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

Abstract

The total room-temperature, velocity-averaged cross section for atom-atom and atom-molecule collisions is well approximated by 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 ($P_{\mathrm{QDU}6}$) 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 $P_{\mathrm{QDU}6}$ 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 between Rb+H${}_2$ and Li+H${}_2$ and using the \textit{ab initio} value of $⟨{\sigma }_{\mathrm{tot}}v{⟩}_{{\mathrm{Li}+\mathrm{H}}_2}$. We find a velocity averaged total collision cross section ratio, $R=⟨{\sigma }_{\mathrm{tot}}v{⟩}_{{\mathrm{Li}+\mathrm{H}}_2}:⟨{\sigma }_{\mathrm{tot}}v{⟩}_{{\mathrm{Rb}+\mathrm{H}}_2}=0.83(5)$. Based on an \textit{ab initio} computation of $⟨{\sigma }_{\mathrm{tot}}v{⟩}_{{\mathrm{Li}+\mathrm{H}}_2}=3.13(6)\times 10^{-15}$ m${}^3$/s, we deduce $⟨{\sigma }_{\mathrm{tot}}v{⟩}_{{\mathrm{Rb}+\mathrm{H}}_2}=3.8(2)\times 10^{-15}$ m${}^3$/s, in agreement with a Rb+H${}_2$ \textit{ab initio} value of $⟨{\sigma }_{\mathrm{tot}}v{⟩}_{\mathrm{Rb}+{\mathrm{H}}_2}=3.57\times 10^{-15}{\mathrm{m}}^3/\mathrm{s}$.By contrast, fitting the Rb+H${}_2$ loss rate as a function of trap depth to the universal function we find $⟨{\sigma }_{\mathrm{tot}}v{⟩}_{{\mathrm{Rb}+\mathrm{H}}_2}=5.52(9)\times 10^{-15}$ m${}^3$/s. Finally, this work demonstrates how to perform a cross-calibration of sensor atoms to extend and enhance the cold atom based pressure sensor.

14 pages, 9 figures

References in corpus (3)

• Development of a new UHV/XHV pressure standard (cold atom vacuum standard)
• Comparison of two multiplexed portable cold-atom vacuum standards
• Measurement of Rb-Rb van der Waals coefficient via Quantum Diffractive Universality

Cited by in corpus (7)

• Ab initio Calculation of Fluid Properties for Precision Metrology
• Accurate measurement of the loss rate of cold atoms due to background gas collisions for the quantum-based cold atom vacuum standard
• Trapped particle evolution driven by residual gas collisions
• On the effect of "glancing" collisions in the cold atom vacuum standard
• Boundaries of universality of thermal collisions for atom-atom scattering
• Hyperfine and Zeeman interactions in ultracold collisions of molecular hydrogen with atomic lithium
• Invariance of quantum scattering rate coefficients to anisotropy of atom-molecule interactions