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Physical Review A

Direct observation of fermion spin superposition by neutron interferometry

Johann Summhammer, G. Badurek, H. Rauch, U. Kischko, Anton Zeilinger

Published May 1, 1983• 137 citations
Publisher

Abstract

The coherent superposition of oppositely polarized neutron beams of equal amplitude results in a final beam polarization perpendicular to the polarization of both initial beams. This polarization can be rotated by purely scalar interaction applied to the beams before superposition, which is equivalent to an additional Larmor precession applied to the beam after superposition. We have directly observed these effects in an experiment performed using the perfect-crystal neutron interferometer at the high-flux reactor at Grenoble. This paper gives the experimental results and discusses their theoretical foundation.

DOI
10.1103/physreva.27.2523

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The coherent superposition of oppositely polarized neutron beams of equal amplitude results in a final beam polarization perpendicular to the polarization of both initial beams. This polarization can be rotated by purely scalar interaction applied to the beams before superposition, which is equivalent to an additional Larmor precession applied to the beam after superposition. We have directly observed these effects in an experiment performed using the perfect-crystal neutron interferometer at the high-flux reactor at Grenoble. This paper gives the experimental results and discusses their theoretical foundation.
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.
If a spin-½ particle is placed in a constant uniform magnetic field for a time t during which, classically, the Larmor precession angle would be θ, then according to quantum mechanics the components of the spin part of the wave function undergo phase changes of ±θ/2. Hence, corresponding to a classical precession of 2π radians, there is a sign change of the spinor, whatever the initial polarization may be. Bernstein pointed out that this sign change can be observed by coherently splitting a fermion beam, subjecting one part to the magnetic field, and coherently recombining the parts. Evidently, the same interference effect can be achieved by subjecting the two parts of the beam to fields which would classically cause precessions of π radians in opposite senses. He noted advantages in studying neutral rather than charged particles, and outlined a proposal for an interferometry experiment with neutrons. The recent invention and application of a remarkable single-crystal neutron interferometer greatly increases the feasibility of observing the sign change. In the experiment of Ref. 3 a neutron beam is split, and the two parts follow paths of different elevations. The interference of the recombined parts exhibits the effect of gravitational potential difference between the two elevations. In the experiment which we propose, the paths could be kept at the same elevation, but phase differences would be produced by appropriate magnetic fields.
The coherent superposition of particle quantum states resulting from different spatial paths shows well-known interference effects. Another type of interference is Larmor precession, which can be described as neutron wave interference in spin space, i.e. interference on the same spatial path. Here we show several new manifestations of interference phenomena of the latter type. The interference is produced by coherent population of different I z = ±½ spin states in a polarized neutron beam between two resonant radio-frequency (RF) spin flippers. Their spin flip probability, and thus the occupation numbers of the spin states, can be tuned between 0 and 1 by changing the RF amplitude. This leads to interference effects in the polarization since the energy exchanged between the RF field and spin yields different phase evolution in the spatial parts of the neutron states. Depending on the preparation of the initial neutron states, five values for the time-independent phase difference between the final neutron states can be observed.
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.
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Recent neutron interferometer experiments focused on coherence measurements and have shown that coherence features are determined by the beam preparation only. The wave function contains information about the particle and about the beam preparation simultaneously which signalizes the connection between quantum system and apparatus. Further experiments investigated the question of quantum decoherence and how a quantum system can evolve into a classical system. The experiments have been performed with a perfect crystal neutron interferometer at the high flux reactor of the Institut Laue‐Langevin in Grenoble. The distinction between dephasing and decoherence will be discussed.