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Article

Single-Qubit Driving Fields and Mathieu Functions

1
School of Engineering and Science, Tecnologico de Monterrey, Atizapán, México 52926, Mexico
2
Centro de Investigación Científica y de Educación Superior de Ensenada, Unidad Monterrey, PIIT Apodaca, Nuevo León 66629, Mexico
3
Instituto Nacional de Astrofísica, Óptica y Electrónica, Apartado Postal 51/216, Puebla 72000, Mexico
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(9), 1172; https://doi.org/10.3390/sym11091172
Received: 13 July 2019 / Revised: 21 August 2019 / Accepted: 7 September 2019 / Published: 16 September 2019
(This article belongs to the Special Issue Quantum Information and Symmetry)
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. View Full-Text
Keywords: quantum control; Mathieu functions; time-dependent driving fields quantum control; Mathieu functions; time-dependent driving fields
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MDPI and ACS Style

Enríquez, M.; Jaimes-Nájera, A.; Delgado, F. Single-Qubit Driving Fields and Mathieu Functions. Symmetry 2019, 11, 1172. https://doi.org/10.3390/sym11091172

AMA Style

Enríquez M, Jaimes-Nájera A, Delgado F. Single-Qubit Driving Fields and Mathieu Functions. Symmetry. 2019; 11(9):1172. https://doi.org/10.3390/sym11091172

Chicago/Turabian Style

Enríquez, Marco; Jaimes-Nájera, Alfonso; Delgado, Francisco. 2019. "Single-Qubit Driving Fields and Mathieu Functions" Symmetry 11, no. 9: 1172. https://doi.org/10.3390/sym11091172

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