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
Nonlinear Magneto-Optical Nonlinear Magneto-Optical RotationRotation
with with Frequency-Modulated LightFrequency-Modulated Light
Derek KimballDmitry Budker
Simon RochesterValeriy Yashchuk
Max Zolotorevand many others...
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
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.
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
Linear Magneto-Optical (Faraday) Linear Magneto-Optical (Faraday) RotationRotation
1898: Voigt connects Faraday rotation to the Zeeman effect
Linear Magneto-Optical (Faraday) Linear Magneto-Optical (Faraday) RotationRotation
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
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!
Nonlinear Magneto-optical Nonlinear Magneto-optical RotationRotation
due to atomic polarizationdue to atomic polarizationThree stage process:
Opticalpumping
Precessionin B-field
Probingvia opticalrotation
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.
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
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
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
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
.
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.
Optical pumping process polarizes atoms.
Optical pumping is most efficient whenlaser frequency (l) is tuned to
atomic resonance frequency (0).
Optical pumpingOptical pumping
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
torque causes polarized atoms to precess: B Precession in Magnetic FieldPrecession in Magnetic Field
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)
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?
Paraffin-coated cellsParaffin-coated cells
Academician Alexandrov hasbrought us some beautiful“holiday ornaments”...
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)
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
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
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
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
+ -
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
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!
Magnetic ShieldingMagnetic Shielding
3-D coils allow controland cancellation of fieldsand gradients inside shields.
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.
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
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?
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.
-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
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.
-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
• 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
• Optical properties of the atomic medium are modulated at 2L.
• A resonance occurs when m = 2L.
Nonlinear Magneto-optical Nonlinear Magneto-optical RotationRotation
• 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
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
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
MagnetometryMagnetometry
Magnetic resonance imaging (MRI) in Earth field?
Measurement of Xe nuclear spins.
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
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
Hexadecapole Hexadecapole ResonanceResonance
Arises due to creation and probing of
hexadecapole moment ( = 4).Yashchuk, Budker, Gawlik, Kimball, Malakyan, Rochester (2003). PRL 90,253001.
Hexadecapole Hexadecapole ResonanceResonance
Highest moment possible: = 2F
No resonancefor F=1
Hexadecapole Hexadecapole ResonanceResonance
At low light powers:
Quadrupole signal I2
Hexadecapole signal I4