Neutron diffraction by a moving grating: theory and experimentisinn.jinr.ru/past-isinns/isinn-23/progr-27_05_2015/... · 2015. 6. 5. · 10 First experimental results 0 5 10 15 20

$Page 1: Neutron diffraction by a moving grating: theory and experimentisinn.jinr.ru/past-isinns/isinn-23/progr-27_05_2015/... · 2015. 6. 5. · 10 First experimental results 0 5 10 15 20$
1

A. Frank FLNP of JINR, Dubna, Russia

[email protected]

Neutron diffraction by a moving

grating: theory and experiment

2

Outline

• Prehistory

• Moving grating as a non stationary phenomenon.

(kinematic theory)

• First observation of the energy splitting

• Application: focusing in time

• Application: gravity experiments

• Found problems

• Progress in theory I – improved kinematic approach

• Progress in theory II– dynamical theory of diffraction

• New experimental approach to the measurement of

diffraction spectra

• Conclusion

A.Frank, ISINN-23, Dubna, 27 May 2015

3

I.M. Frank. On the possible issue of the anomaly in UCN storage

UCN diffraction by the Raleigh waves

results in changing of the normal

components of the k-vector


4 A.Frank, ISINN-23, Dubna, 27 May 2015

5

Matter wave diffraction by a moving grating.

Formulation of the problem

V

0 0exp i k z t

?

V.G. Nosov and A.I.Frank , 1991


6

Neutron diffraction by a moving grating.

Formulation of the problem

V

0 0exp i k z t

s ss

exp i kx t exp i k x ts

1 1 1

2 2 1

s

(2s 1)

T

1/ 2

s

s

2mk


7

Elementary (kinematic) theory.

jj

jjj(z,y,t) a exp[i( t ]qk z y )

02

jq j jq

d

1

2

0

0

1j

k jk

2. Galilean transformation of the wave function.

1. Solving the diffraction problem in a moving

system.

d – space period of a grating

0jj

22 2f

T

V

d

0 1 2j , , ....

0(k L 1)

A.Frank, V.Nosov, 1994

V

k

n = -1

n = +1 n = 0

k

k 1

0

L

j jda T( x )exp( iq x )dx


8

1. Neglecting by the grating form (1D grating)

2. Amplitudes of the diffraction orders don’t depend on the

grating velocity

Main peculiarity of the kinematic approach

For the phase π - modulation 1 0

2

2

d if yT(x)

dexp(i ) if y d

ja 0, j 2s For zero and even orders

j

2a , j 2s 1

i j For odd orders

2

1 2

4a 0.405

E

2E

0E2

V

d


9

Experimental realization - rotating grating

UCN

Monochromator

Phase π -grating

where N is number of grooves

n

L

h

k(n 1)h

E

1 -1

ΔE= ΩΔE= Ω

h = 0.14 mkm


10

First experimental results

0 5 10 15 20 25 30 35 40 45

0,2

0,4

0,6

0,8

1,0

1,2

Co

un

t/se

c

Distance between the filters, cm

Slow spinning (3Hz)

Fit by Gaussian

Fast spinning (89.6 Hz)

Theory

Splitting of the spectrum

A.I.Frank et al. ILL annual report 2001

Phys.Lett.A 311 (2003) 6

0 5 10 15 20 25 30 35 40 45

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,4

2,6

0 5 10 15 20 25 30 35 40 45

0,6

0,8

1,0

1,2

1,4

1,6

0 5 10 15 20 25 30 35 40 45

0,6

0,8

1,0

1,2

1,4

1,60 5 10 15 20 25 30 35 40 45

0,6

0,8

1,0

1,2

1,4

1,6

A=1.679± 0.022

7Hz

A=1.69± 0.047

60 Hz

A=1.579± 0.033

99 Hz

Co

un

t ra

te (

c/se

c)

Distance between the filters (cm)

A=1.657± 0.076

80 Hz

2

10 383 8

expa . ( )

2

10 405

tha .

A.I.Frank et al.Jetp Lett, 81 (2005) 427

Angular period of grating 0.3325mrad (20μ at the middle diameter)

Detector

Monochromator

grating

Analyzer


11

Pulse source and UCN pumping in a trap

UCN

UCN

Source

Chopper UCN

Trap

ST

TG

1

111 G 102 103

1 > - chopper opening time

S – active convertor area

-- area of the trap

- probability of the UCN lost

t

T

F.L. Shapiro, 1972

1915-1973


12

UCN

UCN

Source

UCN

Trap

Guide

in Min

ChopperTime Lens

Pumping option of the pulsed source – time lens

A.I.Frank and R.Gähler. Phys. of Atomic Nuclei, 63, (2000) 545


13

Neutron focusing in time

0,00 0,01 0,02 0,03

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Co

un

t ra

te (

Arb

.un

its)

Time(sec)

t

L

t

a X

A.I.Frank and R.Gähler. Phys. of Atomic Nuclei, 63, (2000) 545


14

Rotating grating as a time lens

1 2 3 4 5 6

0

50

100

150

200

250

Gra

tin

g s

pa

cin

g (

mic

ron

s)

Azimuthal agle (radians)

0 1 2 3 4 5 6

0,00

0,01

0,02

0,03

0,04

0,05

0,06

0,07

Azimuthal angle (radians)

Sp

ac

e f

req

ue

nc

y (

mic

ron

s-1

)

Monochromator

UCN


15

Time lens is working!

0 10 20 30 40 50

0

500

1000

1500

2000

2500

3000C

OU

NT

S

Number of channels

Measured in March 2004

Background

Witdth of the channel is 214 sec

10.3 msec

3.8 msec

A. I. Frank, P. Geltenbort, G. V. Kulin et al. JETP Lett. 78, (2003) 188

S.N. Balashov, I.V. Bondarenko, A.I. Frank et al, Physica B, 350 (2004) 246


16

Test of the weak equivalence principle for neutrons

(2006)

H

E0 E

E

H

The idea was to compare the change of energy mgH

with energy ħΩ transferred to neutron by a moving grating

g n

ΔΩm g =

ΔH

g

g n 3

n loc

m g1 (1.8 2.1) 10

m g

A.I. Frank, P. Geltenbort, M. Jentschel, et al. JETP Letters, 86, 225 (2007)

Frank A.I., Masalovich S.V., Nosov V.G. (ISINN-12). E3-2004-169, 215, Dubna, (2004)


17

φ = 2πft

Comparing the energy mggnH with energy ħΩ as before.

New experiment for the test of weak equivalence principle

for neutron (started in 2010)

Combination of Neutron Interference

Filters with peculiar TOF

spectrometry

TO

F

bas

e

Neutron flux

Modulation

Count rate

oscillations

E1>E2>E3

E1

E2

E3

0,000 0,005 0,010 0,015 0,020 0,025 0,030 0,035 0,040

400

600

800

1000

1200

1400

Co

un

ts

Time (s)


G.V. Kulin et al. NIM A 792 (2015) 38-46

18

Contradictions with kinematic theory (2006-2012)

1. Intensity of the first order DEPENDS on the velocity of the grating

2. The first order line is remarkably wider than initial spectrum

3. The presence of the zero diffraction order was detected

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44

1,0

1,5

2,0

2,5

3,0

3,5

4,0

Co

un

t ra

te (

c/s

ec

)

Distance betwee the filter (cm)

f=45Hz

f=55Hz

f = 64 Hz

f =75Hz

f =95Hz

f =105Hz

Angular period of grating 0.0831mrad

(5μ at the middle diameter)

Scanning curves of the -1 diffraction order measured at different frequencies

of the grating rotation


19

Next step in a theory was made in 2004

It was not taken into account at planning the experiment of 2010-12

a

b

x'

x'

A.I. Frank et al. JINR Communication P3-2004-207

i xcd

i

xi 1 c d

e if 0 x cd

e if cd x dT(x)

e if d x d cd

1 if d cd x 2d

1

0

L

j jda T( x )exp( iq x )dx

,)1(

)exp(122cji

jciB j

0

2

dV

hVc

j

j

cB if j 2sa

B j if j 2s 1


20

0,0 0,2 0,4 0,6 0,8 1,0

0,0

0,1

0,2

0,3

0,4

0,5

Inte

nc

ity

Parameter C

j =0

j = 2

Improved kinematic theory for the moving 3D grating


0

2

dV

hVc

21

1. Intensities of the diffraction waves depends on the grating velocity

2. All waves are independent

3. “Naive” combination of geometric and wave optics

0,0 0,2 0,4 0,6 0,8 1,0

0,0

0,1

0,2

0,3

0,4

0,5

d=5mkm

Conditions of the 2003-04

Inte

nc

ity

Parameter C

j = 1

j =0

j = 2

Conditions of the 2006-12

d=20mkm

Improved kinematic theory for the moving 3D grating


0

2

dV

hVc

0 5 10 15 20 25 30 35 40 45

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

2,2

2,4

2,6

0 5 10 15 20 25 30 35 40 45

0,6

0,8

1,0

1,2

1,4

1,6

0 5 10 15 20 25 30 35 40 45

0,6

0,8

1,0

1,2

1,4

1,60 5 10 15 20 25 30 35 40 45

0,6

0,8

1,0

1,2

1,4

1,6

A=1.679± 0.022

7Hz

A=1.69± 0.047

60 Hz

A=1.579± 0.033

99 Hz

Co

un

t ra

te (

c/se

c)

Distance between the filters (cm)

A=1.657± 0.076

80 Hz

22

New stage of the investigation of neutron diffraction by

a moving grating.

1. Theory: Multiwave dynamic approach.

V.A. Bushuev, A.I. Frank and V.G. Kulin. arXiv:1502.04751v1 [physics.optics]

(to be published in JETP)

2. Experiment: TOF Fourier spectroscopy of UCN’s

Proposed in : V.G. Kulin, D.V. Kustov, A.I. Frank et al. JINR Communication,

P3-2014 -48

G.Kulin (next presentation)


23

Multiwave dynamic theory

0)()]([)( 2 rrr k

( ) 4 N b r r r

n nn

(x) exp(iq x)

0 z h

Moving reference

d1

n nd0

(x)exp( iq x)dx

n 02q n nq

d

m mx 0zm

(x ,z) (z)exp[i(g x g z)]

Sum of the Bloch waves

mx 0x V mg k k q , 2 1/ 2

0z 0z 0g (k )


v

mVk ,

24

002

2

02n

nmnmmm

zm

dz

diq

dz

d

Border conditions

m m m V 0xq [q 2(k k )] where

0 0 m 0z 0 A , z 0 0



25

002

2

02n

nmnmmm

zm

dz

diq

dz

d

Border conditions

m m m V 0xq [q 2(k k )] where

0 0 m 0z 0 A , z 0 0

RF2 1-2 %


0nnmnmm

m iidz

d

nm m 0z n

0z

2g , 2g


2 1/ 2

0z 0z 0g (k )

n 02q n nq

d

26

0,0 0,2 0,4 0,6 0,8 1,0

0,0

0,1

0,2

0,3

0,4

0,5

Inte

nc

ity

Parameter C

j = 1j =0

j = 2

Solid lines –dynamic theory, dash lines - improved kinematics theory


0

2

dV

hVc

27

TOF Fourier mode of the UCN spectrometer (November 2014)

G.Kulin (next presentation)


28

Recent results: TOF spectra and comparing with theory

(December 2014)

Non-destroyed

Atomic Force Microscope Inspection 100 150

0

1

2

3

4

E (nev)

Inte

ncity (

arb

in

its)

60Hz Experiment

Theory


Angular period of grating 0.0665mrad (4μ at the middle diameter)

29

Conclusion

1. Diffraction grating which is moving across the direction of neutron

propagation acts as a nonstationary device. That results in the appearance

of line spectrum.

2. The phenomenon was firstly observed in 2001

3. It may be (and was) used for precise change of the neutron energy. That

was demonstrated in the experiment for neutron focusing in time and

gravity experiments with UCN.

4. Dynamical theory of UCN diffraction by a grating satisfactorily describes

experimental data but the precision of these last is rather pure yet.

5. We plan to continue experimental investigations of the phenomena using

recently tested TOF Fourier method of UCN spectrometry


30

P. Geltenbort, P. Høghøj, M. Jentschel

Many thanks to my co-authors

I.V. Bondarenko, S.V.Goryunov, G.V.Kulin, D.Kustov.

S.N. Balashov, S.V.Masalovich, V.G.Nosov S.N.Strepetov

V. A. Bushuev

Thank you for your attention!

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Neutron diffraction by a moving grating: theory and experimentisinn.jinr.ru/past-isinns/isinn-23/progr-27_05_2015/... · 2015. 6. 5. · 10 First experimental results 0 5 10 15 20