Application of an inverse Holstein-Primakoff transformation to the Jaynes-Cummings model

Abstract

A modification of the Holstein-Primakoff transformation is proposed such that creation and annihilation operators for a bosonic field are rewritten as operators of a $SU(2)$ algebra. Once it is applied to a quantum Hamiltonian, a subsequent application of the prescription by Lieb to obtain the classical limit for spin operators allows one to write efficiently a classical Hamiltonian for the system. This process is illustrated for the $M$-atom Jaynes-Cummings model.Comment: 11 pages, 3 figures, English version of the work published in Anais do XX ENMC -- Encontro Nacional de Modelagem Computacional e VIII ECTM -- Encontro de Ci\^encias e Tecnologia de Materiais, Nova Friburgo, RJ -- 16 a 19 Outubro 2017 Some errors concerning the Jaynes-Cummings model need to be fixed