Self-rotating wave approximation via symmetric ordering of ladder operators

TL;DR

This paper introduces a novel approach to the rotating wave approximation using symmetric ordering of ladder operators, applied to specific models, and discusses its relation to perturbation theory and approximation validity.

Contribution

It presents a new method for Hamiltonian approximation based on symmetric ordering of bosonic ladder operators, expanding the applicability of the rotating wave approximation.

Findings

Method successfully applied to Morse and Mathieu models

Connection established with regular perturbation theory

Discussion on the validity range of the approximation

Abstract

We show how some Hamiltonians may be approximated using rotating wave approximation methods. In order to achieve this we use the algebra of boson ladder operators, and transformation formulas between normal and symmetric ordering of the operators. The method presented is studied in two special cases; the Morse and the Mathiue models. The connection with regular perturbation theory is given and the validity of the approximation is discussed.