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arXiv:2409.11226 · Physical Review A

Effect of glancing collisions in the cold-atom vacuum standard

Stephen Eckel, Daniel S. Barker, James A. Fedchak, Julia K. Scherschligt, Jacek A. Kłos, Eite Tiesinga

Published Feb 12, 2025• 2 citations
arXivHTMLPDF

Abstract

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 $^{7}\mathrm{Li}$ or $^{87}\mathrm{Rb}$ 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 $^{7}\mathrm{Li}$ colliding with noble gases or ${\mathrm{N}}_{2}$ by up to 0.6%. Likewise, we find that in the limit of zero trap depth, the experimentally extracted loss rate coefficients for $^{87}\mathrm{Rb}$ colliding with noble gases or ${\mathrm{N}}_{2}$ shift by as much as 2.2%.

DOI
10.1103/physreva.111.023317

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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^{7}\mathrm{Li}7Li or 87Rb^{87}\mathrm{Rb}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^{7}\mathrm{Li}7Li colliding with noble gases or N2{\mathrm{N}}_{2}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^{87}\mathrm{Rb}87Rb colliding with noble gases or N2{\mathrm{N}}_{2}N2​ shift by as much as 2.2%.
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 describe the cold-atom vacuum standards (CAVS) under development at the National Institute of Standards and Technology (NIST). The CAVS measures pressure in the ultra-high and extreme-high vacuum regimes by measuring the loss rate of sub-millikelvin sensor atoms from a magnetic trap. Ab initio quantum scattering calculations of cross sections and rate coefficients relate the density of background gas molecules or atoms to the loss rate of ultra-cold sensor atoms. The resulting measurement of pressure through the ideal gas law is traceable to the second and the kelvin, making it a primary realization of the pascal. At NIST, two versions of the CAVS have been constructed: a laboratory standard used to achieve the lowest possible uncertainties and pressures, and a portable version that is a potential replacement for the Bayard-Alpert ionization gauge. Both types of CAVSs are connected to a combined extreme-high vacuum flowmeter and dynamic expansion system to enable sensing of a known pressure of gas. In the near future, we anticipate being able to compare the laboratory scale CAVS, the portable CAVS, and the flowmeter/dynamic expansion system to validate the operation of the CAVS as both a standard and vacuum gauge.
We present our progress towards a comparison of NIST's cold atom primary vacuum standard and a dynamic expansion vacuum standard. The cold atom vacuum standard (CAVS) converts the loss rate of atoms from a magnetic trap to a vacuum pressure using ab initio calculations of the quantum atom-molecule collision cross-section. To validate the CAVS, we have constructed a new flowmeter and dynamic expansion system that can produce low-uncertainty pressures in the ultra-high-vacuum range that is required for atom trapping. We discuss the operation and systematics of both the CAVS and flowmeter.
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 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+N2 and Rb+Rb collisions. However, the post-collision energy distribution is expected to deviate from p 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+H2 and Li+H2 collisions. We measure a velocity averaged total collision cross section ratio of R = ⟨ σ tot v ⟩ Li+H 2 : ⟨ σ tot v ⟩ Rb+H 2 = 0.83 ( 5 ) . Based on an ab initio computation of ⟨ σ tot v ⟩ Li+H 2 = 3.104 × 10 − 15 m3 s−1, we deduce ⟨ σ tot v ⟩ Rb+H 2 = 3.6 ( 2 ) × 10