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Geometric phase for degenerate states of spin-1 and spin-1/2 pair

100%

Zhu G.-Q.

Open Physics

2007

tom 5

nr 4

463-470

The geometric phase of a bi-particle model is discussed. One can drive the system to evolve by applying an external magnetic field, thereby controlling the geometric phase. The model has degenerate lowest-energy eigenvectors. The initial state is assumed to be the linear superposition or mixture of the eigenvectors. The relationship between the geometric phase and the structures of the initial state is considered, and the results are extended to a more general model.

Geometric phase decomposition in the basis of Hermite-Gaussian functions

80%

Aleksiejunas R. , Ivaska V.

Open Physics

2012

tom 10

nr 1

66-75

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.

Malus law – interferometric interpretation

80%

Woźniak W. A. , Kurzynowski P. , Zdunek M.

Optica Applicata

2013

tom Vol. 43, nr 2

s. 237--246

The aim of the present work is the description of a novel interferometric approach to the commonly known Malus law. In this approach we have described an analyzer as an element realizing the interference of two waves being the components of the linearly polarized wave emerging from the polarizer. We have proposed a decomposition of the polarization state of the light incident on the analyzer into two different bases. The choice of a first base – linearly polarized – allows interpreting Malus law as an interference of two linearly polarized waves with the same polarization state, different amplitudes and the same phases. The second decomposition, based on circularly polarized vectors, leads to the description in which Malus law can be interpreted as an interference of two waves with the same amplitudes but different phases. This allows the introduction of the concept of the geometric phase into Malus law as well as the visualization of this phase on the Poincaré sphere.