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 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 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%.
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.
Quantum atomic sensors have shown great promise for vacuum metrology. Specifically, the density of 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 total collision rate coefficient for state-changing collisions to convert the rate into a corresponding density. The total collision rate coefficient can be known by various methods, including quantum scattering calculations using a computed interaction potential for the collision pair, measurements of the post-collision sensor-atom momentum recoil distribution, or empirical measurements of the collision rate at a known density. Observed discrepancies between the results of these methods call into question their accuracy. To investigate this, we study the ratio of collision rate measurements of co-located sensor atoms, 87Rb and 6Li, exposed to natural abundance versions of H2, He, N2, Ne, Ar, Kr, and Xe gases. This method does not require knowledge of the test gas density and is, therefore, free of the systematic errors inherent in efforts to introduce the test gas at a known density. Our results are systematically different at the level of 3% to 4% 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.
Abstract In our previous work (Shen et al 2020 Metrologia 57 025015; Booth et al 2019 New J. Phys. 21 102001), we have reported the first primary quantum pressure standard based on the loss rate of cold rubidium atoms from a magnetic trap. We have shown that this standard is self-calibrating. That is, the single parameter required to quantify the pressure or particle flux impinging on the sensor atoms, σ t o t v , can be determined experimentally. In this paper, we refine our procedure to extract the trap loss rate coefficient by expressing the measured trap loss rate of the rubidium atoms as a convolution of the universal loss rate expression from Shen et al (2020 Metrologia 57 025015) and Booth et al (2019 New J. Phys. 21 102001) with the energy distribution of the rubidium atoms in the trap. We report improved σ t o t v values for 87Rb–X (X = He, Ar, Xe, H2, N2, and CO2) collision pairs. All are systematically higher than our previously reported values, although the differences are less than 2%. The calibration factor of an ionization gauge for nitrogen obtained using the cold atom standard, i g = 0.950 (19), agrees with the value obtained by NIST, i g = 0.940 (26) calibrated against their orifice flow standard.
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%.
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.