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Journal of Optics B Quantum and Semiclassical Optics

Eigenstates and spectrum for a class of models describing three-mode multiphoton processes

Ying Wu, Xiaoxue Yang

Published Feb 1, 2004• 5 citations
Publisher

Abstract

By using an efficient approach developed by us, we present explicit analytical expressions for all the eigenenergies and eigenstates in terms of a parameter lambda for a class of models describing three-mode multiphoton processes. The parameter lambda is shown to be determined by the roots of a simple polynomial. We also obtain the exact explicit analytical expressions of infinite eigenstates and eigenenergies without any unknown parameters.

DOI
10.1088/1464-4266/6/2/009

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By using an efficient approach developed by us, we present explicit analytical expressions for all the eigenenergies and eigenstates in terms of a parameter lambda for a class of models describing three-mode multiphoton processes. The parameter lambda is shown to be determined by the roots of a simple polynomial. We also obtain the exact explicit analytical expressions of infinite eigenstates and eigenenergies without any unknown parameters.
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We obtain the exact analytical results of all the eigenvalues and eigenstates for three kinds of models describing N -mode multiphoton process without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter λ for three kinds of models describing N -mode multiphoton process. The parameter is shown to be determined by the roots of a polynomial and is solvable analytically or numerically. Moreover, these three kinds of models can be processed with the same procedure.