polarization for precision measurements · 2015-06-15 · he, p n drop in time dependent ... •...
TRANSCRIPT
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Polarization for precision measurements
Torsten Soldner
Institut Laue Langevin
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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
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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
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Solution I – Detector averages beam
Beam
averageDetector average
Detector average of P
Beam average of P
Beam
averageDetector average
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Solution II – Polarization homogeneos
Beam
averageDetector average
Detector average of P
Beam average of P
Beam
averageDetector average
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Content
• Techniques for polarization and spin flipping
• Polarization analysis
• Pushing P
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Polarization – Supermirrors
B
10-7eV
U
10-7eV10-7eV
BUU
opt
Match index of refraction
Increase critical angle(see optics lecture)
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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
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SM bender – Dependencies
00 qq
Wavelengthdependence
Angledependence
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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
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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
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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
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3He spin filter
PHe=0.7, p=2bar, l=10cm
He)(tanh POPn
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3He spin filter
PHe=0.7, p=2bar, l=10cm
He
)(
n )(coshe POT O
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Cells
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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
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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
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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
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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
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Polarization Analysis
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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
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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)
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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:
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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
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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
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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
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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
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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
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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
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Pushing P
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Combining polarizers?
Polarisers not independent
)(),()(
)(),()(
22
2
11
1
RRfP
RRfP
)()()()( 2121 PPPP
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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
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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
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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
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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:
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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:
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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
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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)
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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
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Depolarisation in super mirrors
Befilter
Selector Electromagnet0.85T
(Basic reflectometer)
C. Klauser, PhD thesis (2013)
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Depolarisation in super mirrors
(Basic reflectometer)
C. Klauser, PhD thesis (2013)
Depolarization can be reduced by • higher magnetizing
field• lower m• choice of material
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SuperADAM
Reflectometer with polarization analysis
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Origin of depolarisation in SMs
Off-specularscattering: scattering by domains that are not aligned
Can be reduced by increasing the magnetizing field
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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
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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