThree stage process:
Opticalpumping
Precessionin B-field
Probingvia opticalrotation
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Circularly polarized light consists of photons
with angular momentum = 1 ħ along z.
M = 1
Optical pumpingOptical pumping
MF = -1 MF = 0 MF = 1
z
F = 1
F’ = 0
Fluorescence has randomdirection and polarization.
Circularly polarized light propagating in z directioncan create orientation along z.
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MF = -1 MF = 0 MF = 1
z
F = 1
F’ = 0
Medium is now transparent to lightwith right circular polarization in z direction!
Circularly polarized light propagating in z directioncan create orientation along z.
Optical pumpingOptical pumping
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MF = -1 MF = 0 MF = 1
z
F = 1
F’ = 0
Light linearly polarized along z can create alignment along z-axis.
Optical pumpingOptical pumping
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MF = -1 MF = 0 MF = 1
z
F = 1
F’ = 0
Light linearly polarized along z can create alignment along z-axis.
Medium is now transparent to lightwith linear polarization along z!
Optical pumpingOptical pumping
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MF = -1 MF = 0 MF = 1
z
F = 1
F’ = 0
Light linearly polarized along z can create alignment along z-axis.
Medium strongly absorbs lightpolarized in orthogonal direction!
Optical pumpingOptical pumping
.
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Aligned“Peanut” with axis
along z preferred axis.
z
x
y
Oriented“Pumpkin” pointing
in z-direction preferred direction.
z
x
y
UnpolarizedSphere centered
at origin,equal probabilityin all directions.
z
x
y
Visualization of Atomic Visualization of Atomic PolarizationPolarization
Draw 3D surface where distance from origin equals the probability to be found in a stretched state (M=F) along this direction.
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Optical pumping process polarizes atoms.
Optical pumping is most efficient whenlaser frequency (l) is tuned to
atomic resonance frequency (0).
Optical pumpingOptical pumping
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Precession in Magnetic FieldPrecession in Magnetic Field
Interaction of the magnetic dipole momentwith a magnetic field causes the angular momentum
to precess – just like a gyroscope!
= dF
dt
= B = B
gF B F B
dFdt B
= =L = gF B B
B
, F
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torque causes polarized atoms to precess: B Precession in Magnetic FieldPrecession in Magnetic Field
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Relaxation and probing of atomic polarizationRelaxation and probing of atomic polarization
• Relaxation of atomic polarization:
• Plane of light polarization is rotated, just as if light had propagated through a set of “polaroid” films.
• Equilibrium conditions result in net atomic polarization at an angle to initial light polarization.
(polarized atoms only)
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Coherence Effects in NMORCoherence Effects in NMOR
2
rel0
rel0
00
00 /21
/2
22sin
2rel
Bg
Bg
l
lBtgedt
l
l
F
FF
t
t
Magnetic-field dependence of NMOR due to atomic polarizationcan be described by the same formula we used for linear Faradayrotation, but rel :
How can we get slowest possible rel?
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Paraffin-coated cellsParaffin-coated cells
Academician Alexandrov hasbrought us some beautiful“holiday ornaments”...
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Paraffin-coated cellsParaffin-coated cells
Alkali atoms work best with paraffin coating...
Most of our work involves Rb:
D1
(794
.8 n
m)
D2
(780
.0 n
m)
5 S 1 /2
2
5 P 1 /2
2
5 P 3 /2
2
6 8 3 5 M H z
8 1 2 M H z
4 9 6 M H z
F = 1
F = 2
F = 1
F = 2
F = 0
F = 3
F = 2F = 1
~~
~~87Rb (I = 3/2)
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Paraffin-coated cellsParaffin-coated cells
Polarized atoms can bounce off the walls of a paraffin-coatedcell ~10,000 times before depolarizing!
This can be seen using the method of “relaxation in the dark.”
B
4
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Relaxation in the DarkRelaxation in the Dark
MF = -1 MF = 0 MF = 1F = 1
F’ = 0
Light can be used to probe ground state atomic polarization:
No absorption of right circularly polarized light.
z
Photodiode
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MF = -1 MF = 0 MF = 1F = 1
F’ = 0
Light can be used to probe ground state atomic polarization:
Significant absorptionof left circularly polarized light.
z
Photodiode
Relaxation in the DarkRelaxation in the Dark
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Paraffin-coated cellsParaffin-coated cells
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Time (s)
0.22
0.23
0.24
0.25
0.26
Pro
be t
rans
mis
sion
(ar
b. u
nits
)
Bx = 100 G
rel = 2 1.004(2) Hz
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+ -
DCpolarimetercalibration
polarizer
magnetic shield
magnetic coil
Rb-cell
lock-in
reference
pre-amplifier
analyzer
polarization-modulator
polarization-rotator
PD1
PD2attenuator
spectrum analyzer
diode laser
P
uncoated Rb cell in magnetic field
/4BS
PD
PD
Dichroic Atomic Vapor Laser Lockdifferentialamplifier
PD
light-pipe
feedbacklaser frequency control
fluorescencecontrol
and dataacquisition
absorption
magnetic field current
first harmonic
Experimental SetupExperimental Setup
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Magnetic ShieldingMagnetic Shielding
ø 24.5" ø 21"
12"
ø 1
8"
25"
20"
16"
Four-layer ferromagnetic magnetic shielding with nearly spherical geometry reduces fields in all directions
by a factor of 106!
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Magnetic ShieldingMagnetic Shielding
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3-D coils allow controland cancellation of fieldsand gradients inside shields.
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NMOR Coherence Effect in Paraffin-coated CellNMOR Coherence Effect in Paraffin-coated Cell
-10 -8 -6 -4 -2 0 2 4 6 8 10
Magnetic Field (G)
-10
-8
-6
-4
-2
0
2
4
6
8
10R
otat
ion
Ang
le (
mra
d)
85Rb D2 Line, I = 50 W/cm2,F=3 F’=4 component
rel = 2 0.9 HzKanorsky, Weis, Skalla (1995). Appl. Phys. B 60, 165.Budker, Yashchuk, Zolotorev (1998). PRL 81, 5788.Budker, Kimball, Rochester, Yashchuk, Zolotorev (2000). PRA 62, 043403.
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Sensitive measurement of magnetic fieldsSensitive measurement of magnetic fields
85Rb D2 line, F=3 F’ component,I = 4.5 mW/cm2
0
10
20
30
40
50
B
z) (
10-1
2 G/H
z1/2 )
-1.2 -0.8 -0.4 -0.0 0.4 0.8 1.2
Relative Frequency (GHz)
0.7
0.8
0.9
1.0
Tra
nsm
issi
on
HzG/ 103 12
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The dynamic range of an NMOR-based magnetometer islimited by the width of the resonance:
-10 -8 -6 -4 -2 0 2 4 6 8 10
Magnetic Field (G)
-10
-8
-6
-4
-2
0
2
4
6
8
10R
otat
ion
Ang
le (
mra
d)
B ~ 2 G
How can we increase the dynamic range?
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NMOR with Frequency-Modulated NMOR with Frequency-Modulated LightLight
• Magnetic field modulates optical properties of medium at 2L.
• There should be a resonance when the frequency of light is modulated at the same rate!
ExperimentalSetup:
Inspired by:Barkov, Zolotorev (1978). JETP Lett. 28, 503.Barkov, Zolotorev, Melik-Pashaev (1988). JETP Lett. 48, 134.
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-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00
Firs
t H
arm
onic
Am
plitu
de (
mra
d)
-1600 -1200 -800 -400 0 400 800 1200 1600
Longitudinal Magnetic Field (G)
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00
In-phase component
Out-of-phase (quadrature) component
m = 21 kHz
= 2220 MHz
P 15 W
87Rb D1 LineF = 2 1
Budker, Kimball,Yashchuk, Zolotorev (2002).PRA 65, 055403.
Nonlinear Magneto-optical Nonlinear Magneto-optical RotationRotation
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Low-field resonance is due to equilibriumrotated atomic polarization – at constant
angle due to balance of pumping, precession, and relaxation.
Low field resonance:L rel
Nonlinear Magneto-optical Nonlinear Magneto-optical RotationRotation
On resonanceOn resonance::Light polarized alongLight polarized along
atomic polarization is transmitted,atomic polarization is transmitted,light of orthogonal polarizationlight of orthogonal polarization
is absorbed.is absorbed.
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-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00
Firs
t H
arm
onic
Am
plitu
de (
mra
d)
-1600 -1200 -800 -400 0 400 800 1200 1600
Longitudinal Magnetic Field (G)
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
0.75
1.00
In-phase component
Out-of-phase (quadrature) component
m = 21 kHz
= 2220 MHz
P 15 W
87Rb D1 LineF = 2 1
Nonlinear Magneto-optical Nonlinear Magneto-optical RotationRotation
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• 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.
High field resonances:L >> rel
Nonlinear Magneto-optical Nonlinear Magneto-optical RotationRotation
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• Optical properties of the atomic medium are modulated at 2L.
• A resonance occurs when m = 2L.
Nonlinear Magneto-optical Nonlinear Magneto-optical RotationRotation
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• Quadrature signals arise due to difference in phase between rotating medium and probe light.
• Second harmonic signals appear for m = L.
Nonlinear Magneto-optical Nonlinear Magneto-optical RotationRotation
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NMOR with Frequency-Modulated NMOR with Frequency-Modulated LightLight
L ase r F req u en cy D e tu n in g (G H z)
0 .9
0
(a )
(b )
Fir
st H
arm
onic
Am
plit
ude
(mra
d)
(c )
(d )F = 2
R b
F = 1, ,
F = 2,
F = 1,
8 5
R b , F = 28 7 R b , F = 18 7
Rot
atio
n (m
rad)
Tra
nsm
issi
on
0 .7
0 .8
1 .0
4
8
1 2
0
1
2
-2
-1
0
1
2
-2
-1
Low field resonance
High field resonance
Note that spectrum ofFM NMOR First Harmonicis related to NMOR spectrum:
f
For 2nd harmonic (not shown):
2
2
s
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0 20 40 60 80 100 120 140 160 180 200Time (s)
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Firs
t Har
mon
ic (
mra
d)
1 G
Measurement of magnetic field with FM NMOR
Demonstrated sensitivity ~ 510-10 Hz/G
MagnetometryMagnetometry
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MagnetometryMagnetometry
Magnetic resonance imaging (MRI) in Earth field?
Measurement of Xe nuclear spins.
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MagnetometryMagnetometry
Magnetic resonance imaging (MRI) in Earth field?
Tim e (m in )
5
0
-5
Mag
neti
c F
ield
(nG
)
1 0
1 5
2 0
129Xe 26% natural abundance, pressure = 5 bar
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A A mystery...mystery...
m = 4 L
See new resonances at
for high light power!
L o n g itu d in a l M ag n e tic F ied ( G )
Qua
drat
ure
Sig
nal
(a
rb. u
n.)
0
4 0 0
P = 2 1 0 W
P = 8 0 0 W
P = 8 0 0 W
-4 0 0
-8 0 0
8 0 0
0 2 0 0
-2 0 0
-4 0 0
4 0 0
0
2 0 0
-2 0 0
-4 0 0
4 0 0 I
n-ph
ase
Sig
nal
(arb
. un.
) I
n-ph
ase
Sig
nal
(arb
. un.
)
(c )
(b )
(a )
x 5
x 5
L a rm o r F req u en cy (H z)
m = 200 Hz
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Hexadecapole Hexadecapole ResonanceResonance
Arises due to creation and probing of
hexadecapole moment ( = 4).Yashchuk, Budker, Gawlik, Kimball, Malakyan, Rochester (2003). PRL 90,253001.
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Hexadecapole Hexadecapole ResonanceResonance
Highest moment possible: = 2F
No resonancefor F=1
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Hexadecapole Hexadecapole ResonanceResonance
At low light powers:
Quadrupole signal I2
Hexadecapole signal I4