Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Noncommuting spinor rotation due to balanced geometrical and dynamical phases

Yuji Hasegawa, G. Badurek

Published Jun 1, 1999• 15 citations
Publisher

Abstract

A neutron polarimetric textbook experiment is performed to demonstrate the noncommutation properties of the Pauli spin operator. The polarization of the transmitted neutron beam depends upon the sequential order of two successive spin-flip devices with mutually inclined precession axes. Furthermore, an interpretation of the observed results is presented in terms of an intrinsic phase shift between two interfering mutually orthogonal spin states, which in a sequence of two successive spinor transformations stores particular information about the intermediate state. This phase shift is discussed with respect to its geometrical and dynamical components, and its formal connection with the noncommuting properties of Pauli spin operators is explicitly shown.

DOI
10.1103/physreva.59.4614

Related papers

Observation of geometric and dynamical phases by neutron interferometry

Brendan E. Allman, Helmut Kaiser, S. A. Werner +3 more

The total phase acquired during an evolution of a quantal system has two components: the usual dynamical phase, $\ensuremath{-}1/\ensuremath{\Elzxh}\ensuremath{\int}H(t)dt,$ given by the integrated expectation value of the Hamiltonian, and a geometric phase ${\ensuremath{\Phi}}_{G}(C)$ which depends only on the geometry of the curve traced in ray space. We have performed an interference experiment using polarized neutrons which clearly demarcates the separate contributions of the dynamical and geometric phases to the total. In the experiment, the two phases arise from two distinct physical operations, a translation and a rotation of a spin flipper within the interferometer, respectively. This work also constitutes the first direct observation of the Pauli anticommutation; a purely geometric phase shift of \ensuremath{\pi} radians appears after a reversal of the current in one of the spin flippers. The experiment was carried out at the 10 MW University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. A detailed description of the experiment and its interpretation is given in this paper.

Physical Review A•Dec 1, 1997•44 citations

Experimental Separation of Geometric and Dynamical Phases Using Neutron Interferometry

Apoorva G. Wagh, Veer Chand Rakhecha, Johann Summhammer +7 more

We present results of the first experiment clearly demarcating geometric and dynamical phases. These two phases arise from two distinct physical operations, a rotation and a linear translation, respectively, performed on two identical spin flippers in a neutron interferometer. A reversal of the current in one flipper results in a pure geometric phase shift of \ensuremath{\pi} radians. This observation constitutes the first direct verification of Pauli anticommutation, implemented in neutron interferometry.

Physical Review Letters•Feb 3, 1997•88 citations

Spin-rotation coupling observed in neutron interferometry

Armin Danner, Demirel, Buelent, Wenzel Kersten +4 more

Einstein's theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle's intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin's coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli-Schrodinger equation.

•Feb 14, 2020•21 citations

Spin-rotation coupling observed in neutron interferometry

Armin Danner, Bülent Demirel, Wenzel Kersten +4 more

Abstract Einstein’s theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle’s intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin’s coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli–Schrödinger equation.

arXiv:1904.07085•npj Quantum Information•Feb 14, 2020•23 citations

Observation of 4π-periodicity of the spinor using neutron resonance interferometry

Wicher H. Kraan, Сергей Валентинович Григорьев, M.Th. Rekveldt

A polarised neutron beam is passed through a gradient resonance flipper. By the amplitude of their RF field, such flippers can be set at flip probability ρ = 0, 1, or ½. At ½, the neutron wave splits into a flipped and a non-flipped part with different precession. We measure the polarisation after a spin-echo (SE) setup with each precession arm made up of 2 such flippers. Offset from SE is made by varying the static fields in one flipper while the other flippers stay unchanged. This shows up as a periodic behaviour of the polarisation. With incoming polarisation parallel to the static field in the flippers–set at ρ = ½–this period is twice the period measured for both ρ = 0 and 1 and with polarisation perpendicular to the static field. In the latter experiments both components of the spinor are affected, whereas in the former experiment we create spin states in which only one spinor component in one state is affected. Hence, this experiment demonstrates explicitly the 4π-periodicity of the spinor.

Europhysics Letters (EPL)•Apr 1, 2004•4 citations

Measurement of the spin–rotation coupling in neutron polarimetry

Bülent Demirel, Stephan Sponar, Yuji Hasegawa

The effect of spin–rotation coupling is measured for the first time with neutrons. The coupling of spin with the angular velocity of a rotating spin turner can be observed as a phase shift in a neutron polarimeter set-up. After the neutron's spin is rotated by 2 π through a rotating magnetic field, different phase shifts are induced for 'up' and 'down' spin eigenstates. This phase difference results in the rotation of the neutron's spin-vector, which turns out to depend solely on the frequency of the rotation of the magnetic field. The experimental results agree well with the solutions acquired by the Pauli–Schrödinger equation.

New Journal of Physics•Feb 24, 2015•20 citations
A neutron polarimetric textbook experiment is performed to demonstrate the noncommutation properties of the Pauli spin operator. The polarization of the transmitted neutron beam depends upon the sequential order of two successive spin-flip devices with mutually inclined precession axes. Furthermore, an interpretation of the observed results is presented in terms of an intrinsic phase shift between two interfering mutually orthogonal spin states, which in a sequence of two successive spinor transformations stores particular information about the intermediate state. This phase shift is discussed with respect to its geometrical and dynamical components, and its formal connection with the noncommuting properties of Pauli spin operators is explicitly shown.
The total phase acquired during an evolution of a quantal system has two components: the usual dynamical phase, $\ensuremath{-}1/\ensuremath{\Elzxh}\ensuremath{\int}H(t)dt,$ given by the integrated expectation value of the Hamiltonian, and a geometric phase ${\ensuremath{\Phi}}_{G}(C)$ which depends only on the geometry of the curve traced in ray space. We have performed an interference experiment using polarized neutrons which clearly demarcates the separate contributions of the dynamical and geometric phases to the total. In the experiment, the two phases arise from two distinct physical operations, a translation and a rotation of a spin flipper within the interferometer, respectively. This work also constitutes the first direct observation of the Pauli anticommutation; a purely geometric phase shift of \ensuremath{\pi} radians appears after a reversal of the current in one of the spin flippers. The experiment was carried out at the 10 MW University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. A detailed description of the experiment and its interpretation is given in this paper.
We present results of the first experiment clearly demarcating geometric and dynamical phases. These two phases arise from two distinct physical operations, a rotation and a linear translation, respectively, performed on two identical spin flippers in a neutron interferometer. A reversal of the current in one flipper results in a pure geometric phase shift of \ensuremath{\pi} radians. This observation constitutes the first direct verification of Pauli anticommutation, implemented in neutron interferometry.
Einstein's theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle's intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin's coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli-Schrodinger equation.
Abstract Einstein’s theory of general relativity and quantum theory form the two major pillars of modern physics. However, certain inertial properties of a particle’s intrinsic spin are inconspicuous while the inertial properties of mass are well known. Here, by performing a neutron interferometric experiment, we observe phase shifts arising as a consequence of the spin’s coupling with the angular velocity of a rotating magnetic field. This coupling is a purely quantum mechanical extension of the Sagnac effect. The resulting phase shifts linearly depend on the frequency of the rotation of the magnetic field. Our results agree with the predictions derived from the Pauli–Schrödinger equation.
A polarised neutron beam is passed through a gradient resonance flipper. By the amplitude of their RF field, such flippers can be set at flip probability ρ = 0, 1, or ½. At ½, the neutron wave splits into a flipped and a non-flipped part with different precession. We measure the polarisation after a spin-echo (SE) setup with each precession arm made up of 2 such flippers. Offset from SE is made by varying the static fields in one flipper while the other flippers stay unchanged. This shows up as a periodic behaviour of the polarisation. With incoming polarisation parallel to the static field in the flippers–set at ρ = ½–this period is twice the period measured for both ρ = 0 and 1 and with polarisation perpendicular to the static field. In the latter experiments both components of the spinor are affected, whereas in the former experiment we create spin states in which only one spinor component in one state is affected. Hence, this experiment demonstrates explicitly the 4π-periodicity of the spinor.
The effect of spin–rotation coupling is measured for the first time with neutrons. The coupling of spin with the angular velocity of a rotating spin turner can be observed as a phase shift in a neutron polarimeter set-up. After the neutron's spin is rotated by 2 π through a rotating magnetic field, different phase shifts are induced for 'up' and 'down' spin eigenstates. This phase difference results in the rotation of the neutron's spin-vector, which turns out to depend solely on the frequency of the rotation of the magnetic field. The experimental results agree well with the solutions acquired by the Pauli–Schrödinger equation.