Features of application of quaternions at the solution of the Bloch equation

Anatolii N. Leukhin; Ivan I. Popov

doi:10.1117/12.562203

20 April 2004 Features of application of quaternions at the solution of the Bloch equation

Anatolii N. Leukhin, Ivan I. Popov

Proceedings Volume 5402, International Workshop on Quantum Optics 2003; (2004) https://doi.org/10.1117/12.562203
Event: International Workshop on Quantum Optics 2003, 2003, St. Petersburg, Russian Federation

Abstract

Quaternion algebra is offered as the mathematical formalism of dynamics of interaction of a two-level quantum system with an electromagnetic field. Condition of two-level atom, densities operator, Bloch vector, “gyrating moment” vector are considered as the elements of a one-dimensional vector space of quaternion H¹, i.e. are represented as quaternion. Bloch equations in a quaternion formalism are noted. Solution method of the differential quaternion Bloch equation is obtained.

Citation Download Citation

Anatolii N. Leukhin and Ivan I. Popov "Features of application of quaternions at the solution of the Bloch equation", Proc. SPIE 5402, International Workshop on Quantum Optics 2003, (20 April 2004); https://doi.org/10.1117/12.562203

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