Geometric phase decomposition in the basis of Hermite-Gaussian functions

Rimvydas Aleksiejunas 1  and Vladislovas Ivaska 1
  • 1 Department of Radiophysics, Vilnius University, Sauletekio al. 9, bldg. III, LT-10222, Vilnius, Lithuania

Abstract

The work presents geometric phase decomposition for analytical signals using Hermite-Gaussian functions. The decomposition is based on the time-frequency distribution with reassigned and multi-tapered spectrogram resulting in increased phase estimation resolution. Numerical analysis is applied to a number of SU(2) evolutions, such as spin-1/2 particle in a static and rotating magnetic field, as well as polarization rotation of a plane wave in optically active medium. Geometric phase decomposition results are provided also for quantum harmonic oscillator and a radiation field of an electric dipole exited by a short pulse.

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