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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

arXiv:2104.06582Optical and Quantum ElectronicsMar 1, 20221 citation

Laser Driven Ion Traps: Beyond the Standard Perturbative Limit

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

Acta Physica Hungarica B) Quantum ElectronicsJan 1, 20042 citations

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

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

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.

arXiv:quant-ph/0301138Jan 24, 20030 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.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:1403.2321Journal of Physics B Atomic Molecular and Optical PhysicsMar 17, 20146 citations

Quantum field theory dynamics in trapped ions

Pan‐Yu Hou

Nature PhysicsSep 25, 20260 citations

Continued fraction solution to the Raman interaction of a trapped ultracold ion with two travelling wave lasers

Mang Feng

Raman interaction of a trapped ultracold ion with two travelling wave lasers has been used extensively in ion-trap experiments. We solve this interaction in the absence of a rotating wave approximation (RWA) by a continued fraction, without considering the restriction of the Lamb-Dicke limit and the weak excitation regime. Some interesting characteristics of the ion-trap system, particularly for the ion outside the weak excitation regime are found. Finally, a comparison of our results with the solution under the RWA is made.Raman interaction of a trapped ultracold ion with two travelling wave lasers has been used extensively in ion-trap experiments. We solve this interaction in the absence of a rotating wave approximation (RWA) by a continued fraction, without considering the restriction of the Lamb-Dicke limit and the weak excitation regime. Some interesting characteristics of the ion-trap system, particularly for the ion outside the weak excitation regime are found. Finally, a comparison of our results with the solution under the RWA is made.

arXiv:quant-ph/0012085Journal of Physics B Atomic Molecular and Optical PhysicsJan 26, 20019 citations

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

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