Perturbative approach to the dynamics of a trapped ion interacting with a light field

Abstract

We present a second-order perturbative analysis of the model describing a two-level trapped ion interacting with a traveling laser field, in the Lamb-Dicke regime. Unlike the customary approach, based on the interaction picture and the rotating wave approximation, we reduce the original Hamiltonian to a time-independent model, unitarily equivalent to a spin-boson model, which features a form well suited to apply the perturbation theory. We determine the first and second-order corrections of eigenstates and eigenvalues. By varying the interaction parameters we identify four regimes characterized by different eigenvalue distributions (possibly including level doublets) and suggest the presence of an intermediate regime where the spectrum undergoes macroscopic changes. In this regime, where the perturbation approach does not hold, our reduced Hamiltonian is shown to reproduce the Jaynes-Cummings model.

9 pages, to appear on J.Phys. B

References in corpus (5)

• Quantum computing with trapped ions
• Mesoscopic Spin-Boson Models of Trapped Ions
• Quantum phase transition and critical fluctuations of an attractive Bose gas in a double well potential
• Localization of phonons in ion traps with controlled quantum disorder
• Quantum interference structures in trapped ion dynamics beyond the Lamb-Dicke and rotating wave approximations