Development of a new UHV/XHV pressure standard (Cold Atom Vacuum Standard)

Elastic and glancing-angle rate coefficients for heating of ultracold Li and Rb atoms by collisions with room-temperature noble gases, H2, and N2

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(XΣ_g ⁺) and Rb(²S)-N₂(X¹Σ_g ⁺) 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(X¹Σ_g ⁺), 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%.

Precise quantum measurement of vacuum with cold atoms

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.

Moving-frame imaging of transiting cold atoms for precise long-range transport

Transporting cold atoms between interconnected vacuum chambers is an important technique for increasing the versatility of cold atom setups, particularly for those that couple atoms to photonic devices. In this report, we introduce a method where we are able to image the atoms at all points during transport via moving optical dipole trap. Cooled ⁸⁷Rb atoms are transported ∼50 cm into an auxiliary vacuum chamber while being monitored with a moving-frame imaging system for which in-situ characterization of the atom transport is demonstrated. Precise positioning of the atoms near photonic devices is also tested across several tapered fibers showing an axial positioning resolution of ∼450 μm.

Coherent Scattering of Low Mass Dark Matter from Optically Trapped Sensors

We propose a search for low mass dark matter particles through momentum recoils caused by their scattering from trapped, nanometer-scale objects. Our projections show that even with a modest array of femtogram-mass sensors, parameter space beyond the reach of existing experiments can be explored. The case of smaller, attogram-mass sensors is also analyzed-where dark matter can coherently scatter from the entire sensor-enabling a large enhancement in the scattering cross-section relative to interactions with single nuclei. Large arrays of such sensors have the potential to investigate new parameter space down to dark matter masses as low as 10 keV. If recoils from dark matter are detected by such sensors, their inherent directional sensitivity would allow an unambiguous identification of a dark matter signal.

A constant pressure flowmeter for extreme-high vacuum

We demonstrate operation of a constant-pressure flowmeter capable of generating and accurately measuring flows as low as 2 × 10^-13 mol/s. Generation of such small flows is accomplished by using a small conductance element with C ≈ 50 nL/s. Accurate measurement then requires both low outgassing materials (< 1 × 10^-15 mol/s) and small volume changes (≈ 70 μL). We outline the present flowmeter's construction, detail its operation, and quantify its uncertainty. The type-B uncertainty is < 0.2 % (k = 1) over the entire operating range. In particular, we present an analysis of its hydraulic system, and quantify the shift and uncertainty due to the slightly compressible oil. Finally, we compare our flowmeter against a NIST standard flowmeter, and find agreement to within 0.5 % (k = 2).

A Bitter-type electromagnet for complex atomic trapping and manipulation

We create a pair of symmetric Bitter-type electromagnet assemblies capable of producing multiple field configurations including uniform magnetic fields, spherical quadruple traps, or Ioffe-Pritchard magnetic bottles. Unlike other designs, our coil allows both radial and azimuthal cooling water flows by incorporating an innovative 3D-printed water distribution manifold. Combined with a double-coil geometry, such orthogonal flows permit stacking of non-concentric Bitter coils. We achieve a low thermal resistance of 4.2(1) °C kW-1 and high water flow rate of 10.0(3) l min-1 at a pressure of 190(10) kPa.

Quantum-Based Photonic Sensors for Pressure, Vacuum, and Temperature Measurements: A Vison of the Future with NIST on a Chip

The NIST on a Chip (NOAC) program's central idea is the idea that measurement technology can be developed to enable metrology to be performed "outside the National Metrology Institute" by the creation of deployed and often miniaturized standards. These standards, when based on fundamental properties of nature, are directly tracible to the international system of units known as the SI. NIST is also developing quantum-based standards for SI traceability known as QSI, or Quantum based International System of units. Specifically, this paper will cover NIST efforts in the area of thermodynamic metrology to develop NOAC standards for pressure, vacuum and temperature measurements.

Collisions of room-temperature helium with ultracold lithium and the van der Waals bound state of HeLi

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 < 10-6 Pa) and extreme-high-vacuum (p < 10-10 Pa) regimes. The analysis involves computing the X 2 Σ+ HeLi Born-Oppenheimer potential followed by the numerical solution of the relevant radial Schrodinger 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 μK Li gas is 1.467(13) × 10-9 cm3/s for 4He + 6Li and 1.471(13) × 10-9 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 -0.0064(43) × hc cm-1 and -0.0122(67) × hc cm-1 for 4He6Li and 4He7Li, respectively. The calculated binding energy of 4He7Li is consistent with the sole experimental determination.

Systematic uncertainty due to background-gas collisions in trapped-ion optical clocks

We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an ²⁷Al⁺ clock to enable a total fractional systematic uncertainty below 10^-18. For this clock, with 38(19) nPa of room-temperature H₂ background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order 10^-16 at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be -0.6(2.4) × 10^-19, where the shift is due to collisional heating time dilation and the uncertainty is dominated by the worst case ±π/2 bound used for collisional phase shift of the ²⁷Al⁺ superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs.

Elastic rate coefficients for Li+H2 collisions in the calibration of a cold-atom vacuum standard

Ongoing efforts at the National Institute of Standards and Technology in creating a cold-atom vacuum standard device have prompted theoretical investigations of atom-molecule collision processes that characterize its operation. Such a device will operate as a primary standard for the ultrahigh-vacuum and extreme-high-vacuum regimes. This device operates by relating loss of ultracold lithium atoms from a conservative trap by collisions with ambient atoms and molecules to the background density and thus pressure through the ideal gas law. The predominant background constituent in these environments is molecular hydrogen H2. We compute the relevant Li+H2 Born-Oppenheimer potential energy surface, paying special attention to its uncertainty. Coupled-channel calculations are then used to obtain total rate coefficients, which include momentum-changing elastic and inelastic processes. We find that inelastic rotational quenching of H2 is negligible near room temperature. For a (T = 300)-K gas of H2 and 1.0-μK gas of Li atoms prepared in a single hyperfine state, the total rate coefficients are 6.0(1) × 10-9 cm3/s for both 6Li and 7Li isotopes, where the number in parentheses corresponds to a one-standard-deviation combined statistical and systematic uncertainty. We find that a 10-K increase in the H2 temperature leads to a 1.9% increase in the rate coefficients for both isotopes. For Li temperatures up to 100 μK, changes are negligible. Finally, a semiclassical Born approximation significantly overestimates the rate coefficients. The difference is at least ten times the uncertainty of the coupled-channel result.

Single-beam Zeeman slower and magneto-optical trap using a nanofabricated grating

We demonstrate a compact (0.25 L) system for laser cooling and trapping atoms from a heated dispenser source. Our system uses a nanofabricated diffraction grating to generate a magnetooptical trap (MOT) using a single input laser beam. An aperture in the grating allows atoms from the dispenser to be loaded from behind the chip, increasing the interaction distance of atoms with the cooling light. To take full advantage of this increased distance, we extend the magnetic field gradient of the MOT to create a Zeeman slower. The MOT traps approximately 10^{6 7}Li atoms emitted from an effusive source with loading rates greater than 10⁶ s^-1. Our design is portable to a variety of atomic and molecular species and could be a principal component of miniaturized cold-atom-based technologies.

Single-beam Zeeman slower and magneto-optical trap using a nanofabricated grating

We demonstrate a compact (0.25 L) system for laser cooling and trapping atoms from a heated dispenser source. Our system uses a nanofabricated diffraction grating to generate a magnetooptical trap (MOT) using a single input laser beam. An aperture in the grating allows atoms from the dispenser to be loaded from behind the chip, increasing the interaction distance of atoms with the cooling light. To take full advantage of this increased distance, we extend the magnetic field gradient of the MOT to create a Zeeman slower. The MOT traps approximately 10^{6 7}Li atoms emitted from an effusive source with loading rates greater than 10⁶ s^-1. Our design is portable to a variety of atomic and molecular species and could be a principal component of miniaturized cold-atom-based technologies.

Light-induced atomic desorption of lithium

We demonstrate loading of a Li magneto-optical trap using light-induced atomic desorption. The magnetooptical trap confines up to approximately 4 × 104 7Li atoms with loading rates up to approximately 4 × 103 atoms per second. We study the Li desorption rate as a function of the desorption wavelength and power. The extracted wavelength threshold for desorption of Li from fused silica is approximately 470 nm. In addition to desorption of lithium, we observe light-induced desorption of background gas molecules. The vacuum pressure increase due to the desorbed background molecules is ≲ 50 % and the vacuum pressure decreases back to its base value with characteristic timescales on the order of seconds when we extinguish the desorption light. By examining both the loading and decay curves of the magneto-optical trap, we are able to disentangle the trap decay rates due to background gases and desorbed lithium. Our results show that light-induced atomic desorption can be a viable Li vapor source for compact devices and sensors.

Note: A 3D-printed alkali metal dispenser

We demonstrate and characterize a source of Li atoms made from direct metal laser sintered titanium. The source's outgassing rate is measured to be 5(2) × 10-7 Pa L s-1 at a temperature T = 330 °C, which optimizes the number of atoms loaded into a magneto-optical trap. The source loads ≈1077Li atoms in the trap in ≈1 s. The loaded source weighs 700 mg and is suitable for a number of deployable sensors based on cold atoms.

Quantum-based vacuum metrology at NIST

The measurement science in realizing and disseminating the unit for pressure in the International System of Units (SI), the pascal (Pa), has been the subject of much interest at NIST. Modern optical-based techniques for pascal metrology have been investigated, including multi-photon ionization and cavity ringdown spectroscopy. Work is ongoing to recast the pascal in terms of quantum properties and fundamental constants and in so doing, make vacuum metrology consistent with the global trend toward quantum-based metrology. NIST has ongoing projects that interrogate the index of refraction of a gas using an optical cavity for low vacuum, and count background particles in high vacuum to extreme high vacuum using trapped laser-cooled atoms.

Recommended practice for calibrating vacuum gauges of the ionization type

This article represents a recommended practice for the calibration of ionization gauges using the comparison method. In this method, ionization gauges are compared to a working standard that has an SI traceable calibration. The ionization gauge is either of the hot-cathode ionization type or the cold-cathode ionization type. Details of the calibration apparatus, the principle of operation of the gauges, data analysis, uncertainty budget, and reporting the uncertainty are given.

Challenges to miniaturizing cold atom technology for deployable vacuum metrology

Cold atoms are excellent metrological tools; they currently realize SI time and, soon, SI pressure in the ultra-high (UHV) and extreme high vacuum (XHV) regimes. The development of primary, vacuum metrology based on cold atoms currently falls under the purview of national metrology institutes. Under the emerging paradigm of the "quantum-SI", these technologies become deployable (relatively easy-to-use sensors that integrate with other vacuum chambers), providing a primary realization of the pascal in the UHV and XHV for the end-user. Here, we discuss the challenges that this goal presents. We investigate, for two different modes of operation, the expected corrections to the ideal cold-atom vacuum gauge and estimate the associated uncertainties. Finally, we discuss the appropriate choice of sensor atom, the light Li atom rather than the heavier Rb.