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.

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'

References in corpus (1)

• Coarse grained and fine dynamics in trapped ion Raman schemes

Cited by in corpus (7)

• Unitary expansion of the time evolution operator
• Interaction-free evolution in the presence of time-dependent Hamiltonians
• Dynamics of a particle confined in a two-dimensional dilating and deforming domain
• Resonant transitions due to changing boundaries
• Evanescent Wave Approximation for Non-Hermitian Hamiltonians
• Perturbative Treatment of the Evolution Operator Associated with Raman Couplings
• On unorthodox solutions of the Bloch equations