The Pancharatnam and the Berry phases in three-level photonic systems

摘要

A theoretical analysis of Pancharatnam and Berry phases is made for biphoton three-level systems, which are produced via frequency degenerate collinear spontaneous parametric down conversion (SPDC). The general theory of Pancharatnam phases is discussed with a special emphasis on geodesic 'curves' in Hilbert space. Explicit expressions for Pancharatnam, dynamic and geometric phases are derived for the transformations produced by linear phase converters. The problem of gauge invariance is treated in this article.