Abstract

We report a new method that uses magnetic birefringence to enhance the contrast in a neutron interferometer. We performed model calculations for interference-fringe contrast in a Mach–Zehnder-type neutron interferometer with an improperly aligned multilayer mirror and inhomogeneous magnetic fields. Our calculations showed that, by using inhomogeneous magnetic fields, we could recover the decreased contrast caused by the improper alignment of the mirrors.

© 2009 Optical Society of America

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References

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  1. H. Rauch and S. A. Werner, Neutron Interferometry (Oxford U. Press, 2000).
  2. H. Rauch, W. Treimer, and U. Bonse, “ Test of a single crystal neutron interferometer,” Phys. Lett. A 47, 369-371 (1974).
    [CrossRef]
  3. M. Kitaguchi, H. Funahashi, T. Nakura, M. Hino, and H. M. Shimizu, “Cold-neutron interferometer of the Jamin type,” Phys. Rev. A 67, 033609 (2003).
    [CrossRef]
  4. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  5. K. Taketani, Y. Seki, H. Funahashi, M. Hino, M. Kitaguchi, Y. Otake, and H. M. Shimizu, “Moiré fringes in a neutron spin interferometer,” J. Phys. Soc. Jpn. 76, 064008 (2007).
    [CrossRef]
  6. M. J. Bastiaan, “Application of the Wigner distribution function to partially coherent light,” J. Opt. Soc. Am. A 3, 1227-1238 (1986).
    [CrossRef]

2007

K. Taketani, Y. Seki, H. Funahashi, M. Hino, M. Kitaguchi, Y. Otake, and H. M. Shimizu, “Moiré fringes in a neutron spin interferometer,” J. Phys. Soc. Jpn. 76, 064008 (2007).
[CrossRef]

2003

M. Kitaguchi, H. Funahashi, T. Nakura, M. Hino, and H. M. Shimizu, “Cold-neutron interferometer of the Jamin type,” Phys. Rev. A 67, 033609 (2003).
[CrossRef]

1986

1974

H. Rauch, W. Treimer, and U. Bonse, “ Test of a single crystal neutron interferometer,” Phys. Lett. A 47, 369-371 (1974).
[CrossRef]

Bastiaan, M. J.

Bonse, U.

H. Rauch, W. Treimer, and U. Bonse, “ Test of a single crystal neutron interferometer,” Phys. Lett. A 47, 369-371 (1974).
[CrossRef]

Funahashi, H.

K. Taketani, Y. Seki, H. Funahashi, M. Hino, M. Kitaguchi, Y. Otake, and H. M. Shimizu, “Moiré fringes in a neutron spin interferometer,” J. Phys. Soc. Jpn. 76, 064008 (2007).
[CrossRef]

M. Kitaguchi, H. Funahashi, T. Nakura, M. Hino, and H. M. Shimizu, “Cold-neutron interferometer of the Jamin type,” Phys. Rev. A 67, 033609 (2003).
[CrossRef]

Hino, M.

K. Taketani, Y. Seki, H. Funahashi, M. Hino, M. Kitaguchi, Y. Otake, and H. M. Shimizu, “Moiré fringes in a neutron spin interferometer,” J. Phys. Soc. Jpn. 76, 064008 (2007).
[CrossRef]

M. Kitaguchi, H. Funahashi, T. Nakura, M. Hino, and H. M. Shimizu, “Cold-neutron interferometer of the Jamin type,” Phys. Rev. A 67, 033609 (2003).
[CrossRef]

Kitaguchi, M.

K. Taketani, Y. Seki, H. Funahashi, M. Hino, M. Kitaguchi, Y. Otake, and H. M. Shimizu, “Moiré fringes in a neutron spin interferometer,” J. Phys. Soc. Jpn. 76, 064008 (2007).
[CrossRef]

M. Kitaguchi, H. Funahashi, T. Nakura, M. Hino, and H. M. Shimizu, “Cold-neutron interferometer of the Jamin type,” Phys. Rev. A 67, 033609 (2003).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Nakura, T.

M. Kitaguchi, H. Funahashi, T. Nakura, M. Hino, and H. M. Shimizu, “Cold-neutron interferometer of the Jamin type,” Phys. Rev. A 67, 033609 (2003).
[CrossRef]

Otake, Y.

K. Taketani, Y. Seki, H. Funahashi, M. Hino, M. Kitaguchi, Y. Otake, and H. M. Shimizu, “Moiré fringes in a neutron spin interferometer,” J. Phys. Soc. Jpn. 76, 064008 (2007).
[CrossRef]

Rauch, H.

H. Rauch, W. Treimer, and U. Bonse, “ Test of a single crystal neutron interferometer,” Phys. Lett. A 47, 369-371 (1974).
[CrossRef]

H. Rauch and S. A. Werner, Neutron Interferometry (Oxford U. Press, 2000).

Seki, Y.

K. Taketani, Y. Seki, H. Funahashi, M. Hino, M. Kitaguchi, Y. Otake, and H. M. Shimizu, “Moiré fringes in a neutron spin interferometer,” J. Phys. Soc. Jpn. 76, 064008 (2007).
[CrossRef]

Shimizu, H. M.

K. Taketani, Y. Seki, H. Funahashi, M. Hino, M. Kitaguchi, Y. Otake, and H. M. Shimizu, “Moiré fringes in a neutron spin interferometer,” J. Phys. Soc. Jpn. 76, 064008 (2007).
[CrossRef]

M. Kitaguchi, H. Funahashi, T. Nakura, M. Hino, and H. M. Shimizu, “Cold-neutron interferometer of the Jamin type,” Phys. Rev. A 67, 033609 (2003).
[CrossRef]

Taketani, K.

K. Taketani, Y. Seki, H. Funahashi, M. Hino, M. Kitaguchi, Y. Otake, and H. M. Shimizu, “Moiré fringes in a neutron spin interferometer,” J. Phys. Soc. Jpn. 76, 064008 (2007).
[CrossRef]

Treimer, W.

H. Rauch, W. Treimer, and U. Bonse, “ Test of a single crystal neutron interferometer,” Phys. Lett. A 47, 369-371 (1974).
[CrossRef]

Werner, S. A.

H. Rauch and S. A. Werner, Neutron Interferometry (Oxford U. Press, 2000).

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

J. Opt. Soc. Am. A

J. Phys. Soc. Jpn.

K. Taketani, Y. Seki, H. Funahashi, M. Hino, M. Kitaguchi, Y. Otake, and H. M. Shimizu, “Moiré fringes in a neutron spin interferometer,” J. Phys. Soc. Jpn. 76, 064008 (2007).
[CrossRef]

Phys. Lett. A

H. Rauch, W. Treimer, and U. Bonse, “ Test of a single crystal neutron interferometer,” Phys. Lett. A 47, 369-371 (1974).
[CrossRef]

Phys. Rev. A

M. Kitaguchi, H. Funahashi, T. Nakura, M. Hino, and H. M. Shimizu, “Cold-neutron interferometer of the Jamin type,” Phys. Rev. A 67, 033609 (2003).
[CrossRef]

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

H. Rauch and S. A. Werner, Neutron Interferometry (Oxford U. Press, 2000).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic view of a Mach–Zehnder-type multilayer interferometer with a displaced mirror; the spin direction of neutrons traveling along one of the paths is opposite to that of the neutron traveling along the other path. (b) Schematic view of the superposition of two spatially separated paths using a pair of gradient magnetic fields. (c) Schematic view of the superposition of two spatially separated paths using a pair of uniform magnetic fields acting over a triangular region.

Fig. 2
Fig. 2

Coordinates used in Eq. (1). ( Y d , Z d ) are the coordinates of the point on the detector plane; ( Y s 1 , Z s ) and ( Y s 2 , Z s ) , the coordinates of the points on the source plane; G I ( Y d , Y s 1 ; Z d , Z s ) , G II ( Y d , Y s 1 ; Z d , Z s ) , G I ( Y d , Y s 2 ; Z d , Z s ) , and G II ( Y d , Y s 2 ; Z d , Z s ) are Green’s functions for a neutron traveling along different interferometer paths. The Mach–Zehnder-type interferometer and NSI system are not shown.

Fig. 3
Fig. 3

Coordinates used to derive the magnetic-field-induced phases for a neutron in the presence of a gradient magnetic field from a quadrupole magnet (case A) and a uniform magnetic field over a triangular region (case B).

Fig. 4
Fig. 4

Parallel displacement by an amount Δ of M c create a difference between the path lengths of the two beams. Virtual sources I and IIa are the images of a point on the source plane in M c and M a , respectively. Virtual source IIb is the image of virtual source IIa in M b , and virtual source II is the image of virtual source IIb in M d . The parallel displacement of M c creates a difference between the distances of a point on the detector plane from virtual sources I and II.

Fig. 5
Fig. 5

Rotation d t of M c about the vertical axis creates a phase difference between the two paths. Virtual sources I and IIa are the images of a point on the source plane in M c and M a , respectively, virtual source IIb is the image of virtual source IIa in M b , and virtual source II is the image of virtual source IIb in M d . Rotation of the mirror creates a difference between the distances from virtual sources I and II to a point on the detector plane.

Equations (62)

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I ( Y d ; Z d ) = 1 2 ( G I ( Y d , Y s 1 ; Z d , Z s ) + G II ( Y d , Y s 1 ; Z d , Z s ) ) ¯ × ( G I ( Y d , Y s 2 ; Z d , Z s ) + G II ( Y d , Y s 1 ; Z d , Z s ) ) Γ ( Y s 1 , Y s 2 ; Z s ) d Y s 1 d Y s 2 .
G I ( Y d , Y s 1 ; Z d , Z s ) = G I MZ ( Y d , Y s 1 ; Z d , Z s ) G I NSI ( Y d , Y s 1 ; Z d , Z s ) ,
G II ( Y d , Y s 1 ; Z d , Z s ) = G II MZ ( Y d , Y s 1 ; Z d , Z s ) G II NSI ( Y d , Y s 1 ; Z d , Z s ) ,
G I ( Y d , Y s 2 ; Z d , Z s ) = G I MZ ( Y d , Y s 2 ; Z d , Z s ) G I NSI ( Y d , Y s 2 ; Z d , Z s ) ,
G II ( Y d , Y s 2 ; Z d , Z s ) = G II MZ ( Y d , Y s 2 ; Z d , Z s ) G II NSI ( Y d , Y s 2 ; Z d , Z s ) ,
I ( Y d ; Z d ) = G I MZ ( Y d , Y s 1 ; Z d , Z s ) ( G I NSI ( Y d , Y s 1 ; Z d , Z s ) + e i δ Φ ( Y d , Y s 1 ; Z d , Z s ) G II NSI ( Y d , Y s 1 ; Z d , Z s ) ) ¯ × G I MZ ( Y d , Y s 2 ; Z d , Z s ) ( G I NSI ( Y d , Y s 2 ; Z d , Z s ) + e i δ Φ ( Y d , Y s 2 ; Z d , Z s ) G II NSI ( Y d , Y s 2 ; Z d , Z s ) ) × Γ ( Y s 1 , Y s 2 ; Z s ) d Y s 1 d Y s 2 / 2 ,
G I NSI ( Y d , Y s 1 ; Z d , Z s ) + e i δ Φ ( Y d , Y s 1 ; Z d , Z s ) G II NSI ( Y d , Y s 1 ; Z d , Z s )
G I NSI ( Y d , Y s 2 ; Z d , Z s ) + e i δ Φ ( Y d , Y s 2 ; Z d , Z s ) G II NSI ( Y d , Y s 2 ; Z d , Z s )
I ( Y d ; Z d ) = d Y s ( G I NSI ( Y d , Y s ; Z d , Z s ) + e i δ Φ ( Y d , Y s ; Z d , Z s ) G II NSI ( Y d , Y s ; Z d , Z s ) ) ¯ × ( G I NSI ( Y d , Y s ; Z d , Z s ) + e i δ Φ ( Y d , Y s ; Z d , Z s ) G II NSI ( Y d , Y s ; Z d , Z s ) ) × J ( Y d , Y s ; Z d , Z s ) ,
J ( Y d , Y s , Z d , Z s ) = G I MZ ( Y d , Y s ρ 2 ; Z d , Z s ) ¯ G I MZ ( Y d , Y s + ρ 2 , Z d , Z s ) × Γ ( Y s ρ 2 , Y s + ρ 2 ; Z s ) d ρ ,
G I NSI ( Y d , Y s ; Z d , Z s ) = exp ( i Φ B ( Y d , Y s ; Z d , Z s ) ) exp ( i Φ B ( Y d , Y s ; Z d , Z s ) ) ,
G II NSI ( Y d , Y s ; Z d , Z s ) = exp ( i Φ B ( Y d , Y s ; Z d , Z s ) ) + exp ( ι Φ B ( Y d , Y s ; Z d , Z s ) ) ,
I ( Y d , Z d ) = d Y s J ( Y d , Y s ; Z d , Z s ) × ( 1 + cos ( 2 Φ B ( Y d , Y s ; Z d , Z s ) + δ Φ ( Y d , Y s ; Z d , Z s ) ) ) .
J ( y d , y v s ; z d , z v s ) = W ( y vs , y d y v s z d z v s p z ; z v s ) ,
W ( y , p y ; z ) = Γ ( y + y 2 , y y 2 ; z ) exp ( i p y y ) d y .
W ( y v s , p y ; z 0 ) = { J 0 when w v 2 < y v s < w v 2 and p min ( y v s ) < p y < p max ( y v s ) , 0 otherwise ,
p max ( y v s ) = p z ( y v s w v 2 ) / ( z d z v s ) ,
p min ( y v s ) = p z ( y v s w v 2 ) / ( z d z v s ) ,
I ( y d ; z d ) = J 0 w v / 2 w v / 2 [ 1 + cos ( δ Φ B ( y d , y s ; z d , z s ) + δ Φ ( y d , y s ; z d , z s ) ) ] d y s ,
I = J 0 - w v / 2 w v / 2 w v / 2 w v / 2 [ 1 + cos ( δ Φ B ( y d , y s ; z d , z s ) + δ Φ ( y d , y s ; z d , z s ) ) ] d y s d y d .
I = J 0 w h / 2 w h / 2 w h / 2 w h / 2 w v / 2 w v / 2 w V / 2 w V / 2 d y s d y d d x s d x d × [ 1 + cos ( δ Φ B ( x d , x s ; y d , y s ; z d , z s ) + δ Φ ( x d , x s ; y d , y s ; z d , z s ) ) ] ,
δ Φ B ( x d , x s ; y d , y s ; z d , z s ) = α I M ( β M β M 0 ) = α I M ( ( z M z v s ) β d ( z d z M ) β v s z d z v s β M 0 ) ,
α = { α Q = m n λ μ l Q 2 π 2 Δ B ( I Q ) I Q for case A , α T = m n λ μ 2 π 2 2 tan ζ 2 B ( I T ) I T for case B ,
I M = { I Q for case A , I T for case B ,
z M = { z Q for case A , z T for case B ,
β d = { y d for case A , x d for case B ,
β M = { y M for case A , x M for case B ,
β vs = { y vs for case A , x vs for case B ,
β M 0 = { y Q 0 for case A , x T 0 for case B .
δ Φ B ( x d , x s ; y d , y s ; z d , z s ) = α I M ( ( z M 1 z v s ) β d ( z d z M 1 ) β v s z d - z v s y M 0 ) α I M ( ( z M 2 z v s ) β d ( z d z M 2 ) β v s z d z v s y M 0 ) = α I M ( L M ( β d β s ) z d z s ) ,
cos θ ( x x m + l ) sin θ ( z z m ) = 0 ,
cos θ ( x x m + 2 l ) sin θ ( z z m ) = 0 ,
cos θ ( x x m Δ ) + sin θ ( z z m ) = 0 ,
cos θ ( x x m + l ) sin θ ( z z m ) = 0.
( x s II y s II z s II ) = ( ( tan 2 θ 1 ) x s + 2 ( z s z m ) tan θ + 2 x m tan 2 θ + 1 y s ( 1 tan 2 θ ) z s + 2 ( x s x m ) tan θ + 2 z m tan 2 θ 1 + tan 2 θ ) ,
( x s I y s I z s I ) = ( x s II + 2 Δ 1 + tan 2 θ y s II z s I - 2 Δ tan θ 1 + tan 2 θ ) .
δ Φ ( x s , y s , z s ; x d , y d , z d ) = l I l II λ ˜ 2 Δ ( x vs x d ) + 2 Δ tan θ ( z d z vs ) λ ( z d - z vs ) ( 1 + tan 2 θ ) .
cos θ ( x x m + l ) sin θ ( z z m ) = 0 ,
cos θ ( x x m + 2 l ) sin θ ( z z m ) = 0 ,
cos ( θ + d t ) ( x x m ) + d f ( y y m ) sin ( θ + d t ) ( z z m ) = 0 ,
cos θ ( x x m + l ) sin θ ( z z m ) = 0.
( x s II y s II z s II ) = ( ( x s x m ) sin 2 θ + z s cos 2 θ + 2 z m sin 2 θ y s ( z s z m ) sin 2 θ + x s cos 2 θ + 2 x m cos 2 θ ) ,
( x s I y s I z s I ) = ( x s II + d t ( ( z s z m ) + 2 θ ( x s x m ) ) 2 y s d f y s II + 2 d f ( ( x m x s ) + θ ( z s z m ) ) z s I + 2 d t ( ( x s x m ) + 2 θ ( z m z s ) ) + 2 θ y s d f ) .
δ Φ ( x s , y s , z s ; x d , y d , z d ) = l I l II λ ˜ d t 2 ( z m z v s ) x d + 2 ( z d z m ) x v s + 2 ( z v s z d ) x m λ ( z d z v s ) + d f 2 θ ( z v s z m ) y d + 2 θ ( z m z d ) y v s λ ( z d z v s ) .
I = J 0 w h / 2 w h / 2 w h / 2 w h / 2 w v / 2 w v / 2 w v / 2 w v / 2 1 + cos ( a y v s + b y d + c x v s + d x d + e ) d y v s d y d d x v s d x d = J 0 w h 2 w v 2 ( 1 + C cos e ) ,
C = sin a w v 2 a w v 2 sin b w v 2 b w v 2 sin c w h 2 c w h 2 sin d w h 2 d w h 2 .
( sin α α ) 2 ,
α = w 2 Δ λ ( z d z vs ) .
( sin α h α h ) 2 ( sin α v α v ) 2
α v = d f θ λ w v 2 ,
α h = d t λ w h 2 .
c = Δ λ 1 z d z s α Q I Q z Q 1 z Q 2 z d z s ,
d = Δ λ 1 z d z s + α Q I Q z Q 1 z Q 2 z d z s .
α Q I Q ( z Q 1 z Q 2 ) = Δ λ .
c = d f θ λ z d z m z d z s + α Q I Q z d z Q z d z s ,
d = d f θ λ z m z s z d z s α Q I Q z m z s z d z s .
α Q I Q = d f θ λ ,
z Q = z m .
a = d t λ z d z m z d z s + α T I T z d z T z d z s ,
b = d t λ z m z s z d z s α T I T z m z s z d z s .
α T I T = d t λ ,
z T = z m .

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