Raúl Juárez-Amaro

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 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 where 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 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 a 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.

Intrinsic decoherence in the interaction of two fields with a two‐level atom

We study the interaction of a two-level atom and two fields, one of them classical. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to neglect some terms in the rotated Hamiltonian. Then we solve a variation of the Schrodinger equation that models decoherence as the system evolves through intrinsic mechanisms beyond conventional quantum mechanics rather than dissipative interaction with an environment.

Reconstruction of quasiprobability distribution functions of the cavity field considering field and atomic decays

Abstract We study the possibility of reconstructing the quantum state of light in a cavity subject to dissipation. We pass atoms, also subject to decay, through the cavity and surprisingly show that both decays allow the measurement of s -parametrized quasiprobability distributions. In fact, if we consider only atomic decay, we show that the Wigner function may be reconstructed. Because these distributions contain whole information of the initial field state, it is possible to recover information after both atomic and field decays occur.

Useful transformations: From ion-laser interactions to master equations

We show a set of transformations that allow one to obtain analytical solutions in several quantum-optical problems. We start with the ion-laser (time-dependent) interaction, continue with the problem of a slow atom interacting with a quantized field, and end with a master equation that describes the losses. In all cases, it is shown that one may find useful transformations that simplify the problems.

Ion-quantized field interaction in two regimes

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.

Exact solution of the ion‐laser interaction in all regimes

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.

Direct measurement of quasiprobabilities in lossy cavities

We show that the state of an electromagnetic field in a lossy cavity can be directly reconstructed by means of a simple scheme, allowing complete knowledge of the state of the field despite dissipation.