Ion–laser interactions: The most complete solution

Abstract

Trapped ions are considered one of the best candidates to perform quantum information processing. By interacting them with laser beams they are, somehow, easy to manipulate, which makes them an excellent choice for the production of nonclassical states of their vibrational motion, the reconstruction of quasiprobability distribution functions, the production of quantum gates, etc. However, most of these effects have been produced in the so-called low intensity regime, this is, when the Rabi frequency (laser intensity) is much smaller than the trap frequency. Because of the possibility to produce faster quantum gates in other regimes it is of importance to study this system in a more complete manner, which is the motivation for this contribution. We start by studying the way ions are trapped in Paul traps in and review the basic mechanisms of trapping. Then we show how the problem may be completely solved for trapping states; i.e., we find (exact) eigenstates of the full Hamiltonian. We show how in the low intensity regime Jaynes-Cummings and anti-Jaynes-Cummings interactions may be obtained, without using the rotating wave approximation and analyze the medium and high intensity regimes were dispersive Hamiltonians are produced. The traditional approach (low intensity regime) is also studied and used for the generation of non-classical states of the vibrational of the vibrational wavefunction. In particular, we show how to add and subtract vibrational quanta to an initial state, how to produce specific superpositions of number states and how to generate NOON states for the two-dimensional vibration of the ion. It is also shown how squeezing may be measured. The time dependent problem is studied by using Lewis-Ermakov methods, we give a solution to the problem when the time dependence of the trap is considered and also analyze an specific (artificial) time dependence that produces squeezing of the initial vibrational wave function. A way to mimic the ion-laser interaction via classical optics is also introduced.

Entropy for the Quantized Field in the Atom-Field Interaction: Initial Thermal Distribution

“…We studied the ideal case of light-matter interaction (i.e., where no interaction of the total system with an environment takes place; see for instance [15]); however, because we are considering initial states with only diagonal terms in the field density matrix, it is expected that for sufficiently small cavity decay, our study describes the interaction well, as the environment severely affects off-diagonal matrix elements, quickly destroying coherent effects. Finally, effects such as the decrease of entropy of a subsystem by swapping purity could also be realized in ion-laser interaction [9,10] and semiconductor microcavities [16], to name some other possibilities.…”

“…Although we are considering here a two-level atom interacting with a quantised field, these kinds of Hamiltonians may also be realized in ion-laser interactions [9,10].…”

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

“…The trapped-ion total Hamiltonian then takes the form (cf., e. g., [10], [11]) (2) where parameter K = λE L has been introduced.…”

“…The intense theoretical work on these systems and the parallel experimental progress in ion trapping are thoroughly reviewed in [1] and [8]- [10].…”

Entangled-state engineering of vibrational modes in a multimembrane optomechanical system

“…[10][11][12][13]). Thus we would like to know whether the entanglement can be generated in the systems of macroscopic mechanical resonators.…”