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American Journal of Physics

The geometric phase: A simple optical demonstration

P. Hariharan

Published Jul 1, 1993• 3 citations
Publisher

Abstract

The fact that the wave function of a quantum system may not return to its original phase after its parameters are cycled around a circuit is now well known. The resultant change in phase, known as the geometric phase, has its analog in optics. This paper describes a simple interferometric arrangement that provides a direct demonstration of the geometric phase.

DOI
10.1119/1.17218

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The fact that the wave function of a quantum system may not return to its original phase after its parameters are cycled around a circuit is now well known. The resultant change in phase, known as the geometric phase, has its analog in optics. This paper describes a simple interferometric arrangement that provides a direct demonstration of the geometric phase.
The wave function of a quantum system may acquire an additional phase factor (the geometric phase), when its parameters undergo a cyclic change. An optical manifestation of the geometric phase is the change in the phase of a light wave produced when its state of polarization is taken around a circuit on the Poincare sphere. This phase change can be verified by interferometric measurements. We describe an interferometer in which the two beams traverse the same path in opposite directions, so that their optical paths are always equal, and the phase difference between them is varied by operating on the geometric phase. Measurements made with this interferometer, at a light level at which the probability of more than one photon being present simultaneously in the interferometer was negligibly small, confirmed that the interference effects observed due to the geometric phase persist down to the single photon level.