Regular Article

Matrix diagonalization and exact solution of the k-photon Jaynes–Cummings model

¹ Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Ed. 9, Unidad Profesional Adolfo López Mateos, Delegación Gustavo A. Madero, C.P. 07738 Ciudad de México, Mexico
² Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz esq. Av. Miguel Othón de Mendizábal, Col. Lindavista, Delegación Gustavo A. Madero, C.P. 07738, Ciudad de México, Mexico

^a e-mail: echorenoo0800@alumno.ipn.mx

Received: 8 March 2018
Published online: 28 August 2018

Abstract

We study and exactly solve the two-photon and k-photon Jaynes–Cummings models by using a novelty algebraic method. This algebraic method is based on the Pauli matrices realization and the tilting transformation of the SU(2) group and let us diagonalize the Hamiltonian of these models by properly choosing the coherent state parameters of the transformation. Finally, we explicitly obtain the energy spectrum and eigenfunctions for each model.