A coupled-channel calculation is carried out to compute rate coefficients for elastic collisions of room-temperature molecular hydrogen with ultracold lithium atoms. The results are relevant for the calibration of a planned cold-atom vacuum standard device that utilizes the rate of collisional loss of trapped atoms to measure background-gas pressures in the UHV and XHV regimes.
A coupled-channel calculation is carried out to compute rate coefficients for elastic collisions of room-temperature molecular hydrogen with ultracold lithium atoms. The results are relevant for the calibration of a planned cold-atom vacuum standard device that utilizes the rate of collisional loss of trapped atoms to measure background-gas pressures in the UHV and XHV regimes.
Trapped ultracold alkali-metal atoms can be used to measure pressure in the ultra-high-vacuum and XHV pressure regimes, those with p < 10−6 Pa. This application for ultracold atoms relies on precise knowledge of collision rate coefficients of alkali-metal atoms with residual room-temperature atoms and molecules in the ambient vacuum or with deliberately introduced gasses. Here, we determine combined elastic and inelastic rate coefficients as well as glancing-angle rate coefficients for ultracold 7Li and 87Rb with room-temperature noble gas atoms as well as H2 and 14N2 molecules. Glancing collisions are those processes where only little momentum is transferred to the alkali-metal atom and this atom is not ejected from its trap. Rate coefficients are found by performing quantum close-coupling scattering calculations using ab initio ground-state electronic Born–Oppenheimer potential energy surfaces. The potentials for Li and Rb with noble gas atoms and also for Rb(2S)–H2(XΣg+) and Rb(2S)–N2(X1Σg+) systems are based on the non-relativistic spin-restricted coupled-cluster method with single, double, and noniterative triple excitations [RCCSD(T)]. For Li(2S)–N2(X1Σg+), the potential is computed at the explicitly correlated spin-restricted RCCSD(T)-F12 level. For Rb, Kr, and Xe atoms, scalar relativistic corrections to the core electrons have been included, while second-order spin–orbit corrections from the valence electrons have been estimated. Data for Li–H2 and Li–He were taken from the existing literature. We estimate standard uncertainties of the rate coefficients by comparing rate coefficients calculated using potentials found with electronic basis sets of increasing size, including estimates of relativistic spin–orbit corrections and the uncertainty of the van der Waals coefficients. The relative uncertainties of rate coefficients are 1%–2% with the exception of 7Li or 87Rb colliding with 20Ne. Those have relative uncertainties of 9% and 8%, respectively. We also show that a commonly used semiclassical approximation for the total elastic rate coefficient agrees with the quantum calculations to 10% with the exception of 7Li and 87Rb collisions with H2, where the semiclassical value underestimates the quantum value by 20%.
We present the measurements of thermalized collisional rate coefficients for ultra-cold 7Li and 87Rb colliding with room-temperature He, Ne, N2, Ar, Kr, and Xe. In our experiments, a combined flowmeter and dynamic expansion system, a vacuum metrology standard, is used to set a known number density for the room-temperature background gas in the vicinity of the magnetically trapped 7Li or 87Rb clouds. Each collision with a background atom or molecule removes a 7Li or 87Rb atom from its trap, and the change in the atom loss rate with background gas density is used to determine the thermalized loss rate coefficients with fractional standard uncertainties better than 1.6% for 7Li and 2.7% for 87Rb. We find consistency—a degree of equivalence of less than one—between the measurements and recent quantum-scattering calculations of the loss rate coefficients [Kłos and Tiesinga, J. Chem. Phys. 158, 014308 (2023)], with the exception of the loss rate coefficient for both 7Li and 87Rb colliding with Ar. Nevertheless, the agreement between theory and experiment for all other studied systems provides validation that a quantum-based measurement of vacuum pressure using cold atoms also serves as a primary standard for vacuum pressure, which we refer to as the cold-atom vacuum standard.
We have computed the thermally averaged total, elastic rate coefficient for the collision of a room-temperature helium atom with an ultracold lithium atom. This rate coefficient has been computed as part of the characterization of a cold-atom vacuum sensor based on laser-cooled 6Li or 7Li atoms that will operate in the ultrahigh-vacuum ($p<{10}^{\ensuremath{-}6}$ Pa) and extreme-high-vacuum ($p<{10}^{\ensuremath{-}10}$ Pa) regimes. The analysis involves computing the $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ HeLi Born-Oppenheimer potential followed by the numerical solution of the relevant radial Schr\"odinger equation. The potential is computed using a single-reference-coupled-cluster electronic-structure method with basis sets of different completeness in order to characterize our uncertainty budget. We predict that the rate coefficient for a 300 K helium gas and a 1 $\ensuremath{\mu}\mathrm{K}$ Li gas is $1.467(13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ cm3/s for 4He+6Li and $1.471(13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ cm3/s for 4He+7Li, where the numbers in parentheses are the one-standard-deviation uncertainties in the last two significant digits. We quantify the temperature dependence as well. Finally, we evaluate the s-wave scattering length and binding of the single van der Waals bound state of HeLi. We predict that this weakly bound level has a binding energy of $\ensuremath{-}0.0064(43)\ifmmode\times\else\texttimes\fi{}hc$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and $\ensuremath{-}0.0122(67)\ifmmode\times\else\texttimes\fi{}hc$ ${\mathrm{cm}}^{\ensuremath{-}1}$ for 4He6Li and 4He7Li, respectively. The calculated binding energy of 4He7Li is consistent with the sole experimental determination.
We theoretically investigate the effect of ``glancing'' collisions on the ultra-high-vacuum pressure readings of the cold-atom vacuum standard (CAVS), based on either ultracold 7Li or 87Rb atoms. Here, glancing collisions are those collisions between ultracold atoms and room-temperature background atoms or molecules in the vacuum that do not impart enough kinetic energy to eject an ultracold atom from its trap. Our model is wholly probabilistic and shows that the number of the ultracold atoms remaining in the trap as a function of time is nonexponential. We update the recent results of a comparison between a traditional pressure standard---a combined flow meter and dynamic expansion system---and the CAVS [D. S. Barker et al., AVS Quantum Sci. 5, 035001 (2023)] to reflect the results of our model. We find that the effect of glancing collisions shifts the theoretical predictions of the total loss rate coefficients for 7Li colliding with noble gases or N2 by up to 0.6%. Likewise, we find that in the limit of zero trap depth, the experimentally extracted loss rate coefficients for 87Rb colliding with noble gases or N2 shift by as much as 2.2%.
Atomic sensors have shown great promise for density and pressure metrology in the high, ultra-high, and extremely-high vacuum regimes. Specifically, the density of background gas particles in vacuum can be determined by measuring the collision rate between the particles and an ensemble of sensor atoms. This requires preparing the sensor atoms in a particular quantum state, observing the rate of changes of that state, and using the cross section coefficient for state-changing collisions to convert the rate into a corresponding density. The cross section can be known by various methods including by quantum scattering calculations using an ansatz for the interaction potential between the collision pair, by measurements of the post-collision sensor-atom momentum recoil distribution, or by empirical calibration of the sensor atom at a known density. Identifying systematic errors in the results of these methods can be aided by direct comparisons between them. Alternatively, measurements of different sensor atoms exposed to the same background gas offers another point of comparison free of the systematic errors inherent in creating a background gas at a known density. Here, we present such measurements for two sensor atoms, 87Rb and 6Li, and a variety of atomic and molecular background gases including H2, N2, Ar, Ne, Kr, and Xe. We find results consistent with, yet statistically different at the level of 3.5(5)%, from recent theoretical and experiment measurements. This work demonstrates a model-free method for transferring the primacy of one atomic standard to another sensor atom and highlights the utility of sensor-atom cross-calibration experiments to check the validity of direct measurements and theoretical predictions.