Zero field splittings in molecules originate from the intrinsic spin and orbital angular momentum of unpaired electrons. Here, we close a knowledge gap on a diatomic molecule built from spin-8 ground-state dysprosium atoms, where zero-field splittings correspond to the energies of states with different alignments of the two spins. We predict a paramagnetic molecular ground state with parallel Dy spins aligned along the internuclear axis. A diamagnetic state with anti-parallel spins is the first excited state with a small energy cost of hc × 2 cm−1 predominantly due to the magnetic dipole-dipole interaction. We also determine the rotations and vibrations of the diatom and show that centrifugal forces double the splittings between these para- and dia-magnetic states. The vibrational spacings and zero-field splittings have similar magnitude. Finally, the Dy2 ground state has a magnetic moment that is twice that of the atom and, thus, arrays of ultracold Dy2 can be used to simulate strongly interacting magnets. Zero-field splittings in molecules arise from the spin and orbital angular momentum of unpaired electrons, yet their behaviour in diatomic molecules with spin-8 dysprosium atoms remains underexplored. Here, the authors predict a paramagnetic ground state with parallel Dy spins and reveal implications for simulating strongly interacting magnets using ultracold Dy2 arrays.

The discovery of the C _60 fullerene opened new horizons to design carbon nanostructures with targeted electronic structure as well as transport and optical properties. For example, endohedral ^12 C _60 molecules were proposed as candidates for functional quantum architectures to store and manipulate encased atomic and molecular qubits. Recent advances in cryogenic buffer-gas cooling and frequency-comb spectroscopy have enabled rovibrational quantum-state-resolved measurements of gas-phase ^12 C _60 , revealing rotational fine structure reflecting its high icosahedral symmetry. Here, we present a perturbative quantum description of the ^12 C _60 molecule interacting with a buffer gas of ^40 Ar atoms at temperatures of order 150 K, including a detailed analysis of their electronic structure, their interaction anisotropies, and the collision-induced rotational quenching of ^12 C _60 in its vibrational and electronic ground state. The role of the icosahedral symmetry on the collisional dynamics is emphasized leading to a complex dependence on the ^12 C _60 rotational quantum number. Finally, we compute the isotropic and anisotropic static and dynamic dipole polarizability of ^12 C _60 in its absolute ground state in order to evaluate the long-range, van der Waals interaction between ^12 C _60 and ^40 Ar.

The discovery of the C60 fullerene opened new horizons to design carbon nanostructures with targeted electronic structure as well as transport and optical properties. For example, endohedral 12C60 molecules were proposed as candidates for functional quantum architectures to store and manipulate encased atomic and molecular qubits. Recent advances in cryogenic buffer-gas cooling and frequency-comb spectroscopy have enabled rovibrational quantum-state-resolved measurements of gas-phase 12C60, revealing rotational fine structure reflecting its high icosahedral symmetry. Here, we present a perturbative quantum description of the 12C60 molecule interacting with a buffer gas of 40Ar atoms at temperatures of order 100 K, including a detailed analysis of their electronic structure, their interaction anisotropies, and the collision-induced rotational quenching of 12C60 in its vibrational and electronic ground state. The role of the icosahedral symmetry on the collisional dynamics is emphasized leading to unusual selection rules. Finally, we compute the isotropic and anisotropic static and dynamic dipole polarizability of 12C60 in its absolute ground state in order to evaluate the long-range, van der Waals interaction between 12C60 and 40Ar.

We present transit time corrections for the diffusive decay of an atomic ground-state population grating formed by spatially periodic optical pumping. We present results corresponding to two configurations, the first of which involves a population grating with a Gaussian envelope that is weakly probed using coherent scattering by a laser beam with a Gaussian spatial profile. The second configuration involves a population grating with a rectangular envelope that is weakly probed using coherent scattering by a laser beam with an idealized rectangular spatial profile of the same size. Recently, these corrections have been used to quantify systematic effects in measurements of Rb-inert gas diffusion coefficients near room temperature. Rubidium diffusion can be used to realize a quantum pressure sensor. (c) 2026 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

We theoretically investigate the effect of "glancing" collisions on the ultra-high vacuum (UHV) 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 non-exponential. We update the recent results of a comparison between a traditional pressure standard-a combined flowmeter and dynamic expansion system-to the CAVS [D.S. Barker, et al., AVS Quantum Science 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 have performed three theoretical simulations relevant for describing collisions among laser-cooled silver atoms and for the formation of Ag2 molecules from these colliding atoms. Firstly, we determined the relativistic electronic structure of Ag2 molecules in ground and low-lying excited states. Secondly, we computed rotational and vibrational levels of the ground and excited electronic states as well as rovibrationally averaged electric transition dipole moments. Using this knowledge, we analyzed a simplified quantum-mechanical model of the one-photon photoassociation process to form electronically excited Ag2 from microkelvin Ag atoms and make predictions for lineshapes and saturation effects as functions of laser frequency and intensity. Finally and thirdly, we performed coupled-channels calculations, numerical solutions of sets of coupled radial Schr & ouml;dinger equations of ultracold ground-state Ag collisions in an external magnetic field. These calculations include the effects of two Born-Oppenheimer potentials as well as hyperfine Fermi-contact and Zeeman interactions. We discuss the expected range of s-wave scattering lengths as well as strengths and distribution of Fano-Feshbach resonances as a function of the magnetic-field strength for the 107Ag and 109Ag isotopes. We highlight the periodicity of the scattering length with small changes in the depths of the Born-Oppenheimer potentials. The Fano-Feshbach resonances can be used to magneto-associate ultracold Ag atoms into weakly bound ground-state Ag2 dimers.

We report the 2022 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 https://physics.nist.gov/cuu/Constants/. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2022. A discussion of the major improvements as well as inconsistencies within the data is given. (c) 2025 by the U.S. Secretary of Commerce on behalf of the United States. All rights reserved.

We present a theoretical study of the low lying adiabatic relativistic electronic states of lanthanide monohydroxide (Ln-OH) molecules near their linear equilibrium geometries. We focus on heavy, magnetic DyOH and ErOH relevant to fundamental symmetry tests. We use a restricted-active-space self-consistent field method combined with spin-orbit coupling as well as a relativistic coupled-cluster method. In addition, electric dipole and magnetic moments are computed with the self-consistent field method. Analysis of the results from both methods shows that the dominant molecular configuration of the ground state is one where an electron from the partially filled and submerged 4f orbital of the lanthanide atom moves to the hydroxyl group, leaving the closed outer-most 6s^2 lone electron pair of the lanthanide atom intact in sharp contrast to the bonding in alkaline-earth monohydroxides and YbOH, where an electron from the outer-most s shell moves to the hydroxyl group. For linear molecules the projection of the total electron angular momentum on the symmetry axis is a conserved quantity with quantum number Ω and we study the polynomial Ω dependence of the energies of the ground states as well as their electric and magnetic moments. We find that the lowest energy states have |Ω|=15/2 and 1/2 for DyOH and ErOH, respectively. The zero field splittings among these Ω states is approximately hc× 1 000 cm^-1. We find that the permanent dipole moments for both triatomics are fairly small at 0.23 atomic units. The magnetic moments are closely related to that of the corresponding atomic Ln^+ ion in an excited electronic state. We also realize that the total electron angular momentum is to good approximation conserved and has a quantum number of 15/2 for both triatomic molecules.

We present comprehensive determinations of the diffusion coefficients D at T = 24 degrees C for trace amounts of naturally abundant Rb atoms in inert, naturally abundant He, Ne, N2, Ar, Kr, and Xe buffer gases using a single measurement technique. They have been measured by establishing a spatially periodic population grating in the Rb sample using two laser beams that intersect at a small angle 0 of a few milliradians. The atomic population grating decays exponentially in time due to diffusive motion induced by momentum-changing elastic collisions between Rb and buffer gas atoms or molecules. This decay is monitored by observing the scattered field from a readout beam aligned along the direction of one of the excitation beams. We distinguish the contribution of diffusion from other collisional processes by measuring the characteristic 02 dependence of the decay rate. We also measure the systematic dependence of the decay rate on the buffer gas pressure over a range of 7000 to 90000 Pa. In this manner, we obtain diffusion coefficients at standard atmospheric pressure of 101 325 Pa and at a temperature of 24.0(5) degrees C. We use two models to correct for systematic effects due to the transit time, one assuming a rectangular profile of the population distribution and a rectangular readout beam profile, and a second using Gaussian profiles. We obtain weighted averages of 0.33(5), 0.214(14), 0.132(7), 0.123(9), 0.093(9), and 0.073(4) cm2/s for Rb in He, Ne, N2, Ar, Kr, and Xe, respectively. The number in parentheses represents one standard deviation of the combined statistical and systematic uncertainty. We also compare these data with diffusion coefficients obtained using quantum, classical, and semiclassical theoretical methods based on the most accurate interatomic interaction potentials from the literature. Near room temperature, simulations of D using classical and quantum methods agree within their intrinsic, sub-1% standard uncertainties. We find that the semiclassical model only gives the correct orders of magnitude for D. Our computed diffusion coefficients based on the quantum theory agree with the experimental determinations when systematic effects are taken into account. Our measurements and modeling are relevant to the optimization of magnetometers, biomedical imaging using spin-polarized noble gases, tests of collision models based on interatomic potentials, and the development of pressure sensors.

We study spin dynamics and quantum magnetism with ultracold highly-magnetic atoms. In particular, we focus on the interactions among rare-earth atoms localized in a site of an optical-lattice potential, modeled as a cylindrically symmetric harmonic oscillator in the presence of a weak external magnetic field. The interactions between the atoms are modeled using a multi-channel Hamiltonian containing multiple spin–spin and anisotropic spin–orbit interactions with strengths that depend on the separation between the atoms. We studied the eigenenergies of the atom pair in a site for different lattice geometries and magnetic field strengths. In parallel, we compared these energies to those found from a simplified approach, where the complex-collisional physics is replaced by a two-length-scale pseudopotential containing the contact and magnetic dipole–dipole interactions. The eigenenergies of this model can be computed analytically within the Born approximation as well as non-perturbatively for strong contact interactions. We have shown that the pseudopotential model can accurately represent the multi-channel Hamiltonian in certain parameter regimes of the shape of the site of an optical lattice. The pseudopotential forms the starting point for many-body, condensed matter simulations involving many atom pairs in different sites of an optical lattice.

We present a theoretical study of the low lying adiabatic relativistic electronic states of lanthanide monohydroxide (Ln-OH) molecules near their linear equilibrium geometries. In particular, we focus on heavy, magnetic DyOH and ErOH relevant to fundamental symmetry tests. We use a restricted-active-space self-consistent field method combined with spin-orbit coupling as well as a relativistic coupled-cluster method to determine ground and excited electronic states. In addition, electric and magnetic dipole moments are computed with the self-consistent field method. Analysis of the results from both methods shows that the dominant molecular configuration of the ground state is one where an electron from the partially filled and anisotropic 4f orbital of the lanthanide atom moves to the hydroxyl group, leaving the closed outer-most [Formula: see text] lone electron pair of the lanthanide atom intact in sharp contrast to the bonding in alkaline-earth monohydroxides and YbOH, where an electron from the outer-most s shell moves to the hydroxyl group. For linear molecules the projection of the total electron angular momentum on the symmetry axis is a conserved quantity with quantum number Ω and we study the polynomial Ω dependence of the energies of the ground states as well as their electric and magnetic moments. We find that for both molecules Ω lies between [Formula: see text] and [Formula: see text], where the degenerate states with the lowest energy have [Formula: see text] and 1/2 for DyOH and ErOH, respectively. The zero field splittings among these Ω states is approximately [Formula: see text] [Formula: see text], where h is the Planck constant and c is the speed of light in vacuum. We find that the permanent dipole moments for both triatomics are fairly small at 0.23 atomic units and are mostly independent of Ω. The magnetic moments are closely related to that of the corresponding atomic [Formula: see text] ion in an excited electronic state. From the polynomial Ω dependences, we also realize that the total electron angular momentum is to good approximation conserved and has a quantum number of 15/2 for both triatomic molecules. We describe how this observation can be used to construct effective Hamiltonians containing spin-spin operators.

Molecules have vibrational, rotational, spin-orbit and hyperfine degrees of freedom or quantum states, each of which responds in a unique fashion to external electromagnetic radiation. The control over superpositions of these quantum states is key to coherent manipulation of molecules. For example, the better the coherence time the longer quantum simulations can last. The important quantity for controlling an ultracold molecule with laser light is its complex-valued molecular dynamic polarizability. Its real part determines the tweezer or trapping potential as felt by the molecule, while its imaginary part limits the coherence time. Here, our study shows that efficient trapping of a molecule in its vibrational ground state can be achieved by selecting a laser frequency with a detuning on the order of tens of GHz relative to an electric-dipole-forbidden molecular transition. Close proximity to this nearly forbidden transition allows to create a sufficiently deep trapping potential for multiple rotational states without sacrificing coherence times among these states from Raman and Rayleigh scattering. In fact, we demonstrate that magic trapping conditions for multiple rotational states of the ultracold ^23Na^87Rb polar molecule can be created.

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.

We present three-dimensional Monte-Carlo simulations of the capture of 1000 K $^7$Li or 500 K $^{87}$Rb atoms by a continuous supersonic $^4$He jet and show that intense alkali-metal beams form with narrow transverse and longitudinal velocity distributions. The nozzle creating the $^4$He jet is held at approximately 4 K. These conditions are similar to those in the cold $^7$Li source developed by some of us as described in [Phy. Rev. A 107, 013302 (2023)]. The simulations use differential cross-sections obtained from quantum scattering calculations of $^7$Li or $^{87}$Rb atoms with $^4$He atoms for relative collision energies between $k\times 1$ mK to $k\times 3000$ K, where $k$ is the Boltzmann constant. For collision energies larger than $\approx k\times 4$ K the collisions favor forward scattering, deflecting the $^7$Li or $^{87}$Rb atoms by no more than a few degrees. From the simulations, we find that about 1$\%$ of the lithium atoms are captured into the $^4$He jet, resulting in a lithium beam with a most probable velocity of about $210$ m/s and number densities on the order of $10^{8}$ cm$^{-3}$. Simulations predict narrow yet asymmetric velocity distributions which are verified by comparing to fluorescence measurements of the seeded $^7$Li atoms. We find agreement between simulated and experimentally measured seeded $^7$Li densities to be better than 50$\%$ across a range of $^4$He flow rates. We make predictions for capture efficiency and cooling of $^{87}$Rb by a supersonic $^4$He jet. The capture efficiency for $^{87}$Rb is expected to be similar to $^7$Li.

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.

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.

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%.

The 53rd Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics will take place from May 30 – June 3, 2022 in Orlando, Fl, USA. Virtual Presenter Help Desk

Received 13 February 2022DOI:https://doi.org/10.1103/PhysRevA.105.029901©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAtom & ion trapping & guidingBose gasesLaser spectroscopyScattering of atoms, molecules, clusters & ionsUltracold collisionsAtomic, Molecular & Optical

The 53rd Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics will take place from May 30 – June 3, 2022 in Orlando, Fl, USA. Virtual Presenter Help Desk