A new perturbative expansion of the time evolution operator associated with a quantum system

Abstract

A novel expansion of the evolution operator associated with a -- in general, time-dependent -- perturbed quantum Hamiltonian is presented. It is shown that it has a wide range of possible realizations that can be fitted according to computational convenience or to satisfy specific requirements. As a remarkable example, the quantum Hamiltonian describing a laser-driven trapped ion is studied in detail.Comment: 32 pages; modified version with examples of my previous paper quant-ph/0404056; to appear on the J. of Optics B: Quantum and Semiclassical Optics, Special Issue on 'Optics and Squeeze Transformations after Einstein