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
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
This work demonstrates that quantum diffractive collisions, those that result in very small momentum and energy transfer, are universal. Specifically, the cumulative energy distribution transferred to an initially stationary sensor particle by a quantum diffractive collision follows a universal function that depends only on the sensor particle mass and the thermally-averaged, total collision cross section. The characteristic energy scale corresponds to the localization length associated with the collision-induced quantum measurement, and the shape of the universal function is determined {\it only} by the analytic form of the interaction potential at long range. Using cold 87Rb sensor atoms confined in a magnetic trap, we observe experimentally the universal function specific to van der Waals collisions, and realize a \emph{self-defining} particle pressure sensor that can be used for any ambient gas. This provides the first primary and quantum definition of the Pascal, applicable to any species and therefore represents a key advance for vacuum and pressure metrology. The quantum pressure standard realized here was compared with a state-of-the-art orifice flow standard transferred by an ionization gauge calibrated for N2. The pressure measurements agreed at the 0.5\% level.
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 We report the realization of the first cold-atom primary standard. This standard is based on a universal law governing quantum diffractive collisions between particles that allows an experimental determination of the velocity averaged total collision cross section, the only parameter required to quantify the pressure or flux of particles given a sensor particle collision rate measurement. Using an ensemble of 87Rb sensor atoms, we show that this new quantum pressure standard can be applied to gases of both atomic (He, Ar, and Xe) and molecular species ( N 2 , C O 2 , and H 2 ), surpassing the scope of existing orifice flow pressure standards. We verify the accuracy of this new standard using an ionization gauge (IG) calibrated for N2 by an orifice flow standard. The gauge calibration factors determined by the cold atom and orifice flow standards differ by less than 0.5% and, thus, agree within their uncertainties of 2% and 2.8% respectively. Using this standard, we evaluate the response of two different IGs to a variety of different gas species and report variations of up to 20% for their measured calibration factors. We also observe a non-linear response of the IG readings for CO2 gas. Finally, we demonstrate the use of a magneto-optical trap (MOT) as a transfer standard to extend the measurement range by a factor of 100 to include pressures up to P ~ 10−5 Pa.
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.
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%.