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Physical Review Letters

Neutron interferometry in a rotating frame of reference

Bahram Mashhoon

Published Dec 5, 1988• 323 citations
Publisher

Abstract

The physical basis for the description of phenomena by a rotating observer is investigated. A simple, yet tentative, extension of the hypothesis of locality is used to determine the interference phase shift induced by the rotation of a neutron interferometer. The result consists of the Sagnac term, which is due to the coupling of the orbital angular momentum of the neutron with the rotation of the frame, and a new term which arises from a similar coupling because of the neutron spin. The latter effect is generally smaller than the Sagnac phase shift by the ratio of de Broglie wavelength of the neutron to the dimension of the interferometer. The possibility of detecting the new effect is briefly discussed.

DOI
10.1103/physrevlett.61.2639

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The physical basis for the description of phenomena by a rotating observer is investigated. A simple, yet tentative, extension of the hypothesis of locality is used to determine the interference phase shift induced by the rotation of a neutron interferometer. The result consists of the Sagnac term, which is due to the coupling of the orbital angular momentum of the neutron with the rotation of the frame, and a new term which arises from a similar coupling because of the neutron spin. The latter effect is generally smaller than the Sagnac phase shift by the ratio of de Broglie wavelength of the neutron to the dimension of the interferometer. The possibility of detecting the new effect is briefly discussed.
Abstract The fundamental dual nature of neutrons –sometimes a particle (when detected) and sometimes a wave (when traversing the interferometer) – is wonderfully mani-fested by the non-local nature of the neutron interferometry experiments discussed in this chapter. We begin with a discussion of the series of experiments, called gravitationally induced quantum interference, in Section 7.1. Then in Section 7.2, the effect of the Earth’s rotation on the phase of a neutron de Broglie wave is described. This is the quantum mechanical analogue of the Michelson et al. (1925) experiment with light. An experiment in which this Sagnac phase shift was observed due to rotation of the interferometer on a turntable phase within the laboratory frame is also discussed (Atwood et al. 1984). An experiment related to the small effective mass of the neutron propagating in a crystal under Bragg reflecting conditions and its deflection due to the Coriolis force is discussed in Section 7.2.3 (Raum et al. 1997). Acceleration-induced interference, which is related to the gravity experiments by the principle of equivalence, is discussed in Section 7.3 (Bonse and Wroblewski 1983). Phase shifts caused by the motion of matter within the interferometer are related to the optical Fizeau effect. Several neutron Fizeau-type experiments are discussed in Section 7.4.
Experiments involving quantum interference of neutron de Broglie waves, having a wavelength A , extending over macroscopic distances of order are described. In particular I discuss interference induced by the Earth's gravitational field and by its rotation (Sagnac effect), the topological phase shifts resulting from the diffraction of the neutron, carrying its magnetic moment , around a charged electrode (Aharonov--Casher effect) and then finally during its passage through a pulsed magnetic field (scalar Aharonov--Bohm effect).
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.
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.
A coupling between Earth's rotation and orbital angular momentum (OAM), known as the Sagnac effect, is observed in entangled neutrons produced using a spin-echo interferometer. After correction for instrument systematics the measured coupling is within 5% of theory, with an uncertainty of 7.2%. The OAM in our setup is transverse to the propagation direction and scales linearly with neutron wavelength (4–12.75 Å), so the Sagnac coupling can be varied without mechanically rotating the device, which avoids systematic errors present in previous experiments. The detected transverse OAM of our beam corresponds to 4098 ± 295 ℏ Å − 1 , 10 5 times lower than in the previous neutron experiments. This demonstrates the feasibility of using the Sagnac effect to definitively measure neutron OAM and paves the way towards a future observation of the quantum Sagnac effect.
The phase shift of matter wave due to the Earth's rotation and gravity has been demonstrated in the neutron-interferometry experiments where the Bragg reflection of the neutron wave from crystals is used to form a closed path. In the literature, the rotation-induced phase shift is ascribed to an extra energy term associated with angular momentum in the Hamiltonian. In this investigation, based on a classical treatment of the collision of neutrons with the lattice planes, the modifications in the particle velocity due to the Earth's rotation as well as those due to gravity are calculated. Then, in conjunction with the relation between the particle velocity and the propagation vector of matter wave, it is shown that the corresponding phase shifts in matter wave are in accord with the interference experiments. Thereby, based on the velocity modification due to collision, a reinterpretation of the effects of the Earth's rotation and gravity on the neutron-wave interference is presented. Meanwhile, a null effect of the Earth's orbital motion is predicted.