Trapped-particle evolution driven by residual gas collisions

We present a comprehensive mathematical model and experimental measurements for the evolution of a trapped-particle ensemble driven by collisions with a room-temperature background vapor. The model accommodates any trap geometry, confining potential, initial trapped distribution, and other experimental details; it only depends on the probability distribution function Pₓ (E) for the collision-induced energy transfer to the trapped ensemble. We describe how to find Pₓ (E) using quantum scattering calculations and how it can be approximated using quantum diffractive universality. We then compare our model to experimental measurements of a ^87Rb ensemble energy evolution exposed to a room-temperature background gas of Ar by means of a single parameter fit for the total collision rate. We extracted a collision rate of =0. 649 (2) 4pt{0ex}s^-1. We further refine our analysis by using monotonic Gaussian process regression to smooth the experimental data, which extracts a collision rate of =0. 646 (1) 4pt{0ex}s^-1. This is compared to a value of 0. 67 (1) s^-1 found by the commonly used method of zero-trap depth extrapolation, a 3. 5% correction that is a result of our model fully taking ensemble loss and heating into account. Finally, we report a fivefold increase in the precision of our collision rate extraction from the experimental data and a tenfold increase in the precision of our collision rate extraction from the smoothed experimental data.