W. Vogel

The vibronic dynamics of a trapped ion in the resolved-sideband regime can be described by the explicitly time-dependent nonlinear Jaynes-Cummings model. It is shown that the expectation value of the interaction Hamiltonian and its non-equal-time commutator can be determined by measuring the electronic-state evolution. This yields direct insight into the time-ordering contributions to the unitary time evolution. In order to prove extraction of the quantities of interest works for possibly real data, we demonstrate the procedure by means of generated data.

A novel robust mechanism for the generation of "trapping states" is shown to exist in the coupling of a two-level system with an oscillator, which is based on nonlinearities in the laser-induced vibronic coupling. This mechanism is exemplified with an ion confined in the potential well of a trap, where the nonlinearities are due to Franck--Condon type overlap integrals of the laser waves with the ionic centre-of-mass wavefunction. In contrast to the coherent trapping mechanism known from micro-maser theory, this mechanism works also in an incoherent regime operated by noisy lasers and is therefore much more robust against external decoherence effects. These features favour the incoherent regime, in particular for the preparation of highly excited trapping states.