nonlinear magneto-optical rotation with frequency-modulated light derek kimball dmitry budker simon...

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. OkunevichH. G. RobinsonA. WeisG. R. Welch

Budker Group:Non-Berkeley Folks:

Technical Support:M. SolarzA. VaynbergG. WeberJ. Davis Funding: ONR

Plan:Plan:• Linear Magneto-Optical (Faraday) Rotation• Nonlinear Magneto-Optical Rotation (NMOR)

– Coherence effects– Paraffin-coated cells– Experiments

• NMOR with Frequency-Modulated light (FM NMOR)– Motivation– Experimental setup– Data: B-field dependence, spectrum, etc.

• A little mystery...• Applications

– Sensitive magnetometry– EDM search?

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


1898: Voigt connects Faraday rotation to the Zeeman effect


-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!

Coherence Effects in NMORCoherence Effects in NMOR

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.

Three-stage process:

112

1 MM

x-polarized light interactswith coherent superpositionof ground state Zeeman sublevels


Optical pumping:

Polarizes atoms Aligns magnetic dipole moments Creates optical anisotropy (linear dichroism)


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.


B torque causes atomic polarization to precess:

Initial axis of dichroism

F

F

F’

F

F

F’

Final axis of dichroism

Action of magneticfield on dipole moments

.B


B torque causes atomic polarization to precess:


• 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)


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 coherence effectscan 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”...

Magical!


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)


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


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.


Low-field FM NMOR resonance is analogousto that seen in conventional NMOR.

Low field resonance: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.

High field resonances:L >> rel


• Optical properties of the atomic medium are modulated at 2L.

• Resonances occur for n m = 2L. Largest amplitude for n = 1.


• Quadrature signals arise due to difference in phase between rotating medium and probe light.

• Second harmonic signals appear for m = L.


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 ~ 10-9 Hz/G

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.


Highest moment possible: = 2F

No resonancefor F=1


At low light powers:

Quadrupole signal I2

Hexadecapole signal I4

ApplicatioApplicationsns

Measurement of decayof hyperpolarized Xe:

(In collaboration with Pines Group)

EDM search?EDM search?

T

P

d

s

s

s

d

d

Permanent EDM violatesparity and time-reversal invariance!

Best limit on electron EDM:Regan, Commins, Schmidt, DeMille (2002). PRL 88, 071805.


E = 5 kV/cm

60 ms


Use nonlinear induced ellipticity to measure electric field:

Enhanced by Bennett structures in the atomic velocity distribution!

m = -1 m = 0 m = + 1

m = 0

y y y

y

F= 1

+ -

y

x

z

In itia lp o la riza tio n

O u tp u tp o la riza tio n

E lec tric fie ld p la te s

L ase r b eam


- 3

- 2

- 1

0

1

85 RbFg =3Fe =2, 3, 4

85 RbFg =2Fe =1, 2, 3

D2

- 2 - 1 0 1 20.6

0.7

0.8

0.9

1

1.1

Elli

pti

city

Hmra

dL

Transm

i ssi

on

LaserDetuning HGHzL

Comparison of experiment to density matrix calculation indicates

atoms see full 5 kV/cm electric field!


0

5

10

15

Cs

Den

sity

(10

9 a

tom

s/cm

3)

Cs Density during Electric Field Reversal

T = 21.7 oC

0 10 20 30 40 50 60 70

Time (min)

-6

-4

-2

0

2

4

6

App

lied

Vol

tage

(kV

)

Future Future directions...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?

nonlinear magneto-optical rotation with frequency-modulated light derek kimball dmitry budker simon...

Documents

linear faraday rotation

b slide

nmor optical pumping

onr slide

g slide

optical properties

nmor torque

plane of light polarization