M. Keller

We describe the operation of an electrodynamic ion trap in which the electric quadrupole field oscillates at two frequencies. This mode of operation allows simultaneous tight confinement of ions with extremely different charge-to-mass ratios, e.g., singly ionised atomic ions together with multiply charged nanoparticles. We derive the stability conditions for two-frequency operation from asymptotic properties of the solutions of the Mathieu equation and give a general treatment of the effect of damping on parametric resonances. Two-frequency operation is effective when the two species' mass ratios and charge ratios are sufficiently large, and further when the frequencies required to optimally trap each species are widely separated. This system resembles two coincident Paul traps, each operating close to a frequency optimized for one of the species, such that both species are tightly confined. This method of operation provides an advantage over single-frequency Paul traps, in which the more weakly confined species forms a sheath around a central core of tightly confined ions. We verify these ideas using numerical simulations and by measuring the parametric heating induced in experiments by the additional driving frequency.

In this work we investigate the theory for three different uni-directional population transfer schemes in trapped multilevel systems which can be utilized to cool molecular ions. The approach we use exploits the laser-induced coupling between the internal and motional degrees of freedom so that the internal state of a molecule can be mapped onto the motion of that molecule in an external trapping potential. By sympathetically cooling the translational motion back into its ground state the mapping process can be employed as part of a cooling scheme for molecular rotational levels. This step is achieved through a common mode involving a laser-cooled atom trapped alongside the molecule. For the coherent mapping we will focus on adiabatic passage techniques which may be expected to provide robust and efficient population transfers. By applying far-detuned chirped adiabatic rapid passage pulses we are able to achieve an efficiency of better than 98% for realistic parameters and including spontaneous emission. Even though our main focus is on cooling molecular states, the analysis of the different adiabatic methods has general features which can be applied to atomic systems.