Application of quaternion algebra for calculation of photon echo signal

Anatolii N. Leukhin; Ivan I. Popov

doi:10.1117/12.562205

20 April 2004 Application of quaternion algebra for calculation of photon echo signal

Anatolii N. Leukhin, Ivan I. Popov

Proceedings Volume 5402, International Workshop on Quantum Optics 2003; (2004) https://doi.org/10.1117/12.562205
Event: International Workshop on Quantum Optics 2003, 2003, St. Petersburg, Russian Federation

Abstract

Mathematical formalism of photon echo exciting at interaction of two-level quantum system with an electromagnetic field within the framework of quaternion algebra is offered. The rotation quaternion is used instead of density operator for representation of interaction dynamics of an exterior field with two-level atom, where the components of rotation quaternion are the coordinates of Bloch vector. Liouville fon-Neumann equation for density matrix evolution is substituted by the differential quaternion equation in a quaternion model. The expression for rotation quaternion appropriating to an unitary operator of rotation in matrix representation is obtained. It is shown that the solution of the differential quaternion equation does not require the difficult mathematical operation connected to an evaluation of an exponent from a matrix. The expression for a quaternion superoperator is obtained.

Citation Download Citation

Anatolii N. Leukhin and Ivan I. Popov "Application of quaternion algebra for calculation of photon echo signal", Proc. SPIE 5402, International Workshop on Quantum Optics 2003, (20 April 2004); https://doi.org/10.1117/12.562205

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