Quantum precession of cold neutron spin using multilayer spin splitters
and a phase-spin-echo interferometer
Toru Ebisawa,
1
Seiji Tasaki,
1
Takeshi Kawai,
1
Masahiro Hino,
1
Norio Achiwa,
2
Yoshie Otake,
3
Haruhiko Funahashi,
4
Dai Yamazaki,
5
and Tsunekazu Akiyoshi
1
1
Research Reactor Institute, Kyoto University, Kumatori, Osaka 590-0494, Japan
2
Department of Physics, Kyushu University, Higashi-ku, Fukuoka 812-8581, Japan
3
The Institute of Physical and Chemical Research (RIKEN), Mikazuki, Hyogo 679-5143, Japan
4
Department of Physics, Kyoto University, Sakyo-Ku, Kyoto 606, Japan
5
Department of Nuclear Engineering, Kyoto University, Sakyo-ku, Kyoto 606-5801, Japan
Received 26 December 1996; revised manuscript received 26 November 1997
We demonstrate a method of inducing neutron spin rotation in a field-free region of space. A multilayer
mirror ‘‘spin splitter’’ is used as an optically active element, providing a longer path length for one spin
eigenstate of a polarized neutron than for the other. This produces a relative phase shift between the two
eigenstates, which is interpreted, quantum mechanically, as precession of the neutron spin. We show that the
spin precession of our technique is equivalent to Larmor precession in a magnetic field, though our method has
no such classical analog and occurs on shorter e.g., 20 nm length scales. We also demonstrate a ‘‘phase
spin-echo’’ interferometer based on a pair of multilayer spin splitters. S1050-29479803906-7
PACS numbers: 03.75.Dg
I. INTRODUCTION
The spin of the neutron has been an interesting subject for
many years, in large part because it provides a system that is
at least superficially simple to consider. The proper descrip-
tion of the neutron spin is quantum mechanical, with a po-
larized neutron state described as a superposition of the
eigenstates along some quantization axis of choice 1–5.
Precession of the neutron spin can then be thought of as the
introduction of a relative phase shift between the spin eigen-
states.
The quantum-mechanical interpretation of spin precession
as a relative phase shift in the eigenstates is both useful and
extremely general. On the one hand, it can be used to explain
effects having clear classical analogs, such as Larmor pre-
cession in magnetic field, while on the other, it permits de-
scription of more general physical effects, including zero-
field precession in the resonance spin-echo technique 6,7
and various neutron optical effects 8–12. We refer to this
general class of phenomena, particularly those without clas-
sical analogs, by the term ‘‘quantum precession.’’
Here, we demonstrate a type of neutron optical device, a
‘‘multilayer spin splitter,’’ that induces quantum precession
of the neutron spin 8,9. It consists of a magnetic multilayer
mirror on top, followed by a gap layer and a nonmagnetic
mirror. The top magnetic mirror reflects one spin eigenstate
while the lower nonmagnetic mirror reflects the other eigen-
state. The presence of the gap layer, however, creates a path-
length difference for the two eigenstates. This results in a
relative phase shift and, therefore, a quantum precession of
the neutron spin.
This paper has four essential sections: 1 description of
the structure and principles of the multilayer spin splitter; 2
demonstration of the operation of our spin splitters in a type
of spin interferometer; 3 demonstration of the equivalency
of the our quantum precession with Larmor precession in a
magnetic field; and 4 demonstration of a type of ‘‘phase-
spin-echo’’ neutron interferometer using a pair of multilayer
spin splitters.
II. QUANTUM PRECESSION OF NEUTRON SPIN
WITH MULTILAYER SPIN SPLITTER
Let us consider a neutron polarized in the ( x , y ) plane
perpendicular to our quantization ( z ) axis. Equations 2.1
and 2.2 then express the neutron state | S
xy
( ) and the
expectation value of the x -component S
x
( ) 1–3, re-
spectively:
| S
xy
=
1
2
| ↑
z
+e
i
| ↓
z
=e
i /2
cos
2
| ↑
x
-i sin
2
| ↓
x
2
2.1
S
x
=cos , 2.2
where is the phase difference between the spin eigenstates.
The validity of this description was demonstrated experimen-
tally by Summhammer et al. using a silicon interferometer
4,5. S
x
( ) is measured by the coupled system of a /2
flipper and an analyzer in a cold neutron spin interferometer,
as used in conventional spin-echo technique.
The equation shows that the polarized neutron is de-
scribed by the coherent superposition of the two spin eigen-
states. gives both the relative phase shift between the spin
eigenstates and the precession of the neutron spin. This per-
mits an expanded concept of spin precession called quantum
precession.
We consider a neutron optical device of a composite
multilayer system consisting of a pair of parallel mirrors on
PHYSICAL REVIEW A JUNE 1998 VOLUME 57, NUMBER 6
57 1050-2947/98/576/472010/$15.00 4720 © 1998 The American Physical Society