Chemistry at ultracold temperatures

Quantum stereodynamics of cold molecular collisions

Advances in quantum state preparations combined with molecular cooling and trapping technologies have enabled unprecedented control of molecular collision dynamics. This progress, achieved over the last two decades, has dramatically improved our understanding of molecular phenomena in the extreme quantum regime characterized by translational temperatures well below a kelvin. In this regime, collision outcomes are dominated by isolated partial waves, quantum threshold and quantum statistics effects, tiny energy splitting at the spin and hyperfine levels, and long-range forces. Collision outcomes are influenced not only by the quantum state preparation of the initial molecular states but also by the polarization of their rotational angular momentum, i.e., stereodynamics of molecular collisions. The Stark-induced adiabatic Raman passage technique developed in the last several years has become a versatile tool to study the stereodynamics of light molecular collisions in which alignment of the molecular bond axis relative to initial collision velocity can be fully controlled. Landmark experiments reported by Zare and coworkers have motivated new theoretical developments, including formalisms to describe four-vector correlations in molecular collisions that are revealed by the experiments. In this Feature article, we provide an overview of recent theoretical developments for the description of stereodynamics of cold molecular collisions and their implications to cold controlled chemistry.

Signatures of Non-universal Quantum Dynamics of Ultracold Chemical Reactions of Polar Alkali Dimer Molecules with Alkali Metal Atoms: Li(2S) + NaLi(a3Σ+) → Na(2S) + Li2(a3Σu+)

Ultracold chemical reactions of weakly bound triplet-state alkali metal dimer molecules have recently attracted much experimental interest. We perform rigorous quantum scattering calculations with a new ab initio potential energy surface to explore the chemical reaction of spin-polarized NaLi(a³Σ⁺) and Li(²S) to form Li₂(a³Σ_u⁺) and Na(²S). The reaction is exothermic and proceeds readily at ultralow temperatures. Significantly, we observe strong sensitivity of the total reaction rate to small variations of the three-body part of the Li₂Na interaction at short range, which we attribute to a relatively small number of open Li₂(a³Σ_u⁺) product channels populated in the reaction. This provides the first signature of highly non-universal dynamics seen in rigorous quantum reactive scattering calculations of an ultracold exothermic insertion reaction involving a polar alkali dimer molecule, opening up the possibility of probing microscopic interactions in atom+molecule collision complexes via ultracold reactive scattering experiments.

Recent advances in quantum theory on ro-vibrationally inelastic scattering

Molecular collisions are of fundamental importance in understanding intermolecular interaction and dynamics. Its importance is accentuated in cold and ultra-cold collisions because of the dominant quantum mechanical nature of the scattering. We review recent advances in the time-independent approach to quantum mechanical characterization of non-reactive scattering in tetratomic systems, which is ideally suited for large collisional de Broglie wavelengths characteristic in cold and ultracold conditions. We discuss quantum scattering algorithms between two diatoms and between a triatom and an atom and their implementation, as well as various approximate schemes. They not only enable the characterization of collision dynamics in realistic systems but also serve as benchmarks for developing more approximate methods.

Quantum-Controlled Collisions of H2 Molecules

The amount of information that can be obtained from a scattering experiment depends upon the precision with which the quantum states are defined in the incoming channel. By precisely defining the incoming states and measuring the outgoing states in a scattering experiment, we set up the boundary condition for experimentally solving the Schrödinger equation. In this Perspective we discuss cold inelastic scattering experiments using the most theoretically tractable H₂ and its isotopologues as the target. We prepare the target in a precisely defined rovibrational (v, j, m) quantum state using a special coherent optical technique called the Stark-induced adiabatic Raman passage (SARP). v and j represent the quantum numbers of the vibrational and rotational energy levels, and m refers to the projection of the rotational angular momentum vector j on a suitable quantization axis in the laboratory frame. Selection of the m quantum numbers defines the alignment of the molecular frame, which is necessary to probe the anisotropic interactions. For us to achieve the collision temperature in the range of a few degrees Kelvin, we co-expand the colliding partners in a mixed supersonic beam that is collimated to define a direction for the collision velocity. When the bond axis is aligned with respect to a well-defined collision velocity, SARP achieves stereodynamic control at the quantum scale. Through various examples of rotationally inelastic cold scattering experiments, we show how SARP coherently controls the dynamics of anisotropic interactions by preparing quantum superpositions of the orientational m states within a single rovibrational (v, j) energy state. A partial wave analysis, which has been developed for the cold scattering experiments, shows dominance of a resonant orbital that leaves its mark in the scattering angular distribution. These highly controlled cold collision experiments at the single partial wave limit allow the most direct comparison with the results of theoretical computations, necessary for accurate modeling of the molecular interaction potential.

Diffuse Basis Functions for Relativistic s and d Block Gaussian Basis Sets

Diffuse s, p, and d functions have been optimized for use with previously reported relativistic basis sets for the s and d blocks of the periodic table. The functions were optimized on the 4:1 weighted average of the s² and p² configurations of the anion, with the d shell in the dⁿ⁺¹ configuration for the d blocks. Exponents were extrapolated for groups 2 and 12, which have unstable or weakly bound anions. The diffuse basis sets have been tested by application to calculations of electron affinities of the group 11 elements (Cu, Ag, and Au), double electron affinities of the group 11 monocations, and potential energy curves of Mg₂ and Ca₂ van der Waals dimers, as well as some response properties of the group 1 anions (Rb^-, Cs^-, and Fr^-), the group 2 elements (Sr, Ba, and Ra), and RbLi, CsLi, and FrLi molecules.

Non-Relativistic Electronic-Structure Computation of Neutral and Cationic Systems [Fr2, Fr-AEM+ (AEM= Ca, Sr, Ba)]

The experimental field of ultracold ion-atom mixtures including an alkali-metal atom and an alkaline-earth-metal ion as well as of homonuclear alkali dimers has paved the way for creating and manipulating the ultracold molecules. The present paper is focused on a study of molecules such us francium dimer and a comparative spectroscopic investigation of the cationic systems Fr-(Ca⁺, Sr⁺, Ba⁺). We adopt a computational scheme without spin-orbit coupling reposed on the full configuration interaction and semi-empirical pseudo-potential theory of the atomic cores Fr⁺, Ca²⁺, Sr²⁺, and Ba²⁺ with extended and optimized basis sets. We have determined the adiabatic potentials with their relative spectroscopic constants, the electric dipole moments and the vibrational levels spacings for the ^1,3Σ_u,g⁺ and ^1,3Σ⁺ electronic states for Fr₂ and Fr-AEM⁺, respectively, correlated toward {Fr(7s) + Fr(7s, 7p, 6d, 8s, 8p)}, {Ca(4s², 4s4p, 4s3d), Sr(5s², 5s5p, 5s4d), Ba(6s², 6s6p, 6s5d) + Fr⁺}, and {Ca⁺(4s, 3d), Sr⁺(5s, 4d), Ba⁺(6s, 5d) + Fr(7s, 7p)}. The accuracy and reliability of the current results are discussed by comparing with theoretical data available in the literature. The occurrence of some avoided crossings between the neighboring electronic states is leading to a charge or excitation transfer for atom-ion collisions in the diverse charge or excited states. The Σ⁺-Σ⁺ transitions are determined in order to evaluate the future radiative lifetimes of vibrational states serving the direct laser cooling.

Laser Cooling with an Intermediate State and Electronic Structure Studies of the Molecules CaCs and CaNa

The ground and excited electronic states of the diatomic molecules CaCs and CaNa have been investigated by implementing the ab initio CASSCF/(MRCI + Q) calculation. The potential energy curves of the doublet and quartet electronic low energy states in the representation ^2s+1Λ^(±) have been determined for the two considered molecules, in addition to the spectroscopic constants T _e, ω_e, B _e, R _e, and the values of the dipole moment μ_e and the dissociation energy D _e. The determination of vibrational constants E _v, B _v, D _v, and the turning points R _min and R _max up to the vibrational level v = 100 was possible with the use of the canonical functions schemes. Additionally, the transition and the static dipole moments curves, Einstein coefficients, the spontaneous radiative lifetime, the emission oscillator strength, and the Franck-Condon factors are computed. These calculations showed that the molecule CaCs is a good candidate for Doppler laser cooling with an intermediate state. A "four laser" cooling scheme is presented, along with the values of Doppler limit temperature T _D = 55.9 μK and the recoil temperature T _r = 132 nK. These results should provide a good reference for experimental spectroscopic and ultra-cold molecular physics studies.

The F + HD(v = 0, 1; j = 0, 1) reactions: stereodynamical properties of orbiting resonances

The excitation functions (reaction cross-section as a function of collision energy) of the F + HD(v = 0, 1; j = 0, 1) benchmark system have been calculated in the 0.01-6 meV collision energy interval using a time-independent hyperspherical quantum dynamics methodology. Special attention has been paid to orbiting resonances, which bring about detailed information on the three-atom interaction during the reactive encounter. The location of the resonances depends on the rovibrational state of the reactants HD(v,j), but is the same for the two product channels HF + D and DF + H, as expected for these resonances that are linked to the van der Waals well at the entrance. The resonance intensities depend both on the entrance and on the exit channels. The peak intensities for the HF + D channel are systematically larger than those for DF + H. Vibrational excitation leads to an increase of the peak intensity by more than an order of magnitude, but rotational excitation has a less drastic effect. It deceases the resonance intensity of the F + HD(v = 1) reaction, but increases somewhat that of F + HD(v = 0). Polarization of the rotational angular momentum with respect to the initial velocity reveals intrinsic directional preferences in the F + HD(v = 0, 1; j = 1) reactions that are manifested in the resonance patterns. The helicities (Ω = 0, Ω = ±1) possible for j = 1 contribute to the resonances, but that from Ω± 1 is, in general, dominant and in some cases exclusive. It corresponds to a preferential alignment of the HD internuclear axis perpendicular to the initial direction of approach and, thus, to side-on collisions. This work also shows that external preparation of the reactants, following the intrinsic preferences, would allow the enhancement or reduction of specific resonance features, and would be of great help for their eventual experimental detection.

Thermometry in a Multipole Ion Trap

We present a characterization of the ions’ translational energy distribution in a multipole ion trap. A linear mapping between the energy distribution of the trapped ions onto the ions’ time-of-flight (TOF) to a detector is demonstrated. For low ion temperatures, a deviation from linearity is observed and can be attributed to the emergence of multiple potential minima. The potential landscape of the trapped ions is modeled via the finite element method, also accounting for subtleties such as surface-charge accumulation. We demonstrate the validity of our thermometry method by simulating the energy distribution of the ion ensemble thermalized with buffer gas using a Molecular Dynamics (MD) simulation. A comparison between the energy distribution of trapped ions in different multipole trap configurations—i.e., with hyperbolic rods, cylindrical rods, and cylindrical wires—is provided. With these findings, one can map the temperature of the trapped ions down to the Kelvin regime using their TOF distributions. This enables future studies on sympathetic cooling and chemical reactions involving ions in multipole traps.

Evidence of Nonrigidity Effects in the Description of Low-Energy Anisotropic Molecular Collisions of Hydrogen Molecules with Excited Metastable Helium Atoms

Cold collisions serve as a sensitive probe of the interaction potential. In the recent study of Klein et al. (Nature Phys.2017, 13, 35–38), the one-parameter scaling of the interaction potential was necessary to obtain agreement between theoretical and observed patterns of the orbiting resonances for excited metastable helium atoms colliding with hydrogen molecules. Here, we show that the effect of nonrigidity of the H₂ molecule on the resonant structure, absent in the previous study, is critical to predict the correct positions of the resonances in that case. We have complemented the theoretical description of the interaction potential and revised reaction rate coefficients by proper inclusion of the flexibility of the molecule. The calculated reaction rate coefficients are in remarkable agreement with the experimental data without empirical adjustment of the interaction potential. We have shown that even state-of-the-art calculations of the interaction energy cannot ensure agreement with the experiment if such an important physical effect as flexibility of the interacting molecule is neglected. Our findings about the significance of the nonrigidity effects can be especially crucial in cold chemistry, where the quantum nature of molecules is pronounced.

Stereodynamical Control of a Quantum Scattering Resonance in Cold Molecular Collisions

Cold collisions of light molecules are often dominated by a single partial wave resonance. For the rotational quenching of HD (v=1, j=2) by collisions with ground state para-H_{2}, the process is dominated by a single L=2 partial wave resonance centered around 0.1 K. Here, we show that this resonance can be switched on or off simply by appropriate alignment of the HD rotational angular momentum relative to the initial velocity vector, thereby enabling complete control of the collision outcome.

Orbiting resonances in the F + HD (v = 0, 1) reaction at very low collision energies. A quantum dynamical study

Time-independent, fully converged, quantum dynamical calculations have been performed for the F + HD (v = 0, j = 0) and F + HD (v = 1, j = 0) reactions on an accurate potential energy surface down to collision energies of 0.01 meV. The two isotopic exit channels, HF + D and DF + H, have been investigated. The calculations reproduce satisfactorily the Feshbach resonance structures for collision energies between 10 and 40 meV, previously reported in the literature for the HF + D channel. Contrary to the results of a former literature work, vibrational excitation of HD is found to enhance reactivity in all cases down to the lowest collision energy investigated. Shape-type orbiting resonances are found for collision energies lower than 2 meV. The resonances appear as peaks in the reaction cross sections that are associated to specific values of the total angular momentum, J. In contrast with the Feshbach resonances at higher energies, the orbiting resonance structure, which is caused by the van der Waals well of the entrance channel, is identical for the HF + D and DF + H exit channels. The orbiting resonance peaks for F + HD (v = 0) are very small, but those for F + HD (v = 1) could be observed, in principle, with a combination of Raman pumping and merged beams methods.

Quantum Dynamics and Kinetics of the F + H2 and F + D2 Reactions at Low and Ultra-Low Temperatures

Integral cross sections and rate constants for the prototypical chemical reactions of the fluorine atom with molecular hydrogen and deuterium have been calculated over a wide interval of collision energy and temperature ranging from the sub-thermal (50 K) down to the ultra-cold regimes (0.5 mK). Rigorous close coupling time-independent quantum reactive scattering calculations have been carried out on two potential energy surfaces, differing only at long-range in the reactants' channel. The results show that tunnel, resonance and virtual state effects enhance under-barrier reactivity giving rise to pronounced deviations from the Arrhenius law as temperature is lowered. Within the ultra-cold domain (below 1 mK), the reactivity is governed by virtual state effects and by tunneling through the reaction barrier; in the cold regime (1 mK–1 K), the shape resonances in the entrance channel of the potential energy surface make the quantum tunneling contribution larger so enhancing cross sections and rate constants by about one order of magnitude; at higher temperatures (above 10 K), the tunneling pathway enhanced by the constructive interference between two Feshbach resonances trapped in the reaction exit channel competes with the thermally activated mechanism, as the energy gets closer to the reaction barrier height. The results show that at low temperatures cross sections and rate constants are extremely sensitive to small changes in the long-range intermolecular interaction in the entrance channel of the potential energy surface, as well as to isotopic substitution.

Continuous Loading of Ultracold Ground-State ^{85}Rb_{2} Molecules in a Dipole Trap Using a Single Light Beam

We have developed an approach to continuously load ultracold ^{85}Rb_{2} vibrational ground-state molecules into a crossed optical dipole trap from a magneto-optical trap. The technique relies on a single high-power light beam with a broad spectrum superimposed onto a narrow peak at an energy of about 9400  cm^{-1}. This single laser source performs all the required steps: the short-range photoassociation creating ground-state molecules after radiative emission, the cooling of the molecular vibrational population down to the lowest vibrational level v_{X}=0, and the optical trapping of these molecules. Furthermore, we probe by depletion spectroscopy and determine that 75% of the v_{X}=0 ground-state molecules are in the three lowest rotational levels J_{X}=0, 1, 2. The lifetime of the ultracold molecules in the optical dipole trap is limited to about 70 ms by off-resonant light scattering. The proposed technique opens perspectives for the formation of new molecular species in the ultracold domain, which are not yet accessible by well-established approaches.

Restricted basis set coupled-channel calculations on atom-molecule collisions in magnetic fields

Rigorous coupled-channel quantum scattering calculations on molecular collisions in external fields are computationally demanding due to the need to account for a large number of coupled channels and multiple total angular momenta J of the collision complex. We show that by restricting the total angular momentum basis to include only the states with helicities K ≤ K_max, it is possible to obtain accurate elastic and inelastic cross sections for low-temperature He + CaH, Li + CaH, and Li + SrOH collisions in the presence of an external magnetic field at a small fraction of the computational cost of the full coupled-channel calculations (where K is the projection of the molecular rotational angular momentum on the atom-diatom axis). The optimal size of the truncated helicity basis set depends on the mechanism of the inelastic process and on the magnitude of the external magnetic field, with the minimal basis set (K_max = 0) producing quantitatively accurate results for, e.g., ultracold Li + CaH and Li + SrOH scattering at low magnetic fields, leading to nearly 90-fold gain in computational efficiency. Larger basis sets are required to accurately describe the resonance structure in the magnetic field dependence of Li + CaH and Li + SrOH inelastic cross sections in the few partial wave-regime as well as indirect spin relaxation in He + CaH collisions. Our calculations indicate that the resonance structure is due to an interplay of the spin-rotation and Coriolis couplings between the basis states of different K and the couplings between the rotational states of the same K induced by the anisotropy of the interaction potential.

Time-Dependent Wave Packet Dynamics Calculations of Cross Sections for Ultracold Scattering of Molecules

Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extension of rigorous quantum calculations of ultracold reaction properties to polyatomic molecules and adds a new powerful tool for the study of ultracold chemistry.

Theoretical Study of the Feasibility of Laser Cooling the 24Mg35Cl Molecule Including Hyperfine Structure and Branching Ratios

The possibility of laser cooling the ²⁴Mg³⁵Cl molecule is investigated using the electronic, rovibrational, and hyperfine structure. Twelve low-lying Λ-S electronic states of the ²⁴Mg³⁵Cl molecule have been calculated at the multireference configuration interaction level of theory. The spin-orbit coupling effects are taken into account in the electronic structure calculations. Spectroscopic constants agree well with previously obtained theoretical and experimental values. On the basis of the potential energy curves and transition dipole moments, the highly diagonally distributed Franck-Condon factors for the A²Π → X²Σ⁺ transition and short radiative lifetime of the A²Π state are determined. Then, employing a quantum effective Hamiltonian approach, we investigate the hyperfine manifolds of the X²Σ⁺ state and obtain the zero-field hyperfine spectrum with the errors relative to the experimental data not exceeding 8-20 kHz. Finally, we design a laser cooling scheme with one cooling main laser beam and two repumping laser beams with modulated sidebands, which is sufficient for the implementation of efficient laser slowing and cooling of the ²⁴Mg³⁵Cl molecule. Moreover, it is important to note that the dissociation energy (2.2593 eV) of the B²Σ⁺ state is obtained for the first time at the multireference configuration interaction level. We hope that this can provide a helpful reference for experimental observation.

Vibrational branching ratios and radiative lifetimes in the laser cooling of AlBr

The feasibility of laser cooling of the AlBr molecule is investigated using ab initio quantum chemistry. Potential energy curves, permanent dipole moments, and transition dipole moments for the ground state X¹Σ⁺ and the first two excited states (a³Π and A¹Π) are calculated using the multi-reference configuration interaction plus Davidson corrections (MRCI+Q) method with the ACVQZ basis set; the spin-orbit coupling effects are also taken into account in electronic structure calculations at the MRCI level. Based on the acquired potential energy curves and transition dipole moments, highly diagonally distributed Franck-Condon factors (f₀₀ = 0.9540, f₁₁ = 0.8172) and vibrational branching ratios (R₀₀ = 0.9708, R₁₁ = 0.8420) for the transition are determined. Radiative lifetime calculations of the A¹Π₁ (ν' = 0-4) state are found to be short (9.16-11.48 ns) enough for rapid laser cooling. The proposed main cycling laser drives the transition at the wavelength λ₀₀ = 279.19 nm. The vibrational branching loss ratios of the A¹Π₁ (ν') state to the intervening states a³Π_0⁺ and a³Π₁ are small (<5.2 × 10^-6) enough to be negligible. The present theoretical results indicate that the AlBr molecule is a promising candidate for laser cooling.

Intrabeam Scattering for Ultracold Collisions

We demonstrate a method to probe cold and ultracold chemistry in a single molecular beam. The approach exploits beam slippage, the velocity difference of different species in the same beam, to establish the relative velocity. Average collision energies of 2.5 mK are achieved but with a spread of 100% or more. However, by implementing a dual-slit chopper that can separately fix the velocities of the two species at the interaction region, we achieve precise control over the relative velocity and narrow its spread. Relative velocities of 7-10 ± 1.1 m/s are achieved with an angular divergence less than 0.25°. In the present study, we observe l-changing collisions occurring between Xe Rydberg atoms and Xe ground state atoms at subKelvin temperatures. We show that in this case the collision energies are tunable between 200 to 450 mK with a root-mean-square deviation of ∼18%. Application of the method to other species and access to much lower energies is straightforward.

Cold molecules: Progress in quantum engineering of chemistry and quantum matter

Cooling atoms to ultralow temperatures has produced a wealth of opportunities in fundamental physics, precision metrology, and quantum science. The more recent application of sophisticated cooling techniques to molecules, which has been more challenging to implement owing to the complexity of molecular structures, has now opened the door to the longstanding goal of precisely controlling molecular internal and external degrees of freedom and the resulting interaction processes. This line of research can leverage fundamental insights into how molecules interact and evolve to enable the control of reaction chemistry and the design and realization of a range of advanced quantum materials.

Electronic structure of the polar molecules XF (X: Be, Mg, Ca) with rovibrational and dipole moment calculations

A theoretical investigation for the feasibility of laser-cooling is performed through the calculation of accurate potential energy curves, static dipole moments, spectroscopic constants and rovibrational calculations for 24, 26 and 27 highly excited electronic states for BeF, CaF and MgF molecules respectively. In order to understand the electronic structure of their lowest lying electronic states and to learn the characteristic behavior of their chemical bonding, a high level of calculation is realized by using the complete active space self-consistent field (CASSCF) with multi-reference configuration interaction MRCI method including single and double excitations with Davidson correction (+Q) for the three considered molecules. The comparison between the values of the present work and those available in the literature for several electronic states shows a good agreement. Fifty new excited electronic states have been investigated, in the present work, for the first time for the three studied molecules.

Ultracold Nonreactive Molecules in an Optical Lattice: Connecting Chemistry to Many-Body Physics

We derive effective lattice models for ultracold bosonic or fermionic nonreactive molecules (NRMs) in an optical lattice, analogous to the Hubbard model that describes ultracold atoms in a lattice. In stark contrast to the Hubbard model, which is commonly assumed to accurately describe NRMs, we find that the single on-site interaction parameter U is replaced by a multichannel interaction, whose properties we elucidate. Because this arises from complex short-range collisional physics, it requires no dipolar interactions and thus occurs even in the absence of an electric field or for homonuclear molecules. We find a crossover between coherent few-channel models and fully incoherent single-channel models as the lattice depth is increased. We show that the effective model parameters can be determined in lattice modulation experiments, which, consequently, measure molecular collision dynamics with a vastly sharper energy resolution than experiments in a free-space ultracold gas.

The H + HeH(+) → He + H2(+) reaction from the ultra-cold regime to the three-body breakup: exact quantum mechanical integral cross sections and rate constants

In this work, we present a quantum mechanical scattering study of the title reaction from 1 mK to 2000 K. Total integral cross sections and thermal rate constants are compared with previous theoretical and experimental data and with simpler theoretical models to understand the range of validity of the approximations used in the previous studies. The obtained quantum reactive observables have been found to be nearly insensitive to the roto-vibrational energy of the reactants at high temperatures. More sensitive to the reactant's roto-vibrational energy are the data in the cold and ultra-cold regimes. The implications of the new data presented here in the early universe scenario are also discussed and analyzed.

Theoretical study of the CsNa molecule: adiabatic and diabatic potential energy and dipole moment

The adiabatic and diabatic potential energy curves of the low-lying electronic states of the NaCs molecule dissociating into Na (3s, 3p) + Cs (6s, 6p, 5d, 7s, 7p, 6d, 8s, 4f) have been investigated. The molecular calculations are performed using an ab initio approach based on nonempirical pseudopotential, parametrized l-dependent polarization potentials and full configuration interaction calculations through the CIPCI quantum chemistry package. The derived spectroscopic constants (Re, De, Te, ωe, ωexe, and Be) of the ground state and lower excited states are compared with the available theoretical and experimental works. Moreover, accurate permanent and transition dipole moment have been determined as a function of the internuclear distance. The adiabatic permanent dipole moment for the first nine (1)Σ(+) electronic states have shown both ionic characters associated with electron transfer related to Cs(+)Na(-) and Cs(-)Na(+) arrangements. By a simple rotation, the diabatic permanent dipole moment is determined and has revealed a linear behavior, particularly at intermediate and large distances. Many peaks around the avoided crossing locations have been observed for the transition dipole moment between neighbor electronic states.

Calculating and modeling the exchange energies of homonuclear and heteronuclear alkali dimers based on the surface integral method

The exchange energies of all homonuclear and heteronuclear alkali dimers are calculated based on the surface integral method. These results are generally in good agreement with both ab initio calculations and experimental results where available. It is also shown that the exchange energies could be fitted by an analytical expression of AR(b) exp(-cR). b and c can be calculated by two simple formulas that are only related to the ionization energies of the constituent atoms. A is the only parameter in this expression. More interestingly, it is found that the parameter A for the heteronuclear dimers could be approximated by a combining rule.

Magnetic trapping of cold bromine atoms

Magnetic trapping of bromine atoms at temperatures in the millikelvin regime is demonstrated for the first time. The atoms are produced by photodissociation of Br2 molecules in a molecular beam. The lab-frame velocity of Br atoms is controlled by the wavelength and polarization of the photodissociation laser. Careful selection of the wavelength results in one of the pair of atoms having sufficient velocity to exactly cancel that of the parent molecule, and it remains stationary in the lab frame. A trap is formed at the null point between two opposing neodymium permanent magnets. Dissociation of molecules at the field minimum results in the slowest fraction of photofragments remaining trapped. After the ballistic escape of the fastest atoms, the trapped slow atoms are lost only by elastic collisions with the chamber background gas. The measured loss rate is consistent with estimates of the total cross section for only those collisions transferring sufficient kinetic energy to overcome the trapping potential.

Laser radiation pressure slowing of a molecular beam

We demonstrate deceleration of a beam of neutral strontium monofluoride molecules using radiative forces. Under certain conditions, the deceleration results in a substantial flux of detected molecules with velocities ≲50  m/s. Simulations and other data indicate that the detection of molecules below this velocity is greatly diminished by transverse divergence from the beam. The observed slowing, from ∼140  m/s, corresponds to scattering ≳10(4) photons. We also observe longitudinal velocity compression under different conditions. Combined with molecular laser cooling techniques, this lays the groundwork to create slow and cold molecular beams suitable for trap loading.