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

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 ($P_{\rm{QDU}6}$) 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 $P_{\rm{QDU}6}$ 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 $\langle \sigma_{\rm{tot}} \, v \rangle_{\rm{Li+H}_2}$. We find a velocity averaged total collision cross section ratio, $R = \langle \sigma_{\rm{tot}} \, v \rangle_{\rm{Li+H}_2} : \langle \sigma_{\rm{tot}} \, v \rangle_{\rm{Rb+H}_2} = 0.83(5)$. Based on an \textit{ab initio} computation of $\langle \sigma_{\rm{tot}} \, v \rangle_{\rm{Li+H}_2} = 3.13(6)\times 10^{-15}$ m$^3$/s, we deduce $\langle \sigma_{\rm{tot}} \, v \rangle_{\rm{Rb+H}_2} = 3.8(2) \times 10^{-15}$ m$^3$/s, in agreement with a Rb+H$_2$ \textit{ab initio} value of $\langle \sigma_{\mathrm{tot}} v \rangle_{\mathrm{Rb+H_2}} = 3.57 \times 10^{-15} \mathrm{m}^3/\mathrm{s}$.By contrast, fitting the Rb+H$_2$ loss rate as a function of trap depth to the universal function we find $\langle \sigma_{\rm{tot}} \, v \rangle_{\rm{Rb+H}_2} = 5.52(9) \times 10^{-15}$ 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.Comment: 14 pages, 9 figure

Development of a cold atom pressure standard

In this thesis, we report the realization of the world's first cold atom based pressure standard for the high- and ultra-high vacuum (UHV) regimes, < 10⁻⁶ Pa (1 Pa=1N/m²). This standard is a fundamentally new approach to vacuum metrology as it is based on a universal law governing quantum diffractive collisions between particles. We show that a measurement of trap loss rate versus trap depth provides the velocity averaged total collision cross-section, , - the only parameter required to quantify the pressure of background particles given a measurement of the collision rate with a sensor atom. This new quantum measurement standard is fully empirical, based on unchanging and fundamental atomic constants, and does not rely on computations of total collision cross-sections based on theoretical interaction potentials. We demonstrate, using a sensor ensemble of ⁸⁷Rb atoms, that this new quantum pressure standard can be applied to gases of both atomic species (He, Ar, and Xe) and molecular species (N₂, CO₂, and H₂), surpassing the scope of existing orifice flow pressure standards. The accuracy of this new standard was also verified by comparing it with an N₂ calibrated ionization gauge traced back to an orifice flow standard. They agree within 0.5%. A complete uncertainty analysis of this cold atom pressure standard is provided here. Moreover, using this standard, we are able to observe and quantify the performance limits of two industry-standard ionization gauges. Using this universal law, we can precisely measure the total collision cross-section for the collision system of interest. As an example, we show a precision measurement of for collisions between Rb and Ar. The experimentally determined value of agrees with the theoretical computation result within 1.0 %. Next, we demonstrate the use of a magneto-optical trap (MOT) as a transfer pressure standard to extend the operational range of the cold atom pressure standard by a factor of 100, from P < 10⁻⁷ Pa to include pressures up to P < 10⁻⁵ Pa. Finally, a proposal for using a MOT as a primary pressure standard is presented.Science, Faculty ofPhysics and Astronomy, Department ofGraduat