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 $P_t\left(E\right)$ for the collision-induced energy transfer to the trapped ensemble. We describe how to find $P_t\left(E\right)$ using quantum scattering calculations and how it can be approximated using quantum diffractive universality. We then compare our model to experimental measurements of a ${}_{87}\mathrm{Rb}$ ensemble energy evolution exposed to a room-temperature background gas of Ar by means of a single parameter fit for the total collision rate $\Gamma$. We extracted a collision rate of $\Gamma =0.649\left(2\right){\text{s}}^{-1}$. We further refine our analysis by using monotonic Gaussian process regression to smooth the experimental data, which extracts a collision rate of $\Gamma =0.646\left(1\right){\text{s}}^{-1}$. This is compared to a value of 0.67(1) ${\text{s}}^{-1}$ 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.