Interacción de un láser con un ion atrapado incluyendo dependencia temporal

Abstract

Nowadays 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 paper, starting from the Hamiltonian of a trapped ion in a harmonic potential, we show that it 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 internal and vibrational states of the ion proportionally to the vibrational frequency of the ion; these transitions are useful because make it 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. Also, 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 system. Also, we show a particular case of time-dependency of the trap.