Collisional Re-ordering of Ionic Crystals

We advance a computational model for temperature and pressure dependent collisions between background gas and a three-ion linear ionic crystal in a vacuum chamber. We consider ion loss and chain reordering from the perspective of error minimization in quantum computing. This model can be used to extract the required temperature (or pressure) to achieve a given error rate in a linear ion trap with a given set of radial and axial frequencies. For example, a three-ion crystal in a trap with radial frequency 4MHz and axial frequency 0.4MHz at 300K needs to be pumped to a pressure of ~3.2*10^-12 torr in order to maintain an ion order lifetime of 1 hour. Ongoing improvements to this model based on the partial pressures of each element or molecule present in the vacuum chamber will improve our predictive abilities. This model will subsequently be extended to address arbitrary ion chain lengths, collisionally induced heating, the impact of micromotion, and site-selective cooling. We also hope to examine the impact of non-equilibrium gas dynamics in the proximity of surfaces (such as outgassing from the trap itself). The ultimate goal of this project is to create a computational model of collisional dynamics in linear ion traps that matches the observed phenomena including the anomalous scaling of re-ordering with longer ionic crystals.