Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0301138

Trapped ions interacting with laser fields: a perturbative analysis without rotating wave approximation

Paolo Aniello, Vladimir I. Man’ko, Giuseppe Marmo, A. Porzio, S. Solimeno, F. Zaccaria

Published Jan 24, 2003• 0 citations
arXivHTMLPDF

Abstract

The Hamiltonian describing a single ion placed in a potential trap in interaction with a laser beam is studied by means of a suitable perturbative approach. It is shown, in particular, that the rotating wave approximation does not provide the correct expression, at the first perturbative order, of the evolution operator of the system.
DOI
10.48550/arxiv.quant-ph/0301138

Related papers

Trapped Ions Interacting with Laser Fields: a Perturbative Analysis without the Rotating Wave Approximation

Paolo Aniello, Vladimir I. Man’ko, Giuseppe Marmo +3 more

Journal of Russian Laser Research•Jan 1, 2004•8 citations

A family of exact eigenstates for a single trapped ion interacting with a laser field

H. M. Moya-Cessa, Daniel Jonathan, P. L. Knight

We show that, under certain combinations of the parameters governing the interaction of a harmonically trapped ion with a laser beam, it is possible to find one or more exact eigenstates of the Hamiltonian, with no approximations except the optical rotating-wave approximation. These are related via a unitary equivalence to exact eigenstates of the full Jaynes-Cummings model (including counter-rotating terms) supplemented by a static driving term.

arXiv:quant-ph/0110167•Journal of Modern Optics•Jan 1, 2003•34 citations

Approximate Solutions for the Ion-Laser Interaction in the High Intensity Regime: Matrix Method Perturbative Analysis

Braulio Misael Villegas-Martínez, H. M. Moya-Cessa, Francisco Soto

Abstract We provide an explicit expression for the second-order perturbative solution of a single trapped-ion interactingwith a lser field in the strong excitation regime. From the perturbative analytical solution, based on a matrix methodand a final normalization of the perturbed solutions, we show that the probability to find the ion in its excited statefits well with former results.

•Apr 19, 2021•0 citations

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

Vittorio Penna, Francesco Antonino Raffa

We present a second-order perturbative analysis of the model describing a two-level trapped ion interacting with a travelling 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.

arXiv:1403.2321•Journal of Physics B Atomic Molecular and Optical Physics•Mar 17, 2014•6 citations

Complete Rabi oscillations in the ion–laser interaction

Marco A. García-Márquez

We present the dynamics of a single harmonically trapped ion interacting with a laser, considering a linear combination of two eigenstates of the system as the initial state.The conditions on the physical parameters that allow for the evolution of the system are discussed.We are able to obtain analytical results using no other approximation than the optical rotating-wave approximation and are able to show Rabi oscillations for such initial states.

arXiv:2412.15357•Optica Pura y Aplicada•Mar 31, 2025•0 citations

Unitary transformation approach for the trapped ion dynamics

H. M. Moya-Cessa, A. Vidiella-Barranco, José Antonio Roversi +1 more

We present a method of treating the problem of the interaction of a single trapped ion with laser beams based on successive applications of unitary transformations onto the Hamiltonian. This allows the diagonalization of the Hamiltonian, by means of recursive relations, without performing the Lamb-Dicke approximation.

arXiv:quant-ph/0002080•Journal of Optics B Quantum and Semiclassical Optics•Jan 19, 2000•7 citations
We present a second-order perturbative analysis of the model describing a two-level trapped ion interacting with a travelling 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.