Analysis of Multipolar Linear Paul Traps for Ion–Atom Ultracold Collision Experiments

We evaluate the performance of multipole, linear Paul traps for the purpose of studying cold ion–atom collisions. A combination of numerical simulations and analysis based on the virial theorem is used to draw conclusions on the differences that result, by considering the trapping details of several multipole trap types. Starting with an analysis of how a low energy collision takes place between a fully compensated, ultracold trapped ion and an stationary atom, we show that a higher order multipole trap is, in principle, advantageous in terms of collisional heating. The virial analysis of multipole traps then follows, along with the computation of trapped ion trajectories in the quadrupole, hexapole, octopole and do-decapole radio frequency traps. A detailed analysis of the motion of trapped ions as a function of the amplitude, phase and stability of the ion’s motion is used to evaluate the experimental prospects for such traps. The present analysis has the virtue of providing definitive answers for the merits of the various configurations, using first principles.

Low-temperature chemistry using the R-matrix method

Techniques for producing cold and ultracold molecules are enabling the study of chemical reactions and scattering at the quantum scattering limit, with only a few partial waves contributing to the incident channel, leading to the observation and even full control of state-to-state collisions in this regime. A new R-matrix formalism is presented for tackling problems involving low- and ultra-low energy collisions. This general formalism is particularly appropriate for slow collisions occurring on potential energy surfaces with deep wells. The many resonance states make such systems hard to treat theoretically but offer the best prospects for novel physics: resonances are already being widely used to control diatomic systems and should provide the route to steering ultracold reactions. Our R-matrix-based formalism builds on the progress made in variational calculations of molecular spectra by using these methods to provide wavefunctions for the whole system at short internuclear distances, (a regime known as the inner region). These wavefunctions are used to construct collision energy-dependent R-matrices which can then be propagated to give cross sections at each collision energy. The method is formulated for ultracold collision systems with differing numbers of atoms.

Collisions and reactions of ultracold molecules

It is argued that collision dynamics of atoms and molecules at ultracold temperatures (below 1 mK) are not readily predictable from knowledge of collision dynamics above 100 K. In the case of elastic collisions, it is well known that the collision cross section is constant as T → 0 K but mass and symmetry effects are dramatic. The cases of inelastic and reactive collisions are less studied, but a T–1/2 dependence of the cross section as T → 0 K is expected. It seems that extrapolations of high-temperature inelastic and reactive behavior normally greatly underestimate ultracold-temperature rates. The prospects for experimental observation of ultracold collision dynamics are rapidly improving.Key words: ultracold molecules, collisions, reactions, hydrogen, scattering length.