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Physical Review Letters

Evolving Geometric Phase and Its Dynamical Manifestation as a Frequency Shift: An Optical Experiment

R. Simon, Harry J. Kimble, E. C. G. Sudarshan

Published Jul 4, 1988• 229 citations
Publisher

Abstract

We show that an evolving geometric phase induces a frequency shift. We report an optical experiment where we employ this effect to offset the frequency of a laser beam.
DOI
10.1103/physrevlett.61.19

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Geometric phases arise in a number of physical situations and often lead to systematic shifts in frequencies or phases measured in precision experiments. We describe, by working through some simple examples, a method to calculate geometric phases that relies only on standard quantum mechanical calculations of energy level shifts. This connection between geometric phases and off-resonant energy shifts simplifies calculation of the effect in certain situations. More generally, it also provides a way to understand and calculate geometric phases without recourse to topology.
We investigate the phenomenon that a Berry phase evolving linearly in time induces a frequency shift of the resonance transition between two eigenstates, regardless of whether or not they are superposed. Using the magnetic-field-insensitive two-photon microwave---radio-frequency transition, which is free of any other dynamical frequency shift, we demonstrate that the frequency shift caused by a uniform rotation of the magnetic field corresponds to the derivative of the Berry phase with respect to time and depends on the direction of rotation of the magnetic field.