N eutron Interferometry

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N IST Center for N eutron Research

Home to a 20 MW reactor that provides neutrons for scientific research

Dozens of instruments (most for Solid State applications) Some instruments for the study of Fundamental Physics

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Public domain image

The Neutron Interferometer and Optics Facility

Public domain image

Inside the N CN R

Reactor Core

Fuel Elements LH 2

Guide Hall

7 Neutron Guides

NIOF

Public domain images

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Neutr on coming out of the r eactor is a wa v epack et: Sum of man y plane wa v es with diff er ent wa v en umber k [not a stationar y state: e v olv es (mo v es!) in time]

x

F ourier T ransf orm Pair

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 k

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Monoch r omator

Monochr omator selects a small range of momenta

Source: Pushin, Dmitry A. "Coherent Control of Neutron Interferometry." Ph.D. Thesis, MIT, 2006.

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x

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 k

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Neut r on Interf e r ometer

3- blade interf er ometer fr om single Si cr ystal

Public domain image (source: NIST).

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5- blade interf er ometer fr om single Si cr ystal

Photo courtesy of Dmitry Pushin. Used with permission.

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W a v epac k et ➙ Plane w a v e

p

2 p

3 p

4 p

5 p

6 p

7 p

8 p

9 p

10 p

x

Photo courtesy of Dmitry Pushin. Used with permission.

W a v epack et ∆ x ≫ Interf er ometer ➞ consider ∆ x = ∞

or neutr on = plane wa v e k = ϕ k ( x ) =

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1

p 2 π

e ik x

Momentum eigenfunctions

| - k i

| k i

| k i

courtesy of Dmitry Pushin. Used with permission.

W e c a n a n a l y z e t h e n e u t r o n i n t e r f e r o m e t e r looking onl y at the momentum eigenfunctions: S T A TIONA R Y SOLUTION (no time e v olution)

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| ( 0) i = | k i

The neutr on is a plain wa v e with k>0. The first blade is a beam splitter (50/50% pr obability of g oing up or do wn)

p 2 ( | k i + | - k i )

1

t 1

| 1 i =

After the first blade , the state is a superposition.

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| 2 i =

1

p 2 ( | - k i + | k i )

t 2

The second blade is a mir r o r , exchanging neutr ons

with positiv e and negativ e 14 k

| 3 i =

1 i '

p 2 ( e

| - k i + | k i )

t 3

N e u t r o n s i n t h e u p p e r p a t h ( w i t h n e g a t i v e

momentum) g o thr ough t h 1 e 5 phase flag (an object)

ϕ | i = cos ϕ | k i + s i n ϕ | - k i

them to interf er e .

The thir d blade r ecombines the beams and allo ws

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ϕ

The detector measur e the neutr on

Detector

P (+ k ) = cos 2 ( ϕ )

intensity

flux

(n umber of neutr ons

per u n 17 it time).

Courtesy of Dmitry Pushin. Used with permission.

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Flux of par ticles

• Plane wa v e wa v efunction not pr operl y normalized

( x ) = Ae ik x is

• It is difficult to interpr et as

| ( x ) | 2

as the

pr obability of finding a par ticle at position x.

• Interpr et

v | ( x ) | 2 = I

as a flux of par ticles

set

A = mI

~ k 19

Scattering

of W a v es and Par ticles

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H

Region I

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Region II

Energ y > P otential Step E=T+V ➜ mv 0 2 /2 > mgH

H

Region I

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Region II

Energ y > P otential Step E=T+V ➜ mv 0 2 /2 > mgH

H

Region I

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Region II

Energ y < P otential Step E=T+V ➜ mv 0 2 /2 < mgH

H

Region I

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Region II

Energ y < P otential Step E=T+V ➜ mv 0 2 /2 < mgH

Reflected wa v e

e — ik x

T ransmitted wa v e

e ik x

Incoming wa v e

e ik x

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Reflected wa v e

e — ik x

T ransmitted wa v e

e ik x

Incoming wa v e

e ik x

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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 .

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 .