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Physical Review Letters

Measurement of Berry’s phase for noncyclic evolution

Harald Weinfurter, G. Badurek

Published Mar 19, 1990• 88 citations
Publisher

Abstract

Tracing the neutron spin on its passage through a magnetic field which rotates at various frequencies it was possible to observe geometrically induced phase shifts of a quantum-mechanical state even for incomplete revolutions of this field. The experiments show that we can extract such purely geometric effects also from nonadiabatic evolutions.

DOI
10.1103/physrevlett.64.1318

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Molecular Physics•Dec 20, 1994•4 citations
Tracing the neutron spin on its passage through a magnetic field which rotates at various frequencies it was possible to observe geometrically induced phase shifts of a quantum-mechanical state even for incomplete revolutions of this field. The experiments show that we can extract such purely geometric effects also from nonadiabatic evolutions.
Off-diagonal geometric phases acquired in the evolution of a spin-1/2 system have been investigated by means of a polarized neutron interferometer. Final counts with and without polarization analysis enable us to observe simultaneously the off-diagonal and diagonal geometric phases in two detectors. We have quantitatively measured the off-diagonal geometric phase for noncyclic evolutions, confirming the theoretical predictions. We discuss the significance of our experiment in terms of geometric phases (both diagonal and off- diagonal) and in terms of the quantum-erasing phenomenon.
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.