Cross-calibration of atomic pressure sensors and deviation from quantum diffractive collision universality for light particles

Abstract

The room-temperature, velocity-averaged, total cross section for atom–atom and atom–molecule collisions can be approximated using a universal function depending only on the magnitude of the leading order dispersion coefficient, C _6 . This feature of the total cross section together with the universal function for the energy distribution transferred by glancing angle collisions ( $p_{\textrm{QDU6}}$ (Booth et al 2019 New J. Phys. 21 102001)) can be used to empirically determine the total collision cross section and realize a self-calibrating, vacuum pressure standard. This was previously validated for Rb+N _2 and Rb+Rb collisions. However, the post-collision energy distribution is expected to deviate from $p_{\textrm{QDU6}}$ in the limit of small C _6 and small reduced mass. Here we observe this deviation experimentally by performing a direct cross-species loss rate comparison for Rb+H _2 and Li+H _2 collisions. We measure a velocity averaged total collision cross section ratio of $R = \langle \sigma_{\textrm{tot}} \, v \rangle_{{\textrm{Li+H}}_2} : \langle \sigma_{\textrm{tot}} \, v \rangle_{{\textrm{Rb+H}}_2} = 0.83(5)$ . Based on an ab initio computation of $\langle \sigma_{\textrm{tot}} \, v \rangle_{{\textrm{Li+H}}_2} =$ $3.104 \times 10^{-15}$ m ^3 s ^−1 , we deduce $\langle \sigma_{\textrm{tot}} \, v \rangle_{{\textrm{Rb+H}}_2} = 3.6(2) \times 10^{-15}$ m ^3 s ^−1 , in agreement with a Rb+H _2 ab initio value of $\langle \sigma_{\mathrm{tot}} v \rangle_{\mathrm{Rb+H_2}} = 3.574 \times 10^{-15} \mathrm{m}^3\,\mathrm{s}^{-1}$ . By contrast, fitting the Rb+H _2 loss rate as a function of trap depth to the universal function we find $\langle \sigma_{\textrm{tot}} \, v \rangle_{{\textrm{Rb+H}}_2} =$ $5.52(9) \times 10^{-15}$ m ^3 s ^−1 . This work demonstrates the utility of sensor-atom cross-calibration experiments to check the validity of theoretical computations to extend and enhance the performance of cold atom based pressure sensors.

Keywords

• cold atoms
• quantum metrology
• cold collisions
• quantum pressure standard
• quantum diffractive collisions universality
• ab initio calculations