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arXiv:2312.15446

Cross-calibration of atomic sensors for pressure metrology

Erik Frieling, Riley A. Stewart, James L. Booth, Kirk W. Madison

Published Dec 24, 2023• 1 citation
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Abstract

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, $^{87}$Rb and $^6$Li, and a variety of atomic and molecular background gases including H$_2$, N$_2$, 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.

DOI
10.48550/arxiv.2312.15446

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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, 87^{87}87Rb and 6^66Li, and a variety of atomic and molecular background gases including H2_22​, N2_22​, 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.
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.
We describe how laser-cooled and trapped alkali-metal atoms have been used as pressure sensors in the high- and ultra-high-vacuum regimes operating with relative uncertainties of just over a percent at pressures from a few nPa and up to a few tens of μμμPa. These sensors can serve as primary standards of pressure as the determination of pressure requires only knowledge of collision cross sections between atoms and molecules, eliminating the need for calibration with other devices. The collision cross sections can be measured independently or computed with rigorous quantum methods at percent relative accuracies. We argue that this technology has advanced sufficiently to provide an alternative to the existing, expensive pressure standard in the ultra-high vacuum regime, the orifice flow standard. Experiments with trapped atoms can be used to calibrate cheaper pressure sensors (such as devices based on ionization gauges). However, the technology has not yet matured enough to be of use in other research fields because of the complexity and cost of the experiments. We propose a roadmap for this new pressure standard for vacuum metrology.
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
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 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 (, , and ), 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.
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.