Trapped particle evolution driven by residual gas collisions

TL;DR

This paper develops a comprehensive mathematical model for the evolution of trapped particles due to residual gas collisions, validated by experiments with rubidium atoms, and improves the precision of collision rate measurements.

Contribution

It introduces a versatile model that accounts for trap geometry and potential, and demonstrates enhanced accuracy in collision rate estimation from experimental data.

Findings

Collision rate of 0.646(1) s^{-1} extracted from the model.

Model reduces discrepancy with traditional zero-trap depth extrapolation method.

Five-fold increase in precision of collision rate measurement.

Abstract

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 the probability distribution function $P_t(E)$ for the collision-induced energy transfer to the trapped ensemble. We describe how to find $P_t(E)$ using quantum scattering calculations and how it can be approximated using quantum diffractive universality. We then compare our model to experimental measurements of a $^{87}$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 $\Gamma = 0.646(1)\ \text{s}^{-1}$. This is compared to a value of $0.664(4)\ \text{s}^{-1}$ found by the commonly used method of zero-trap depth extrapolation, a $2.8\%$ correction that is a result of our model fully taking ensemble loss and heating into account. Finally, we report a five-fold increase in the precision of our collision rate extraction from the experimental data.