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Canadian Journal of Physics

Spinor interferometry by nuclear magnetic resonance

R. I. Kaiser

Published Oct 1, 1978• 7 citations
Publisher

Abstract

The components of spinors corresponding to half integral spin value transform under rotation of the spatial coordinate system with a matrix of even dimensionality. This leads to a state function phase factor with period 4π rad in the rotation angle. A spectroscopic interference experiment to observe such phase factors is described in analogy with double-beam interferometry. The experiment is performed with the techniques of high resolution nuclear magnetic resonance spectroscopy and the rotational symmetry of composite spin [Formula: see text], 1, and [Formula: see text] particles is explored by calculation and observation. Side effects relating to inhomogeneity dephasing and relaxation are evident in the experimental recordings, but they are discussed only briefly. A relation is established between the spectroscopic interference experiment and earlier "spin tickling" experiments.

DOI
10.1139/p78-173

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The components of spinors corresponding to half integral spin value transform under rotation of the spatial coordinate system with a matrix of even dimensionality. This leads to a state function phase factor with period 4π rad in the rotation angle. A spectroscopic interference experiment to observe such phase factors is described in analogy with double-beam interferometry. The experiment is performed with the techniques of high resolution nuclear magnetic resonance spectroscopy and the rotational symmetry of composite spin [Formula: see text], 1, and [Formula: see text] particles is explored by calculation and observation. Side effects relating to inhomogeneity dephasing and relaxation are evident in the experimental recordings, but they are discussed only briefly. A relation is established between the spectroscopic interference experiment and earlier "spin tickling" experiments.
The results of a nuclear-magnetic-resonance experiment are presented which directly demonstrate the spinor character of a spin-\textonehalf{} nucleus, 13C^{13}\mathrm{C}13C. The interferometric spectroscopic technique used and its potential applications are discussed.
Since its advent in 1974, the neutron interferometry technique is a powerful tool for tests of quantum mechanics by matter waves. High order interference pattern could be observed and an upper limit for nonlinear terms in the Schroedinger equation has been given. The 4..pi..-symmetry of a spinor wave function was verified in 1975. Afterwards a precision measurement of this 4..pi..-symmetry effect has been performed which yields, after corrections for the new values of the fundamental constants, a periodicity factor of ..cap alpha.. = 715.87 +- 3.8 deg which does not include the expected 720 deg within its simple error limits. Alternative formulations of quantum mechanics predict a deviation of the 4..pi..-periodicity factor in the region of strong interaction. Therefore, a precision measurement of the influence of strong interactions is proposed where the spinor rotation is observed within the region of additional strong interactions caused by a nonmagnetic material of heavy nuclei inserted alternatively into the beam paths of the interferometer. It is expected to reach an accuracy concerning the additional phase shift in the range of 10/sup -5/ which corresponds to deviation factors within the region of strong interactions of about 20% from the standard formulation. Various factors limiting themore » accuracy are discussed.« less
The observation of the 4π symmetry of spinor wave functions was one of the first and highly debated neutron interference experiments. Polarized neutrons have been used to verify the spin-superposition principle on a macroscopic level when the spin in one beam path is inverted with respect to the other one. This results in a spin polarization perpendicular to both initial spins. When a Rabi flipper is used the final spin polarization rotates in this perpendicular plane with the Larmor frequency of the flipper field. Thus, it produces a “frozen” Larmor spin rotation in free space. In this case the spin-flip is associated with an energy (photon) transfer which causes this effect. A magnetic Josephson effect-like situation exists when spin-flippers with slightly different resonance frequencies are used in both beam paths. When such a spin reversal is done in both beam paths a magnetic Josephson effect analog has been realized which shows a remarkably high energy resolution. Multiphoton exchange can be achieved when off-resonance fields are used.
Experimental detection of geometric phase effects is based on interferometry techniques. The observation of a nonadiabatic geometric phase in nuclear magnetic resonance has been reported by D. Suter, K. T. Mueller, and A. Pines (1988, Phys. Rev. Lett., 60, 1218). A rigorous interpretation of their results is presented here. The experiment exploits the concept of fictitious spin-1/2 subsystems embedded in a spin system of higher order. A relevant expression for the geometric phase is derived here using the Euler rotation representation for the SU(2) group. In order to correlate the experimental data to the geometric phase, a decomposition of the density matrix in a basis of pure states is used and the isomorphism between the cyclic evolution of pure states and mixed states is constructed. Rigorous treatment of the dynamic phase, along with technical aspects of the experiment, shows that the observed echo shift is related directly to the geometric phase, in agreement with Suter et al. The observed geometric phase is classified as a frame-related phase.
Since the invention of perfect crystal neutron interferometry this technique has become an important tool in the realization of many textbook experiments in quantum mechanics. Widely separated coherent beams of thermal neutrons are produced and superposed by dynamical Bragg diffraction from a properly shaped perfect crystal. The observed interference patterns show the characteristic coherence properties of matter waves which arc influenced by the individual particle and by the properties of the experimental device. The verification of the 4π-periodicity of spinor wavefunctions and the realization of thc spin-superposition experiment on B macroscopic scale has become feasible by this technique. A new kind of a quantum beat effect with an energy sensitivity of 2.7 × 20−-19 eV has been observed in a double coil resonance experiment. The influence of gravity and of the Earth's rotation on the wavefunction become visible at a level of an elementary particle with non-zero mass. All the results are in agreement with the formulation of quantum mechanics but, nevertheless, they stimulate discussion about its interpretation. The particle-wave dualism becomes obvious on a macroscopic scale and with a beam of massive particles.