Trapped particle evolution driven by residual gas collisions

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.

14 pages, 6 figures

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Cited by in corpus (3)

• On the effect of "glancing" collisions in the cold atom vacuum standard
• Boundaries of universality of thermal collisions for atom-atom scattering
• Invariance of quantum scattering rate coefficients to anisotropy of atom-molecule interactions