Polarization for precision measurements

Torsten Soldner

Institut Laue Langevin

Polarization – Definition

More precisely: spin polarization

• Degree to which the spin of particles is aligned with a given direction

• For spin ½ particles:

• Property of an ensemble of particles, not of a single particle!

• Polarization vector:

NN

NNP

NP

N

i i

1

Asymmetry measurements

epPAW

1d

d

d

BeamDetector

d 1 epPAN

BeamDetectorBeam

BeamDetector

d )(d )( ee prPprP

BeamDetector

d 1 epPAN

BeamDetector

d

epPA

NN

NN

Solution I – Detector averages beam

Beam

averageDetector average

Detector average of P

Beam average of P

Beam

averageDetector average

Solution II – Polarization homogeneos

Beam

averageDetector average

Detector average of P

Beam average of P

Beam

averageDetector average

Content

• Techniques for polarization and spin flipping

• Polarization analysis

• Pushing P

Polarization – Supermirrors

B

10-7eV

U

10-7eV10-7eV

BUU

opt

Match index of refraction

Increase critical angle(see optics lecture)

Example: m=4 FeSi super mirror

Picture from Swiss Neutronics web page

Matching works better for CoTi, but activation worse

Note expanded scale for P

SM bender – Dependencies

00 qq

qq

Wavelengthdependence

Angledependence

SM bender – angular dependence

-8 -6 -4 -2 0 2 4 6 8 100.93

0.94

0.95

0.96

0.97

0.98

0.99

1.00

AP

Position [mrad]

Single Analyzer

Crossed Analyzer

Old example, modern polarizers are much better

SM bender – wavelength dependence

Old example, modern polarizers are much better

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.75

0.80

0.85

0.90

0.95

1.00

1.05

AP

[A]

Single Analyzer

Crossed Analyzer

3He spin filter

Angle-independent (cos(θ))Pn up to 100%

PHe, Pn drop in time dependent

σc,0 = 5333(7) barn

σc↑↓/ σc,0 =1.010(32)(often assumed that σc↑↑ = 0 but known only on % level)

σc↑↓>>σc↑↑

n+3He t + p

)1(]He[exp2

1He0 PlT

He)(tanh POPn lpOÅ cmbar

0733.0)( opacity

He

)(

n )(coshe POT O

0e)0()( HeHe

T

t

PtP

relaxation of hyperpolarized 3He

3He spin filter

PHe=0.7, p=2bar, l=10cm

He)(tanh POPn

3He spin filter

PHe=0.7, p=2bar, l=10cm

He

)(

n )(coshe POT O

Cells

Techniques

MEOP (metastability exchange optical pumping)

• Pump 3He to metastable state

• Polarize nuclei

• Works at mbar pressure offline pumping, compression

SEOP (spin exchange optical pumping)

• Pump electrons in alkali metal

• Transfer to 3He by collision

• Works at bar pressure online pumping

• Strong performance loss in high neutron flux

Flipper I – Current sheet

Non-adiabatic transition

B

B

• Good for fast neutrons, bad for slow (adiabaticity)• Difficult to adjust:

OFF: adiabatic transport ON: non-adiabatic transition, no other field components

• Requires material in the beam, scattering may be current-dependent

Typical parameters:Wire: D = 1mmCurrent: I = 10 A

Flippers II – Adiabatic fast passage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.985

0.990

0.995

1.000

1.005

Radio Frequency Flipper

<f> = 0.9993±0.0001

Current Sheet Fliper

Flip

pe

r e

ffic

ien

cy

[A]

ω

Frame rotating with ω:

ω=γBR

ΔB=B(x)-BR

B1

B0(x)

xB1

Typical values: f=ω/2π=50 kHz, BR=17 G

Flippers III – Small-band

Mezei flipper:Non-adiabatic transition, adiabatic rotation

• For π/2 flip (as needed for EDM or spin echo experiments)• Works only for fixed wavelength (tunable to λ at pulsed beam)

More complex configuration for arbitrary rotation angle

Resonance spin flipperSee Florian’s lecture

Polarization Analysis

A handy formalism I

Particles spin up

Particles spin down

1

1

2

nBUnpolarized beam

P

P

10

01PPolarizer

P

Pn

1

1

2PB P

NN

NN

A handy formalism II

Particles spin up

Particles spin down

1

1

2

nBUnpolarized beam

P

P

10

01PPolarizer

FF

FF

1

1FSpin flipper

)21(1

)21(1

2 FP

FPnFPB )21( FP

NN

NN

F Spin flip efficiency ε = 1-F Spin flip inefficiencyf = 2F-1 Flipper efficiency (modification of beam polarization

by flipper)

A handy formalism III

Particles spin up

Particles spin down

1

1

2

nBUnpolarized beam

P

P

10

01PPolarizer

FF

FF

1

1FSpin flipper

ddDDetector Insensitive to polarization

A

A

10

01AAnalyzer

Detection efficiencyndN (...)... BD

Detected neutrons:

Polarization analysis I – One flipper

B P F A D

Flipper off dbAPN )1(0 DAPB

Flipper on dbAPFAPN )21(1 DAFPB

)1(110

10

FAP

APF

NN

NN

)21(1

1

1

0

FAP

AP

N

Nr

APF cannot be separated

Flipping ratio10

10

1

1

NN

NN

r

r

Polarization analysis II – Two flippers

B P F1 A DF2

PBFFAD

PBFAD

PBFAD

PBAD

1

1

211

201

10

00

N

N

N

N

0001

10111 1

2

1

NN

NNF

0010

01112 1

2

1

NN

NNF

01101100

01001000

NNNN

NNNNAP

AP cannot be separatedF1 and F2 can

Requires a lot of statistics

White

Black

Black

White

Polarization analysis with SM?

F1 F2P1 P2

0001

10111 1

2

1

NN

NNF

0010

01112 1

2

1

NN

NNF

01101100

01001000

NNNN

NNNNAP

APP ________ (assuming A=P) does not work, strictly speaking

)()()()( 2121 PPPP

P is property ofdevice AND beam

Polarization analysis III – Analyzer flip

B P F A D

AP cannot be separatedF can

10

20

NN

NNF

10

10

NN

NNAP

PBFAD

PBAD

PBAD

)(

)(

)(

2

1

0

AN

AN

AN

White

Black

Black

Works for 3He analyzerWe have 3He flippers with ε ~ 3∙10-6

This can be measured easily by performing many flips

He)(tanh POPn

Example X-SM geometry

0 2 4 6 8 10 12 14 16 18 20-0,950

-0,955

-0,960

-0,965

-0,970

-0,975

-0,980

-0,985

-0,990

-0,995

-1,000

Pola

riza

tio

n

Neutron wavelength (A)

<P> = (99.72 +/- 0.10)%

p0 5.5 Bar

p1 4.0 Bar

p2 2.1 Bar

p3 1.5 Bar

p4 1.0 Bar

p5 0.67 Bar

Spectrum

Used in PERKEO II, Mund et al, PRL 110 (2013) 172502

Analysis of inhomogeneous polarization

Accurate scan of beam:• Same areas for intensity

and polarization scansAccurate average

Exploit features of 3He:• No angular dependence• large area average

possible

Pushing P

Combining polarizers?

Polarisers not independent

)(),()(

)(),()(

22

2

11

1

RRfP

RRfP

)()()()( 2121 PPPP

The X-SM geometryalso known as “crossed”, but different meaning in optics

Polarizers independent

)(),()(

)(),()(

22

2

11

1

yyy

xxx

RRfP

RRfP

yxyxyxyx PPPP

)()()()( 21,21

Polarization analysis with X-SM?

F1 F2P1 P2

0001

10111 1

2

1

NN

NNF

0010

01112 1

2

1

NN

NNF

01101100

01001000

NNNN

NNNNAP

yxyxyxyx PPPP

)()()()( 21,21

A and P independent, but numbers depend on beam (incoming divergence…) Cannot separate

P is property ofdevice AND beam

But very powerful polarizer

n

P1 P2R

BB

BY

ZX

n

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.75

0.80

0.85

0.90

0.95

1.00

1.05

P

[A]

Measured single Polarizer

Prediction for Crossed Geometry

2112 TTT

Predictable Polarisation...

...and Transmission

21

2112

1 PP

PPP

)1)(1(2

11 2112 PPP

adiabatic rotation

Measured performance

-8 -6 -4 -2 0 2 4 6 8 100.93

0.94

0.95

0.96

0.97

0.98

0.99

1.00

AP

Position [mrad]

Single Analyzer

Crossed Analyzer

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.75

0.80

0.85

0.90

0.95

1.00

1.05

AP

[A]

Single Analyzer

Crossed Analyzer

(with old polarizers)

)1)(1(2

11 2112 PPP

Pi = 0.95 expect P12 =0.999

Much more than measured!

But:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.96

0.97

0.98

0.99

1.00

AP

[A]

Fields in Polarizer / Analyzer

BP=200 G, B

A=200 G

BP=200 G, B

A=350 G

BP=350 G, B

A=350 G

State of the art ILL SM Polariser

Magnetic housing field 1 kG

Limit of X-SM polarizer

Magnetic layers still not completely saturated

X-SM polarizer with X-SM analyzer:

Accuracy of 3He spin filters

– The opaque test bench –

P>99.995% A>99.995%F>99.999%

He)(tanh POP He)(tanh POA

Idea:Clean systematics by pure ↑ beam

Motivation:• Test ultimate performance of 3He spin filters• Precision characterization of polarizing elements

Analysing Power of 3He

Befilter

Chopper

→ Accuracy better than 10-4

l = 14cmpHe = 1.69 bar(and: 1.0 bar, 1.4 bar)

He)(tanh POP

C. Klauser, PhD thesis (2013)

AFP Flipper

Befilter

Chopper

→ F > 99.99%from 3 to 9 Å

10

2011NN

NNf

C. Klauser, PhD thesis (2013)

2

1

0

N

N

N

Detects only unflippedneutrons very sensitive

Depolarisation in super mirrors

Befilter

Selector Electromagnet0.85T

(Basic reflectometer)

C. Klauser, PhD thesis (2013)

Depolarisation in super mirrors

(Basic reflectometer)

C. Klauser, PhD thesis (2013)

Depolarization can be reduced by • higher magnetizing

field• lower m• choice of material

SuperADAM

Reflectometer with polarization analysis

Origin of depolarisation in SMs

Off-specularscattering: scattering by domains that are not aligned

Can be reduced by increasing the magnetizing field

Apply to X-SM

Befilter

Selector Electromagnet0.85T

(Basic reflectometer)

C. Klauser, PhD thesis (2013)

0.9970

0.9975

0.9980

0.9985

0.9990

0.9995

1.0000

0 0.2 0.4 0.6 0.8 1

AP

Magnetising-Field 1st Mirror [Tesla]

2.0 FeSi

2.0 CoTi

→ P = 99.970(3)%achieved with SMs only

Summary

Super mirrors

• Constant in time

• Wavelength dependent

• Angle dependent

98% routine

99.7% with X-SM

99.97% with pushed X-SM

3He spin filters

• Changes in time

• Wavelength dependent

• Negligible angle dependence

> 99.99% possible

AFP flipper

> 99.99% possible in λ range

10-4 accuracy achievable but requires careful design of polarizer and analysis