Neutron Interferometry
1
NIST Center for Neutron Research
Home to a 20 MW reactor that provides neutrons for scien>fic research
Dozens of instruments (most for Solid State applica>ons)
Some instruments for the study of Fundamental Physics Public domain image
2
The Neutron Interferometer and Optics Facility
Public domain image
Isolated 40,000 Kg room is supported by six airsprings
Active Vibration Control eliminates vibrations less than 10Hz
3
Temperature Controlled to +/- 5 mK
Inside the NCNR
Reactor Core
Fuel Elements
LH2
Guide Hall 7 Neutron
Guides
NIOF
Public domain images
4
Wavepacket
Neutron coming out of the reactor is a wavepacket:
Sum of many plane waves with different wavenumber k
[not a stationary state: evolves (moves!) in time]
p
2p
3p
4p
5p
6p
7p
8p
9p
10 p
x
Fourier Transform Pair
1
2
3
4
5
6
7
8
5
9
10
11
12
13
14
15
k
Monochromator
Monochromator selects a small range of momenta
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6
Wavepacket
p
1
2p
2
3p
3
4
4p
5
6
5p
7
6p
8
7
9
7p
10
11
8p
12
9p
13
14
10 p
15
k
x
Neutron Interferometer
3-blade interferometer from single Si crystal
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8
5-blade interferometer from single Si crystal
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9
Wavepacket ➙ Plane wave
p
2p
3p
4p
5p
6p
7p
8p
9p
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Wavepacket ∆x ≫ Interferometer ➞ consider ∆x =∞
1 ikx
or neutron = plane wave |ki = 'k (x) = p e
2⇡
10
10 p
x
Momentum eigenfunctions
|-ki
|ki
|ki
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We can analyze the neutron interferometer
looking only at the momentum eigenfunctions:
STATIONARY SOLUTION (no time evolution)
11
Interference
(Calculations: 1)
| (0)i = |ki
The neutron is a plain wave with k>0. The first blade is a
beam splitter (50/50% probability of going up or down)
12
Interference
(Calculations: 2)
1
| 1 i = p (|ki + |-ki)
2
t1
After the first blade, the state is a superposition.
13
Interference
(Calculations: 3)
1
| 2 i = p (|-ki + |ki)
2
t2
The second blade is a mirror, exchanging neutrons
with positive and negative k
14
Interference
(Calculations: 4)
1 i'
| 3 i = p (e |-ki + |ki)
2
t3
Neutrons in the upper path (with negative
momentum) go through the phase flag (an object)
15
Interference
(Calculations: 5)
'
| i = cos ' |ki + sin ' |-ki
The third blade recombines the beams and allows
them to interfere.
16
Interference
'
Detector
P (+k) = cos2 (')
The detector measure the neutron flux intensity
(number of neutrons per unit time).
17
Interference
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18
Flux of particles
•
•
•
Plane wave wavefunction
not properly normalized
(x) = Aeikx is
2
|
(x)|
It is difficult to interpret as
as the
probability of finding a particle at position x.
Interpret v| (x)|2 = I
set
A=
r
mI
~k
19
as a flux of particles
Scattering
of Waves and Particles
20
Transmission
Energy > Potential Step
E=T+V
➜ mv02/2 > mgH
H
Region I
21
Region II
Transmission
Energy > Potential Step
E=T+V
➜ mv02/2 > mgH
H
Region I
22
Region II
Reflection
Energy < Potential Step
E=T+V
➜ mv02/2 < mgH
H
Region I
23
Region II
Reflection
Energy < Potential Step
E=T+V
➜ mv02/2 < mgH
H
Region I
24
Region II
Reflection/Transmission
Reflected wave
e
Incoming wave
ikx
Transmitted wave
ikx
e
25
ikx
e
Reflection/Transmission
Reflected wave
e
Incoming wave
ikx
Transmitted wave
ikx
e
26
ikx
e
MIT OpenCourseWare
http://ocw.mit.edu
22.02 Introduction to Applied Nuclear Physics
Spring 2012
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
MIT OpenCourseWare
http://ocw.mit.edu
22.02 Introduction to Applied Nuclear Physics
Spring 2012
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.