Journal of Modern Optics

Ion-laser interaction in dispersive regimes: solution using squeeze operators

Arturo Zúñiga-Segundo, H. M. Moya-Cessa

Published May 26, 2015• 0 citations

Abstract

We study the resonant interaction between a trapped ion and a laser field. By tuning the field intensity far away from the trapping frequency, namely low and high intensity regimes, we arrive at so-called dispersive Hamiltonians that may be simplified via the application of squeezing transformations. We analyse the system dynamics in phase space.

DOI: 10.1080/09500340.2015.1045436

Related papers

Exact solution of the ion‐laser interaction in all regimes

Arturo Zúñiga-Segundo, R. Juárez‐Amaro, J.M. Vargas‐Martínez +1 more

Abstract We show that in the trapped ion‐laser interaction all the regimes may be considered analytically. We may solve not only for different laser intensities, but also away from resonance and from the Lamb‐Dicke regime. It is found a dispersive Hamiltonian for the high intensity regime, that, being diagonal, its evolution operator may be easily calculated.

arXiv:1005.3974Annalen der PhysikAug 4, 20112 citations

Ion-quantized field interaction in two regimes

Arturo Zúñiga-Segundo, Raúl Juárez-Amaro, Francisco Soto +1 more

By taking advantage of the superposition principle inherent to quantum mechanics, we show that it is possible, by interacting a quantized field with a trapped ion, to reach both high intensity and low intensity regimes simultaneously. We use the London operator in order to simplify the Hamiltonians involved in the problem.

Physica ScriptaNov 18, 20140 citations

Estudio de la interacción de un láser con un ion atrapado

Jose Manuel Vargas Martinez

Actually it is possible to trap single ions in Paul or Penning traps, charged particles are confined in space via electromagnetic fields. A trapped ion can have a lot vibrational energy which is undesirable in some applications. In this thesis, starting from the Hamiltonian of a trapped ion in a harmonic potential, it is shown that is possible to get Jaynes-Cummings and anti- Jaynes- Cummings¬like transitions in the intermediate intensity regime, that is, adjusting the intensity of the laser that induce the coupling between the intemal and vibrational states of the ion proportionally to the vibrational frequency of the ion; these transitions are useful because make possible to extract the vibrational energy. In our treatment we consider that the ion and the laser are in resonance what eliminate the need of using tuned lasers.\nAlso, the problem of a trapped ion in a trap with time-dependent parameters interacting with a laser field is analyzed. By using a set of time-dependent unitary transformations is shown that this system is equivalent to the interaction between a quantized field and a two level system with time dependent parameters. The Hamiltonian is linearized in such a way that can be solved with methods that are found in some papers and that involve time-dependent parameters. The linearization is free of approximations and assumptions on the parameters of the system as are, for instance, the Lamb-Dicke parameter, the time-dependency of the frequency trap and the detuning, with what we can obtain the best solution for this kind of sytem.

Jan 1, 20080 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, 20210 citations

A trapped ion with time-dependent frequency interaction with a laser field

J. Minguez Martinez, H. M. Moya-Cessa

We analyse the problem of a trapped ion with time-dependent frequency interacting with a laser field. By using a set of unitary time-dependent transformations we show that this system is equivalent to the interaction between a quantized field and a double level with time-dependent interaction parameters. In passing, we show that in the on-resonance case different vibrational transitions may be achieved by using time-dependent parameters.

Journal of Optics B Quantum and Semiclassical OpticsMay 29, 20044 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