Quantum scattering of icosahedron fullerene C60 with noble-gas atoms.

There exist multiple ways to cool neutral molecules. A front runner is the technique of buffer gas cooling, where momentum-changing collisions with abundant cold noble-gas atoms cool the molecules. This approach can, in principle, produce the most diverse samples of cold molecules. We present quantum mechanical and semiclassical calculations of the elastic scattering differential cross sections and rate coefficients of the C60 fullerene with He and Ar noble-gas atoms in order to quantify the effectiveness of buffer gas cooling for this molecule. We also develop new three-dimensional potential energy surfaces for this purpose using dispersion-corrected density functional theory (DFT) with counterpoise correction. The icosahedral anisotropy of the molecular system is reproduced by expanding the potential in terms of symmetry-allowed spherical harmonics. Long-range dispersion coefficients have been computed from frequency dependent polarizabilities of C60 and the noble-gas atoms. We find that the potential of the fullerene with He is about five times shallower than that with Ar. Anisotropic corrections are very weak for both systems and omitted in the quantum scattering calculations giving us a nearly quantitative estimate of elastic scattering observables. Finally, we have computed differential cross sections at the collision energies used in experiments by Han et al. (Chem Phys Lett 235:211, 1995), corrected for the sensitivity of their apparatus, and we find satisfactory agreement for C60 scattering with Ar.

Quantum Control of Atom-Ion Charge Exchange via Light-Induced Conical Intersections.

Conical intersections are crossing points or lines between two or more adiabatic electronic potential energy surfaces in the multidimensional coordinate space of colliding atoms and molecules. Conical intersections and corresponding nonadiabatic coupling can greatly affect molecular dynamics and chemical properties. In this paper, we predict significant or measurable nonadiabatic effects in an ultracold atom-ion charge-exchange reaction in the presence of laser-induced conical intersections (LICIs). We investigate the fundamental physics of these LICIs on molecular reactivity under unique conditions: those of relatively low laser intensity of 108 W/cm2 and ultracold temperatures below 1 mK. We predict irregular interference effects in the charge-exchange rate coefficients between K and Ca+ as functions of the laser frequency. These irregularities occur in our system due to the presence of two LICIs. To further elucidate the role of the LICIs on the reaction dynamics, we compare these rate coefficients with those computed for a system where the CIs have been "removed". In the laser frequency window, where conical interactions are present, the difference in rate coefficients can be as large as 1 × 10-9 cm3/s.

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(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%.

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.

Roaming pathways and survival probability in real-time collisional dynamics of cold and controlled bialkali molecules.

Perfectly controlled molecules are at the forefront of the quest to explore chemical reactivity at ultra low temperatures. Here, we investigate for the first time the formation of the long-lived intermediates in the time-dependent scattering of cold bialkali [Formula: see text]Rb molecules with and without the presence of infrared trapping light. During the nearly 50 nanoseconds mean collision time of the intermediate complex, we observe unconventional roaming when for a few tens of picoseconds either NaRb or [Formula: see text] and [Formula: see text] molecules with large relative separation are formed before returning to the four-atom complex. We also determine the likelihood of molecular loss when the trapping laser is present during the collision. We find that at a wavelength of 1064 nm the [Formula: see text] complex is quickly destroyed and thus that the [Formula: see text]Rb molecules are rapidly lost.

CODATA Recommended Values of the Fundamental Physical Constants: 2018.

We report the 2018 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council. The recommended values can also be found at physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure constant and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck constant. Further, because the elementary charge, Boltzmann constant, and Avogadro constant also have exact values in the revised SI, many other constants are either exact or have significantly reduced uncertainties. Inconsistencies remain for the gravitational constant and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels.

CODATA recommended values of the fundamental physical constants: 2018.

We report the 2018 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council (CODATA). The recommended values can also be found at physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure constant and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck constant. Further, because the elementary charge, Boltzmann constant, and Avogadro constant also have exact values in the revised SI, many other constants are either exact or have significantly reduced uncertainties. Inconsistencies remain for the gravitational constant and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels.

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.

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Feshbach Resonances in p-Wave Three-Body Recombination within Fermi-Fermi Mixtures of Open-Shell 6Li and Closed-Shell 173Yb Atoms.

We report on the observation of magnetic Feshbach resonances in a Fermi-Fermi mixture of ultracold atoms with extreme mass imbalance and on their unique p-wave dominated three-body recombination processes. Our system consists of open-shell alkali-metal 6Li and closed-shell 173Yb atoms, both spin polarized and held at various temperatures between 1 and 20 µK. We confirm that Feshbach resonances in this system are solely the result of a weak separation-dependent hyperfine coupling between the electronic spin of 6Li and the nuclear spin of 173Yb. Our analysis also shows that three-body recombination rates are controlled by the identical fermion nature of the mixture, even in the presence of s-wave collisions between the two species and with recombination rate coefficients outside the Wigner threshold regime at our lowest temperature. Specifically, a comparison of experimental and theoretical line shapes of the recombination process indicates that the characteristic asymmetric line shape as a function of applied magnetic field and a maximum recombination rate coefficient that is independent of temperature can only be explained by triatomic collisions with nonzero, p-wave total orbital angular momentum. The resonances can be used to form ultracold doublet ground-state molecules and to simulate quantum superfluidity in mass-imbalanced mixtures.

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.

Observation of bound state self-interaction in a nano-eV atom collider.

Quantum mechanical scattering resonances for colliding particles occur when a continuum scattering state couples to a discrete bound state between them. The coupling also causes the bound state to interact with itself via the continuum and leads to a shift in the bound state energy, but, lacking knowledge of the bare bound state energy, measuring this self-energy via the resonance position has remained elusive. Here, we report on the direct observation of self-interaction by using a nano-eV atom collider to track the position of a magnetically-tunable Feshbach resonance through a parameter space spanned by energy and magnetic field. Our system of potassium and rubidium atoms displays a strongly non-monotonic resonance trajectory with an exceptionally large self-interaction energy arising from an interplay between the Feshbach bound state and a different, virtual bound state at a fixed energy near threshold.

Fractal universality in near-threshold magnetic lanthanide dimers.

Ergodic quantum systems are often quite alike, whereas nonergodic, fractal systems are unique and display characteristic properties. We explore one of these fractal systems, weakly bound dysprosium lanthanide molecules, in an external magnetic field. As recently shown, colliding ultracold magnetic dysprosium atoms display a soft chaotic behavior with a small degree of disorder. We broaden this classification by investigating the generalized inverse participation ratio and fractal dimensions for large sets of molecular wave functions. Our exact close-coupling simulations reveal a dynamic phase transition from partially localized states to totally delocalized states and universality in its distribution by increasing the magnetic field strength to only a hundred Gauss (or 10 mT). Finally, we prove the existence of nonergodic delocalized phase in the system and explain the violation of ergodicity by strong coupling between near-threshold molecular states and the nearby continuum.

Orbital quantum magnetism in spin dynamics of strongly interacting magnetic lanthanide atoms.

Laser-cooled lanthanide atoms are ideal candidates with which to study strong and unconventional quantum magnetism with exotic phases. Here, we use state-of-the-art closed-coupling simulations to model quantum magnetism for pairs of ultracold spin-6 erbium lanthanide atoms placed in a deep optical lattice. In contrast to the widely used single-channel Hubbard model description of atoms and molecules in an optical lattice, we focus on the single-site multichannel spin evolution due to spin-dependent contact, anisotropic van der Waals, and dipolar forces. This has allowed us to identify the leading mechanism, orbital anisotropy, that governs molecular spin dynamics among erbium atoms. The large magnetic moment and combined orbital angular momentum of the 4f -shell electrons are responsible for these strong anisotropic interactions and unconventional quantum magnetism. Multichannel simulations of magnetic Cr atoms under similar trapping conditions show that their spin evolution is controlled by spin-dependent contact interactions that are distinct in nature from the orbital anisotropy in Er. The role of an external magnetic field and the aspect ratio of the lattice site on spin dynamics is also investigated.

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.

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

The National Institute of Standards and Technology has recently begun a program to develop a primary pressure standard that is based on ultra-cold atoms, covering a pressure range of 1 × 10-6 Pa to 1 × 10-10 Pa and possibly lower. These pressures correspond to the entire ultra-high vacuum (UHV) range and extend into the extreme-high vacuum (XHV). This cold-atom vacuum standard (CAVS) is both a primary standard and absolute sensor of vacuum. The CAVS is based on the loss of cold, sensor atoms (such as the alkali-metal lithium) from a magnetic trap due to collisions with the background gas (primarily H2) in the vacuum. The pressure is determined from a thermally-averaged collision cross section, which is a fundamental atomic property, and the measured loss rate. The CAVS is primary because it will use collision cross sections determined from ab initio calculations for the Li + H2 system. Primary traceability is transferred to other systems of interest using sensitivity coefficients.

Above-threshold scattering about a Feshbach resonance for ultracold atoms in an optical collider.

Ultracold atomic gases have realized numerous paradigms of condensed matter physics, where control over interactions has crucially been afforded by tunable Feshbach resonances. So far, the characterization of these Feshbach resonances has almost exclusively relied on experiments in the threshold regime near zero energy. Here, we use a laser-based collider to probe a narrow magnetic Feshbach resonance of rubidium above threshold. By measuring the overall atomic loss from colliding clouds as a function of magnetic field, we track the energy-dependent resonance position. At higher energy, our collider scheme broadens the loss feature, making the identification of the narrow resonance challenging. However, we observe that the collisions give rise to shifts in the center-of-mass positions of outgoing clouds. The shifts cross zero at the resonance and this allows us to accurately determine its location well above threshold. Our inferred resonance positions are in excellent agreement with theory.Studies on energy-dependent scattering of ultracold atoms were previously carried out near zero collision energies. Here, the authors observe a magnetic Feshbach resonance in ultracold Rb collisions for above-threshold energies and their method can also be used to detect higher partial wave resonances.

Pendular trapping conditions for ultracold polar molecules enforced by external electric fields.

We theoretically investigate trapping conditions for ultracold polar molecules in optical lattices, when external magnetic and electric fields are simultaneously applied. Our results are based on an accurate electronic-structure calculation of the polar 23Na40K polar molecule in its absolute ground state combined with a calculation of its rovibrational-hyperfine motion. We find that an electric field strength of 5.26(15) kV/cm and an angle of 54.7° between this field and the polarization of the optical laser lead to a trapping design for 23Na40K molecules where decoherences due laser-intensity fluctuations and fluctuations in the direction of its polarization are kept to a minimum. One standard deviation systematic and statistical uncertainties are given in parenthesis. Under such conditions pairs of hyperfine-rotational states of v = 0 molecules, used to induce tunable dipole-dipole interactions between them, experience ultrastable, matching trapping forces.

Dispersive optical detection of magnetic Feshbach resonances in ultracold gases.

Magnetically tunable Feshbach resonances in ultracold atomic systems are chiefly identified and characterized through time-consuming atom loss spectroscopy. We describe an off-resonant dispersive optical probing technique to rapidly locate Feshbach resonances and demonstrate the method by locating four resonances of 87Rb, between the |F = 1,mF = 1〉 and |F = 2,mF = 0〉 states. Despite the loss features being ≲0.1 G wide, we require only 21 experimental runs to explore a magnetic field range >18 G, where 1G = 10-4 T. The resonances consist of two known s-wave features in the vicinity of 9 G and 18 G and two previously unreported p-wave features near 5G and 10 G. We further utilize the dispersive approach to directly characterize the two-body loss dynamics for each Feshbach resonance.

Wannier functions using a discrete variable representation for optical lattices.

We propose a numerical method using the discrete variable representation (DVR) for constructing real-valued Wannier functions localized in a unit cell for both symmetric and asymmetric periodic potentials. We apply these results to finding Wannier functions for ultracold atoms trapped in laser-generated optical lattices. Following S. Kivelson [Phys. Rev. B 26, 4269 (1982)], for a symmetric lattice with inversion symmetry, we construct Wannier functions as eigenstates of the position operators x̂, y, and z restricted to single-particle Bloch functions belonging to one or more bands. To ensure that the Wannier functions are real-valued, we numerically obtain the band structure and real-valued eigenstates using a uniform Fourier grid DVR. We then show, by a comparison of tunneling energies, that the Wannier functions are accurate for both inversion-symmetric and asymmetric potentials to better than 10 significant digits when using double-precision arithmetic. The calculations are performed for an optical lattice with double-wells per unit cell with tunable asymmetry along the x axis and a single sinusoidal potential along the perpendicular directions. Localized functions at the two potential minima within each unit cell are similarly constructed, but using a superposition of single-particle solutions from the two lowest bands. We finally use these localized basis functions to determine the two-body interaction energies in the Bose-Hubbard model and show the dependence of these energies on lattice asymmetry.