We demonstrated the noncyclic Berry phase based on the geodesic rule proposed by Samuel and Bhandari using two dynamical phase-free systems in a spin-redirection evolution. In the atom interferometer with a noncyclic rotating magnetic field, the quasi-geodesic arc was realized by a straight line connecting the initial and the final points. The phase shifts were measured for noncyclic evolutions and cyclic evolutions connected by several quasi-geodesic arcs. The other system to observe the noncyclic Berry phase for change in the propagation direction of light was a single mode fiber wounded on an auxiliary cylinder to realize strictly back along the real geodesic arc joining the final to the initial point. Theses observed phase shifts were in good agreement with the theoretical values of the noncyclic Berry phase based on the geodesic rule.We demonstrated the noncyclic Berry phase based on the geodesic rule proposed by Samuel and Bhandari using two dynamical phase-free systems in a spin-redirection evolution. In the atom interferometer with a noncyclic rotating magnetic field, the quasi-geodesic arc was realized by a straight line connecting the initial and the final points. The phase shifts were measured for noncyclic evolutions and cyclic evolutions connected by several quasi-geodesic arcs. The other system to observe the noncyclic Berry phase for change in the propagation direction of light was a single mode fiber wounded on an auxiliary cylinder to realize strictly back along the real geodesic arc joining the final to the initial point. Theses observed phase shifts were in good agreement with the theoretical values of the noncyclic Berry phase based on the geodesic rule.

Journal of the Physical Society of JapanOct 25, 20133 citations

A new approach to calculating the Berry phase

Lian-Ao Wu, Jing Sun, Ji-Yu Zhong

Physics Letters ADec 1, 199316 citations

The stability of Berry's phases

Stefan Giller, Cezary Gonera, Piotr Kosiński +1 more

Physics Letters ADec 1, 19940 citations

Noncyclic continuous Pancharatnam—Berry phase in dual-beam interference

Aleksi Leinonen, Antti Hannonen, Henri Partanen +4 more

Abstract The geometric phase for classical electromagnetic light beams, in its original formulation as introduced by Pancharatnam, concerns fields experiencing cyclic, discrete in-phase polarization-state changes. A similar phase was later recognized by Berry to govern the behavior of adiabatic quantum systems, with consequent extensions to nonadiabatic and noncyclic evolutions of the quantum state. However, no optical counterpart for the noncyclic, adiabatic (continuous) evolution has been demonstrated. Here we employ a modified Young’s two-pinhole setup with controlled pinhole polarizations and intensities to generate on interference an arbitrary continuous spatial evolution of the polarization state, an optical analogue to the adiabatic case. The customized arrangement allows separating at any point the accumulated dynamical and geometric phases from the total phase, enabling a detailed study of the noncyclic Pancharatnam–Berry phase in a continuous transformation. Our theoretical and experimental results are in excellent agreement and consistent with the geodesic rule for noncyclic evolutions.Abstract The geometric phase for classical electromagnetic light beams, in its original formulation as introduced by Pancharatnam, concerns fields experiencing cyclic, discrete in-phase polarization-state changes. A similar phase was later recognized by Berry to govern the behavior of adiabatic quantum systems, with consequent extensions to nonadiabatic and noncyclic evolutions of the quantum state. However, no optical counterpart for the noncyclic, adiabatic (continuous) evolution has been demonstrated. Here we employ a modified Young’s two-pinhole setup with controlled pinhole polarizations and intensities to generate on interference an arbitrary continuous spatial evolution of the polarization state, an optical analogue to the adiabatic case. The customized arrangement allows separating at any point the accumulated dynamical and geometric phases from the total phase, enabling a detailed study of the noncyclic Pancharatnam–Berry phase in a continuous transformation. Our theoretical and experimental results are in excellent agreement and consistent with the geodesic rule for noncyclic evolutions.

Communications PhysicsJun 7, 202318 citations

Berry’s phase for a noncyclic rotation of light in a helically wound optical fiber

Atsuo Morinaga, Akinori Monma, Kazuhito Honda +1 more

We investigated Berry's phase for noncyclic evolution using the rotation of a polarization azimuth of linearly polarized light in a partially wound optical fiber over the surface of a cylinder. Using a rotation gauge around the rotation axis, the observed rotation of the polarization azimuth corresponds to the area of a spherical rectangle over the surface enclosed by the contour $C$ of actual evolution, a large circle on the equator, and a longitudinal line connecting them, whereas the rotation of the polar gauge encloses a spherical triangle connecting the zenith of the sphere. The observed values were converted to Berry's phase by transformation from the rotation gauge to the geodesic gauge. Consequently, we could confirm that Berry's phase for a noncyclic evolution is given by the geodesic rule proposed by Samuel and Bhandari.We investigated Berry's phase for noncyclic evolution using the rotation of a polarization azimuth of linearly polarized light in a partially wound optical fiber over the surface of a cylinder. Using a rotation gauge around the rotation axis, the observed rotation of the polarization azimuth corresponds to the area of a spherical rectangle over the surface enclosed by the contour $C$ of actual evolution, a large circle on the equator, and a longitudinal line connecting them, whereas the rotation of the polar gauge encloses a spherical triangle connecting the zenith of the sphere. The observed values were converted to Berry's phase by transformation from the rotation gauge to the geodesic gauge. Consequently, we could confirm that Berry's phase for a noncyclic evolution is given by the geodesic rule proposed by Samuel and Bhandari.

Physical Review ANov 16, 200714 citations

An Optical Measurement of Berry's Phase

Arthur L. Robinson

ScienceOct 24, 198615 citations

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of actual evolution, a large circle on the equator, and a longitudinal line connecting them, whereas the rotation of the polar gauge encloses a spherical triangle connecting the zenith of the sphere. The observed values were converted to Berry's phase by transformation from the rotation gauge to the geodesic gauge. Consequently, we could confirm that Berry's phase for a noncyclic evolution is given by the geodesic rule proposed by Samuel and Bhandari.