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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Photon echo as a method of optical processor construction for realization of computing operations above hypercomplex numbers

Vera T. Nigmatullina, Ivan I. Popov, Vadim A. Kozlov, Anatolii N. Leukhin

Published Mar 3, 2008• 1 citation
Publisher

Abstract

We inform on modelling a photon echo (PhE) shaping conditions as analog process which substitutes a part of labourconsuming computing operations at numerical calculation PhE in a formalism of quaternions algebra, and about its application for a computer construction (CC) for quaternion magnitudes.
DOI
10.1117/12.801687

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Application of quaternion algebra for calculation of photon echo signal

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 20, 2004•1 citation
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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.