Pancharatnam-Berry Phase in Quantum Optics

Nian-Hua Liu

We study the modulation of Pancharatnam-Berry phase by lonexugitudinal electro-optical modulator which is an uniaxial crystal inserted into Sagnac interferometer.Because the difference of optical paths between clockwise and anticlockwise loop is zero,under the condition of zero-phase-difference related to the optical paths,the Pancharatnam-Berry phase between clockwise and anticlockwise loop can be distinguished more favorably.The results show that when the applied voltage vary continuously,the Pancharatnam-Berry phase jumps twice due to the characteristics of uniaxial crystal,while the coherent superposition intensity vary continuously.

R. Y. Chiao, Paul G. Kwiat, Ivan Deutsch +1 more

Estevan Nunez

In 1950, Ramsey and Hahn separately described a method using separated oscillatory magnetic fields and electronic levels to measure interference in atomic states. Today, similar physics is exploited to make atom interferometer sensors utilizing what is called the spin-echo sequence. In 1956, Pancharatnam described the geometric phase difference between two polarized states of light. In 1984 Berry described the phase accrued in cyclic and adiabatic quantum systems. A Pancharatnam-Berry phase experiment involving a quarter-wave – half-wave – quarter-wave plate stack of optics and an experiment using the spin-echo sequence are based on seemingly different phenomena in optics versus atomic optics, respectively. However, the mathematical representations used to describe the Pancharatnam-Berry phase in optics are identical to those used to describe the spin-echo sequence. Therefore, the relationship between the spin-echo sequence and the Pancharatnam-Berry phase was explored. Experiments to test the comparisons using a pre-existing cold atom experiment, ~150 μK, were performed. The mathematical connection between the two types of experiments was explained more deeply.

Antti Hannonen, Henri Partanen, Jani Tervo +2 more

Young's two-beam interference and the Pancharatnam-Berry geometric phase constitute two landmark results in optical physics. Employing the spectral interference law of electromagnetic waves, we establish a general expression for the Pancharatnam-Berry phase in Young's two-pinhole setup. We show that the phase is elegantly specified by the electric field Stokes parameters at the openings. The geometric phase can also be deduced from the interference pattern using Pancharatnam's definition of the generalized phase, as we demonstrate both numerically and experimentally. Our results imply a way to control the phase differences in two-beam electromagnetic interference by adjusting the input-field intensities and polarization states.

Pratul Bandyopadhyay