Change of the Pancharatnam phase under unitary transformation and application to a model three-level [Gamma]-type system specified by a pair of dipole-coupled excited states

The interdependence of total, dynamic and geometric (Pancharatnam) phases of the state vector of a quantum system that are determined in different representations is considered. One finds that the phases calculated using two different bases of the Hilbert space, which are related by a time-dependent...

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Bibliographic Details
Published in:Physica scripta 2012-01, Vol.85 (1), p.1-5
Main Authors: Mendas, Istok P, Popovic, Duska B
Format: Article
Language:English
Subjects:
Dynamical systems
Dynamics
Excitation
Invariants
Phase transformations
Representations
State vectors
Transformations
Online Access:Get full text
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Summary:The interdependence of total, dynamic and geometric (Pancharatnam) phases of the state vector of a quantum system that are determined in different representations is considered. One finds that the phases calculated using two different bases of the Hilbert space, which are related by a time-dependent unitary transformation, are not invariant under this transformation; rather they are connected by non-trivial and well-defined relations. We determine the general relationships between the phases in different representations and then apply and verify these transformations in the case of the physically interesting model of the three-level [Gamma]-type system specified by a pair of dipole-coupled excited states.
ISSN:0031-8949
1402-4896
DOI:10.1088/0031-8949/85/01/015008