arXiv:quant-ph/0207151v3 16 Dec 2002 Evolution of the N -ion Jaynes-Cummings model beyond the standard rotating wave approximation P. Aniello 1 , A. Porzio 2 * and S. Solimeno 2 Dipartimento di Scienze Fisiche, Universit`a di Napoli “Federico II” and 1 Istituto Nazionale di Fisica Nucleare, Sezione di Napoli 2 ”Coherentia” - INFM, Unit`a di Napoli Complesso Universitario Monte Sant’Angelo, via Cintia, I–80126 Napoli, Italy. February 1, 2008 Abstract A unitary transformation of the N -ion Jaynes-Cummings Hamiltonian is proposed. It is shown that any approximate expression of the evolution operator associated with the transformed Hamiltonian retains its validity independently from the intensity of the external driving field. In partic- ular, using the rotating wave approximation, one obtains a solution for the N -ion Jaynes-Cummings model which improves the standard rotating wave approximation solution. 1 Introduction The classical Jaynes-Cummings model (JCM)[1], with Hamiltonian H JC = νa † a + 1 2 ω ge σ z +Ω R ( aσ + + a † σ − ) , has become, so to say, the drosophila of quantum optics, since it gives a simple description of the main properties of many physical systems consisting of atoms in interaction with electromagnetic fields [2]. For instance, it has been for long at center of the attention for the study of laser cooling of ions placed in parabolic traps [3][4]. The main features of some approximate solutions of the JCM have been extensively studied, in particular the ‘collapse and revival’ phenomenon [5][6]. * Alberto Porzio, tel:+39-081-676233; fax:+39-081-676346, e–mail: al- berto.porzio@na.infn.it 1