A generalized Pancharatnam geometric phase formula for three-level quantum systems. (English) Zbl 0928.46056
Summary: We describe a recently developed generalization of the Poincaré sphere method, to represent pure states of a three-level quantum system in a convenient geometrical manner. The construction depends on the properties of the group SU(3) and its generators in the defining representation, and uses geometrical objects and operations in an eight-dimensional real Euclidean space. This construction is then used to develop a generalization of the well known Pancharatnam geometric phase formula, for evolution of a three-level system along a geodesic triangle in state space.
MSC:
46N50 | Applications of functional analysis in quantum physics |
81Q99 | General mathematical topics and methods in quantum theory |
81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |