Single-Qubit Driving Fields and Mathieu Functions

We report a new family of time-dependent single-qubit radiation fields for which the correspondent evolution operator can be disentangled in an exact way via the Wei−Norman formalism. Such fields are characterized in terms of the Mathieu functions. We show that the regions of stability of...

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Bibliographic Details
Main Authors: Marco Enríquez, Alfonso Jaimes-Nájera, Francisco Delgado
Format: Article
Language:English
Published: MDPI AG 2019-09-01
Series:Symmetry
Subjects:
Online Access:https://www.mdpi.com/2073-8994/11/9/1172
Description
Summary:We report a new family of time-dependent single-qubit radiation fields for which the correspondent evolution operator can be disentangled in an exact way via the Wei−Norman formalism. Such fields are characterized in terms of the Mathieu functions. We show that the regions of stability of the Mathieu functions determine the nature of the driving fields: For parameters in the stable region, the fields are oscillating, being able to be periodic under certain conditions. Whereas, for parameters in the instability region, the fields are pulse-like. In addition, in the stability region, this family admits solutions for evolution loops in quantum control. We obtain some prescriptions to reach such a control effect. Geometric phases in the evolution are also analyzed and discussed.
ISSN:2073-8994