Quantum-state controlled chemical reactions of ultracold potassium-rubidium molecules

Observation of Bose-Einstein condensation of dipolar molecules

Ensembles of particles governed by quantum mechanical laws exhibit intriguing emergent behaviour. Atomic quantum gases1,2, liquid helium3,4 and electrons in quantum materials5-7 all exhibit distinct properties because of their composition and interactions. Quantum degenerate samples of ultracold dipolar molecules promise the realization of new phases of matter and new avenues for quantum simulation8 and quantum computation9. However, rapid losses10, even when reduced through collisional shielding techniques11-13, have so far prevented evaporative cooling to a Bose-Einstein condensate (BEC). Here we report on the realization of a BEC of dipolar molecules. By strongly suppressing two- and three-body losses via enhanced collisional shielding, we evaporatively cool sodium-caesium molecules to quantum degeneracy and cross the phase transition to a BEC. The BEC reveals itself by a bimodal distribution when the phase-space density exceeds 1. BECs with a condensate fraction of 60(10)% and a temperature of 6(2) nK are created and found to be stable with a lifetime close to 2 s. This work opens the door to the exploration of dipolar quantum matter in regimes that have been inaccessible so far, promising the creation of exotic dipolar droplets14, self-organized crystal phases15 and dipolar spin liquids in optical lattices16.

Quantum interference in atom-exchange reactions

Chemical reactions, where bonds break and form, are highly dynamic quantum processes. A fundamental question is whether coherence can be preserved in chemical reactions and then harnessed to generate entangled products. Here we investigated this question by studying the 2KRb → K2 + Rb2 reaction at 500 nK, focusing on the nuclear spin degrees of freedom. We prepared the initial nuclear spins in KRb in an entangled state by lowering the magnetic field to where the spin-spin interaction dominates and characterized the preserved coherence in nuclear spin wavefunction after the reaction. We observed an interference pattern that is consistent with full coherence at the end of the reaction, suggesting that entanglement prepared within the reactants could be redistributed through the atom-exchange process.

Essay: Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics

Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today's realization, we wonder what doors of basic science can these tools unlock. We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier. Part of a series of Essays which concisely present author visions for the future of their field.

Scheme for Deterministic Loading of Laser-Cooled Molecules into Optical Tweezers

We propose to repeatedly load laser-cooled molecules into optical tweezers, and transfer them to storage states that are rotationally excited by two additional quanta. Collisional loss of molecules in these storage states is suppressed, and a dipolar blockade prevents the accumulation of more than one molecule. Applying three cycles loads tweezers with single molecules at an 80% success rate, limited by residual collisional loss. This improved loading efficiency reduces the time needed for rearrangement of tweezer arrays, which would otherwise limit the scalability of neutral molecule quantum computers.

Entanglement Generation of Polar Molecules via Deep Reinforcement Learning

Polar molecules are a promising platform for achieving scalable quantum information processing because of their long-range electric dipole-dipole interactions. Here, we take the coupled ultracold CaF molecules in an external electric field with gradient as qubits and concentrate on the creation of intermolecular entanglement with the method of deep reinforcement learning (RL). After sufficient training episodes, the educated RL agents can discover optimal time-dependent control fields that steer the molecular systems from separate states to two-qubit and three-qubit entangled states with high fidelities. We analyze the fidelities and the negativities (characterizing entanglement) of the generated states as a function of training episodes. Moreover, we present the population dynamics of the molecular systems under the influence of control fields discovered by the agents. Compared with the schemes for creating molecular entangled states based on optimal control theory, some conditions (e.g., molecular spacing and electric field gradient) adopted in this work are more feasible in the experiment. Our results demonstrate the potential of machine learning to effectively solve quantum control problems in polar molecular systems.

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.

Benchmark Study of the Electronic States of the LiRb Molecule: Ab Initio Calculations with the Fock Space Coupled Cluster Approach

Accurate potential energy curves (PECs) are determined for the twenty-two electronic states of LiRb. In contrast to previous studies, the applied approach relies on the first principle calculations involving correlation among all electrons. The current methodology is founded on the multireference coupled cluster (CC) scheme constructed within the Fock space (FS) formalism, specifically for the (2,0) sector. The FS methodology is established within the framework of the intermediate Hamiltonian formalism and offers an intruder-free, efficient computational scheme. This method has a distinctive feature that, when applied to the doubly ionized system, provides the characteristics of the neutral case. This proves especially beneficial when investigating PECs in situations where a closed-shell molecule dissociates into open-shell fragments, yet its double positive ion forms closed-shell species. In every instance, we successfully computed continuous PECs spanning the entire range of interatomic distances, from the equilibrium to the dissociation limit. Moreover, the spectroscopic characteristic of various electronic states is presented, including relativistic effects. Relativistic corrections included at the third-order Douglas-Kroll level have a non-negligible effect on the accuracy of the determined spectroscopic constants.

Laser Scheme for Doppler Cooling of the Hydroxyl Cation (OH+)

We report on a cycling scheme for Doppler cooling of trapped OH+ ions using transitions between the electronic ground state X3Σ- and the first excited triplet state A3Π. We have identified relevant transitions for photon cycling and repumping, have found that coupling into other electronic states is strongly suppressed, and have calculated the number of photon scatterings required to cool OH+ to a temperature where Raman sideband cooling can take over. In contrast to the standard approach, where molecular ions are sympathetically cooled, our scheme does not require co-trapping of another species and opens the door to the creation of pure samples of cold molecular ions with potential applications in quantum information, quantum chemistry, and astrochemistry. The laser cooling scheme identified for OH+ is efficient despite the absence of near-diagonal Franck-Condon factors, suggesting that broader classes of molecules and molecular ions are amenable to laser cooling than commonly assumed.

Modeling Photoassociative Spectra of Ultracold NaK + K

A model for photoassociation of ultracold atoms and molecules is presented and applied to the case of 39K and 23Na39K bosonic particles. The model relies on the assumption that photoassociation is dominated by long-range atom-molecule interactions well outside the chemical bond region. The frequency of the photoassociation laser is chosen close to a bound-bound rovibronic transition from the X1Σ+ ground state toward the metastable b3Π lowest excited state of 23Na39K, allowing us to neglect any other excitation, which could hinder the photoassociation detection. The energy level structure of the long-range 39K···23Na39K excited super-dimer is computed in the space-fixed frame by solving coupled-channel equations, involving the coupling between the 23Na39K internal rotation and the mechanical rotation of the super-dimer complex. A quite rich structure is obtained, and the corresponding photoassociation rates are presented. Other possible photoassociation transitions are discussed in the context of the proposed model.

Cold collisions of hot molecules

In this Perspective, we review our recent work on rotationally inelastic collisions of highly vibrationally excited NO molecules prepared in single rotational and parity levels at v = 10 using stimulated emission pumping (SEP). This state preparation is employed in a recently developed crossed molecular beam apparatus where two nearly copropagating molecular beams achieve an intersection angle of 4° at the interaction region. This near-copropagating beam geometry of the molecular beams permits very wide tuning of the collision energy, from far above room temperature down to 2 K where we test the theoretical treatment of the attractive part of the potentials and the difference potential for the first time. We have obtained differential cross sections for state-to-state collisions of NO (v = 10) with Ar and Ne in both spin-orbit manifolds using velocity map imaging. Overall good agreement of the experimental results was seen with quantum mechanical close-coupling calculations done on both coupled-cluster and multi-reference configuration interaction potential energy surfaces. Probing cold collisions of NO carrying ∼2 eV of vibrational excitation allows us to test state-of-the-art theory in this extreme nonequilibrium regime.

Potential Energy Surfaces and Arrangement Effects of RbNa2 Complex

Ab initio calculations of alkaline diatomic molecule interactions with alkaline atoms provide detailed information about their electronic structure, vibrational frequencies, and spectroscopic properties, which are difficult to measure experimentally. This knowledge can aid in designing and interpreting experiments and guide the development of computational models and advanced dynamical calculation. Using the quantum chemistry ab initio methods based on multi-reference configuration interaction with Davidson correction (MCSCF/MRCI + Q), atomic effective core potentials, core-polarization potentials, and the interactions between the sodium atom and the NaRb diatomic molecule are investigated. To describe the potential energy surfaces of the RbNa2 system, we introduce two geometries described in the Z-matrix coordinates (Re, R, θ). Potential energy surfaces of the ground state 12A' and the first excited state 22A' were calculated for different approach directions of the sodium atom to the NaRb molecule and two geometries were considered. The first geometry is where the Na atom approaches the Rb atom of the RbNa dimer, and the second one is when it approaches the Na atom of the RbNa dimer. Global minima of the ground and first excited states and conical intersections between these states are determined for both geometries. The RbNa dimer in interaction with the sodium atom is found to be strongly attractive in its first excited state, which may be important for the experimenters particularly in the field of cold alkali polar dimers. Thereafter, the potential energy curves correlated to the lowest-lying dissociation limits are calculated in the linear form for the two geometrical cases (angle θ at 180°) and the atomic arrangement effect is observed.

Temperature-Dependent Contact of Weakly Interacting Single-Component Fermi Gases and Loss Rate of Degenerate Polar Molecules

Motivated by the experimental realization of single-component degenerate Fermi gases of polar ground state KRb molecules with intrinsic two-body losses [L. De Marco et al., A degenerate Fermi gas of polar molecules, Science 363, 853 (2019).SCIEAS0036-807510.1126/science.aau7230], this work studies the finite-temperature loss rate of single-component Fermi gases with weak interactions. First, we establish a relationship between the two-body loss rate and the p-wave contact. Second, we evaluate the contact of the homogeneous system in the low-temperature regime using p-wave Fermi liquid theory and in the high-temperature regime using the second-order virial expansion. Third, conjecturing that there are no phase transitions between the two temperature regimes, we smoothly interpolate the results to intermediate temperatures. It is found that the contact is constant at temperatures close to zero and increases first quadratically with increasing temperature and finally-in agreement with the Bethe-Wigner threshold law-linearly at high temperatures. Fourth, applying the local-density approximation, we obtain the loss-rate coefficient for the harmonically trapped system, reproducing the experimental KRb loss measurements within a unified theoretical framework over a wide temperature regime without fitting parameters. Our results for the contact are not only applicable to molecular p-wave gases but also to atomic single-component Fermi gases, such as ^{40}K and ^{6}Li.

Enhancing reactivity of SiO+ ions by controlled excitation to extreme rotational states

Optical pumping of molecules provides unique opportunities for control of chemical reactions at a wide range of rotational energies. This work reports a chemical reaction with extreme rotational excitation of a reactant and its kinetic characterization. We investigate the chemical reactivity for the hydrogen abstraction reaction SiO⁺ + H₂ → SiOH⁺ + H in an ion trap. The SiO⁺ cations are prepared in a narrow rotational state distribution, including super-rotor states with rotational quantum number (j) as high as 170, using a broad-band optical pumping method. We show that the super-rotor states of SiO⁺ substantially enhance the reaction rate, a trend reproduced by complementary theoretical studies. We reveal the mechanism for the rotational enhancement of the reactivity to be a strong coupling of the SiO⁺ rotational mode with the reaction coordinate at the transition state on the dominant dynamical pathway.

Intensity-Borrowing Mechanisms Pertinent to Laser Cooling of Linear Polyatomic Molecules

A study of the intensity-borrowing mechanisms important to optical cycling transitions in laser-coolable polyatomic molecules arising from non-adiabatic coupling, contributions beyond the Franck-Condon approximation, and Fermi resonances is reported. It has been shown to be necessary to include non-adiabatic coupling to obtain computational accuracy that is sufficient to be useful for laser cooling of molecules. The predicted vibronic branching ratios using perturbation theory based on the non-adiabatic mechanisms have been demonstrated to agree well with those obtained from variational discrete variable representation calculations for representative molecules including CaOH, SrOH, and YbOH. The electron-correlation and basis-set effects on the calculated transition properties, including the vibronic coupling constants, the spin-orbit coupling matrix elements, and the transition dipole moments, and on the calculated branching ratios have been thoroughly studied. The vibronic branching ratios predicted using the present methodologies demonstrate that RaOH is a promising radioactive molecule candidate for laser cooling.

Universal behavior in complex-mediated reactions: Dynamics of S(1D) + o-D2 → D + SD at low collision energies

Reactive and elastic cross sections and rate coefficients have been calculated for the S(1D) + D2(v = 0, j = 0) reaction using a modified hyperspherical quantum reactive scattering method. The considered collision energy ranges from the ultracold regime, where only one partial wave is open, up to the Langevin regime, where many of them contribute. This work presents the extension of the quantum calculations, which in a previous study were compared with the experimental results, down to energies in the cold and ultracold domains. Results are analyzed and compared with the universal case of the quantum defect theory by Jachymski et al. [Phys. Rev. Lett. 110, 213202 (2013)]. State-to-state integral and differential cross sections are also shown covering the ranges of low-thermal, cold, and ultracold collision energy regimes. It is found that at E/kB < 1 K, there are substantial departures from the expected statistical behavior and that dynamical features become increasingly important with decreasing collision energy, leading to vibrational excitation.

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.

Globally Accurate Gaussian Process Potential Energy Surface and Quantum Dynamics Studies on the Li(2S) + Na2 → LiNa + Na Reaction at Low Collision Energies

The LiNa2 reactive system has recently received great attention in the experimental study of ultracold chemical reactions, but the corresponding theoretical calculations have not been carried out. Here, we report the first globally accurate ground-state LiNa2 potential energy surface (PES) using a Gaussian process model based on only 1776 actively selected high-level ab initio training points. The constructed PES had high precision and strong generalization capability. On the new PES, the quantum dynamics calculations on the Li(2S) + Na2(v = 0, j = 0) → LiNa + Na reaction were carried out in the 0.001–0.01 eV collision energy range using an improved time-dependent wave packet method. The calculated results indicate that this reaction is dominated by a complex-forming mechanism at low collision energies. The presented dynamics data provide guidance for experimental research, and the newly constructed PES could be further used for ultracold reaction dynamics calculations on this reactive system.

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.

Symmetry Breaking in Sticky Collisions between Ultracold Molecules

Ultracold molecules undergo "sticky collisions" that result in loss even for chemically nonreactive molecules. Sticking times can be enhanced by orders of magnitude by interactions that lead to nonconservation of nuclear spin or total angular momentum. We present a quantitative theory of the required strength of such symmetry-breaking interactions based on classical simulation of collision complexes. We find static electric fields as small as 10  V/cm can lead to nonconservation of angular momentum, while we find nuclear spin is conserved during collisions. We also compute loss of collision complexes due to spontaneous emission and absorption of black-body radiation, which are found to be slow.

Internal Electric Field-Induced Formation of Exotic Linear Acetonitrile Chains

The application of external electric and magnetic fields is a powerful tool for aligning molecules in a controlled way, if the thermal fluctuations are small. Here we demonstrate that the same holds for internal electric fields in a molecular cluster. The electric field of a single molecular dipole, HCl, is used to manipulate the aggregation mechanism of subsequently added acetonitrile molecules. As a result, we could form exotic linear acetonitrile (CH₃CN) chains at 0.37 K, as confirmed by infrared spectroscopy in superfluid helium nanodroplets. These linear chains are not observed in the absence of HCl and can be observed only when the internal electric field created by an HCl molecule is present. The accompanying simulations provide mechanistic insights into steric control, explain the selectivity of the process, and show that non-additive electronic polarization effects systematically enhance the dipole moment of these linear chains. Thus, adding more CH₃CN monomers even supports further quasi-linear chain growth.

Resonant Control of Elastic Collisions between ^{23}Na^{40}K Molecules and ^{40}K Atoms

We have demonstrated the resonant control of the elastic scattering cross sections in the vicinity of Feshbach resonances between ^{23}Na^{40}K molecules and ^{40}K atoms by studying the thermalization between them. The elastic scattering cross sections vary by more than 2 orders of magnitude close to the resonance, and can be well described by an asymmetric Fano profile. The parameters that characterize the magnetically tunable s-wave scattering length are determined from the elastic scattering cross sections. The observation of resonantly controlled elastic scattering cross sections opens up the possibility to study strongly interacting atom-molecule mixtures and improve our understanding of the complex atom-molecule Feshbach resonances.

Interaction Potential for NaCs for Ultracold Scattering and Spectroscopy

We obtain the interaction potential for NaCs by fitting to experiments on ultracold scattering and spectroscopy in optical tweezers. The central region of the potential has been accurately determined from Fourier transform spectroscopy at higher temperatures, so we focus on adjusting the long-range and short-range parts. We use coupled-channel calculations of binding energies and wave functions to understand the nature of the molecular states observed in ultracold spectroscopy and of the state that causes the Feshbach resonance used to create ultracold NaCs molecules. We elucidate the relationships between the experimental quantities and features of the interaction potential. We establish the combinations of experimental quantities that determine particular features of the potential. We find that the long-range dispersion coefficient C₆ must be increased by about 0.9% to 3256(1)E_ha₀⁶ to fit the experimental results. We use coupled-channel calculations on the final potential to predict bound-state energies and resonance positions.

Differential Cross Sections for Cold, State-to-State Spin-Orbit Changing Collisions of NO(v = 10) with Neon

Inelastic scattering processes have proven a powerful means of investigating molecular interactions, and much current effort is focused on the cold and ultracold regime where quantum phenomena are clearly manifested. Studies of collisions of the open shell nitric oxide (NO) molecule have been central in this effort since the pioneering work of Houston and co-workers in the early 1990s. State-to-state scattering of vibrationally excited molecules in the cold regime introduces challenges that test the suitability of current theoretical methods for ab initio determination of intermolecular potentials, and concomitant electronically nonadiabatic processes raise the bar further. Here we report measurements of differential cross sections for state-to-state spin-orbit changing collisions of NO (v = 10, Ω″ = 1.5, and j″ = 1.5) with neon from 2.3 to 3.5 cm^-1 collision energy using our recently developed near-copropagating beam technique. The experimental results are compared with those obtained from quantum scattering calculations on a high-level set of coupled cluster potential energy surfaces and are shown to be in good agreement. The theoretical results suggest that distinct backscattering in the 2.3 cm^-1 case arises from overlapping resonances.

Electric-Field-Controlled Cold Dipolar Collisions between Trapped CH_{3}F Molecules

Reaching high densities is a key step toward cold-collision experiments with polyatomic molecules. We use a cryofuge to load up to 2×10^{7} CH_{3}F molecules into a boxlike electric trap, achieving densities up to 10^{7}/cm^{3} at temperatures around 350 mK where the elastic dipolar cross section exceeds 7×10^{-12}  cm^{2}. We measure inelastic rate constants below 4×10^{-8}  cm^{3}/s and control these by tuning a homogeneous electric field that covers a large fraction of the trap volume. Comparison to ab initio calculations gives excellent agreement with dipolar relaxation. Our techniques and findings are generic and immediately relevant for other cold-molecule collision experiments.

A combined experimental and computational study on the transition of the calcium isopropoxide radical as a candidate for direct laser cooling

Vibronically resolved laser-induced fluorescence/dispersed fluorescence (LIF/DF) and cavity ring-down (CRD) spectra of the electronic transition of the calcium isopropoxide [CaOCH(CH₃)₂] radical have been obtained under jet-cooled conditions. An essentially constant energy separation of 68 cm^-1 has been observed for the vibrational ground levels and all fundamental vibrational levels accessed in the LIF measurement. To simulate the experimental spectra and assign the recorded vibronic bands, Franck-Condon (FC) factors and vibrational branching ratios (VBRs) are predicted from vibrational modes and their frequencies calculated using the complete-active-space self-consistent field (CASSCF) and equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) methods. Combined with the calculated electronic transition energy, the computational results, especially those from the EOM-CCSD calculations, reproduced the experimental spectra with considerable accuracy. The experimental and computational results suggest that the FC matrix for the studied electronic transition is largely diagonal, but transitions from the vibrationless levels of the à state to the X̃-state levels of the CCC bending (ν₁₄ and ν₁₅), CaO stretch (ν₁₃), and CaOC asymmetric stretch (ν₉ and ν₁₁) modes also have considerable intensities. Transitions to low-frequency in-plane [ν₁₇(a')] and out-of-plane [ν₃₀(a'')] CaOC bending modes were observed in the experimental LIF/DF spectra, the latter being FC-forbidden but induced by the pseudo-Jahn-Teller (pJT) effect. Both bending modes are coupled to the CaOC asymmetric stretch mode via the Duschinsky rotation, as demonstrated in the DF spectra obtained by pumping non-origin vibronic transitions. The pJT interaction also induces transitions to the ground-state vibrational level of the ν₁₀(a') mode, which has the CaOC bending character. Our combined experimental and computational results provide critical information for future direct laser cooling of the target molecule and other alkaline earth monoalkoxide radicals.

Reactions between layer-resolved molecules mediated by dipolar spin exchange

Microscopic control over polar molecules with tunable interactions enables the realization of distinct quantum phenomena. Using an electric field gradient, we demonstrated layer-resolved state preparation and imaging of ultracold potassium-rubidium molecules confined to two-dimensional planes in an optical lattice. The rotational coherence was maximized by rotating the electric field relative to the light polarization for state-insensitive trapping. Spatially separated molecules in adjacent layers interact through dipolar spin exchange of rotational angular momentum; by adjusting these interactions, we regulated the local chemical reaction rate. The resonance width of the exchange process vastly exceeded the dipolar interaction energy, an effect attributed to thermal energy. This work realized precise control of interacting molecules, enabling electric field microscopy on subwavelength scales and allowing access to unexplored physics in two-dimensional systems.

Control of reactive collisions by quantum interference

In this study, we achieved magnetic control of reactive scattering in an ultracold mixture of ²³Na atoms and ²³Na⁶Li molecules. In most molecular collisions, particles react or are lost near short range with unity probability, leading to the so-called universal rate. By contrast, the Na + NaLi system was shown to have only ~4% loss probability in a fully spin-polarized state. By controlling the phase of the scattering wave function via a Feshbach resonance, we modified the loss rate by more than a factor of 100, from far below to far above the universal limit. The results are explained in analogy with an optical Fabry-Perot resonator by interference of reflections at short and long range. Our work demonstrates quantum control of chemistry by magnetic fields with the full dynamic range predicted by our models.

Stereodynamical Control of Cold Collisions of Polyatomic Molecules with Atoms

Scattering between atomic and/or molecular species can be controlled by manipulating the orientation or alignment of the collision partners. Such stereodynamics is particularly pronounced at cold (∼1 K) collision temperatures because of the presence of resonances. Comparing to the extensively studied atomic and diatomic species, polyatomic molecules with strong steric anisotropy could provide a more sophisticated platform for studying such stereodynamics. Here, we provide the quantum mechanical framework for understanding state-to-state stereodynamics in rotationally inelastic scattering of polyatomic molecules with atoms and apply it to cold collision of oriented H₂O with He on a highly accurate potential energy surface. It is shown that strong stereodynamical control can be achieved near 1 K via shape resonances. Furthermore, quantum interference in scattering of a coherently prepared initial state of the H₂O species is explored, which is shown to be significant.

Quantum control of reactions and collisions at ultralow temperatures

At temperatures close to absolute zero, the molecular reactions and collisions are dominantly governed by quantum mechanics. Remarkable quantum phenomena such as quantum tunneling, quantum threshold behavior, quantum resonances, quantum interference, and quantum statistics are expected to be the main features in ultracold reactions and collisions. Ultracold molecules offer great opportunities and challenges in the study of these intriguing quantum phenomena in molecular processes. In this article, we review the recent progress in the preparation of ultracold molecules and the study of ultracold reactions and collisions using ultracold molecules. We focus on the controlled ultracold chemistry and the scattering resonances at ultralow temperatures. The challenges in understanding the complex ultracold reactions and collisions are also discussed.

The effect of spin-orbit coupling on molecular properties: Potential energy curve, transition dipole moment and laser cooling scheme of NH

The influence of spin-orbit coupling on the cooling of NH molecular laser is investigated based on the ab initio theory. The potential energy curves (PECs) and spectral constants for four Λ-S states (X³Σ^-, a¹Δ, b¹Σ⁺ and A³Π) and eight Ω states [Formula: see text] a¹Δ₂, [Formula: see text] and [Formula: see text] ) of NH molecule are obtained by the multi-reference configuration interaction (MRCI) plus Davidson correction. The spectroscopic constants (R_e, ω_e, ω_eχ_e, B_e, D_e) are obtained by solving the one dimensional radial Schrödinger equation, and the results are almost the same as the previously reported data. In addition, the transition dipole moment, permanent dipole moment, Franck-Condon factors, and radiative lifetime of NH molecule are also acquired. Also, the effects of the intermediate state on the [Formula: see text] , [Formula: see text] and [Formula: see text] transitions are considered. The feasible laser cooling schemes using a single laser are formulated. In the proposed cooling scheme, there wavelengths for the [Formula: see text] are used, the main pump lasers are λ₀₀ = 335.74 nm. The feasible transition is based on this. It is found that spin-orbit coupling has a significant effect on potential energy curves, permanent dipole moments, transition dipole moments and vibration energy levels.

Evidence for the association of triatomic molecules in ultracold 23Na40K + 40K mixtures

Ultracold assembly of diatomic molecules has enabled great advances in controlled chemistry, ultracold chemical physics and quantum simulation with molecules^1-3. Extending the ultracold association to triatomic molecules will offer many new research opportunities and challenges in these fields. A possible approach is to form triatomic molecules in a mixture of ultracold atoms and diatomic molecules by using a Feshbach resonance between them^4,5. Although ultracold atom-diatomic-molecule Feshbach resonances have been observed recently^6,7, using these resonances to form triatomic molecules remains challenging. Here we report on evidence of the association of triatomic molecules near the Feshbach resonance between ²³Na⁴⁰K molecules in the rovibrational ground state and ⁴⁰K atoms. We apply a radio-frequency pulse to drive the free-bound transition in ultracold mixtures of ²³Na⁴⁰K and ⁴⁰K and monitor the loss of ²³Na⁴⁰K molecules. The association of triatomic molecules manifests itself as an additional loss feature in the radio-frequency spectra, which can be distinguished from the atomic loss feature. The observation that the distance between the association feature and the atomic transition changes with the magnetic field provides strong evidence for the formation of triatomic molecules. The binding energy of the triatomic molecules is estimated from the measurements. Our work contributes to the understanding of the complex ultracold atom-molecule Feshbach resonances and may open up an avenue towards the preparation and control of ultracold triatomic molecules.

Theoretical Electronic Structure with a Feasibility Study of Laser Cooling of LaNa Molecule with Spin Orbit Effect

The electronic structure with the spin orbit effect of the molecule LaNa has been studied in the present work using the Multi-Reference Configuration Interaction MRCI calculations including Davidson correction (+Q)....

Bimolecular Chemistry in the Ultracold Regime

Advances in atomic, molecular, and optical physics techniques allowed the cooling of simple molecules down to the ultracold regime ([Formula: see text]1 mK) and opened opportunities to study chemical reactions with unprecedented levels of control. This review covers recent developments in studying bimolecular chemistry at ultralow temperatures. We begin with a brief overview of methods for producing, manipulating, and detecting ultracold molecules. We then survey experimental works that exploit the controllability of ultracold molecules to probe and modify their long-range interactions. Further combining the use of physical chemistry techniques such as mass spectrometry and ion imaging significantly improved the detection of ultracold reactions and enabled explorations of their dynamics in the short range. We discuss a series of studies on the reaction KRb + KRb → K₂ + Rb₂ initiated below 1 [Formula: see text]K, including the direct observation of a long-lived complex, the demonstration of product rotational state control via conserved nuclear spins, and a test of the statistical model using the complete quantum state distribution of the products. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Quantum Wave Packet Treatment of Cold Nonadiabatic Reactive Scattering at the State-To-State Level

Cold and ultracold collisions are dominated by quantum effects, such as resonances, tunneling, and nonadiabatic transitions between different electronic states. Due to the extremely long de Broglie wavelength in such processes, quantum reactive scattering is most conveniently characterized using the time-independent close-coupling (TICC) methods. However, the TICC approach is difficult for systems with a large number of channels because of its steep numerical scaling laws. Here, a recently proposed quantum wave packet (WP) approach for solving adiabatic reactive scattering problems at low collision energies is extended to include nonadiabatic transitions. To impose the outgoing boundary conditions, the total scattering wavefunction is split into three parts, the interaction, the asymptotic, and the long-range regions. Each region is associated with a different set of basis functions, which could be optimized separately. In this way, an extremely long grid can be used to accommodate the characteristic long de Broglie wavelengths in the scattering coordinate. The better numerical scaling laws of the WP approach have the potential for handling larger nonadiabatic reactive systems at low temperatures in the future.

Control of Chemical Reactions through Coherent Excitation of Eigenlevels: A Demonstration via Vibronic Coupling in SO2

Through coherent excitation of a pair of vibronically coupled eigenlevels, an oscillation of 130 kcal/mol in energy excitation between electronic and vibrational motions (on a time scale of 10^-8 s) is created for the triatomic molecule, sulfur dioxide (SO₂). The reactivity of the molecule can be influenced depending upon whether the molecule is vibrationally or electronically excited with this substantial amount of energy. The effect of excitation on reactivity is demonstrated through SO₂ photodissociation as a function of time following coherent excitation, monitored by multiphoton ionization of the SO product.

Probing Photoinduced Two-Body Loss of Ultracold Nonreactive Bosonic ^{23}Na^{87}Rb and ^{23}Na^{39}K Molecules

We probe photoinduced loss for chemically stable bosonic ^{23}Na^{87}Rb and ^{23}Na^{39}K molecules in chopped optical dipole traps, where the molecules spend a significant time in the dark. We expect the effective two-body decay to be significantly suppressed due to the small expected complex lifetimes of about 13 and 6  μs for ^{23}Na^{87}Rb and ^{23}Na^{39}K, respectively. However, instead we do not observe any suppression of the two-body loss in parameter ranges where large loss suppressions are expected. We believe these unexpected results are most probably due to drastic underestimation of the complex lifetime by at least 1-2 orders of magnitude.

Optimizing pulsed-laser ablation production of AlCl molecules for laser cooling

Aluminum monochloride (AlCl) has been proposed as a promising candidate for laser cooling to ultracold temperatures, and recent spectroscopy results support this prediction. It is challenging to produce large numbers of AlCl molecules because it is a highly reactive open-shell molecule and must be generated in situ. Here we show that pulsed-laser ablation of stable, non-toxic mixtures of Al with alkali or alkaline earth chlorides, denoted XCl_n, can provide a robust and reliable source of cold AlCl molecules. Both the chemical identity of XCl_n and the Al : XCl_n molar ratio are varied, and the yield of AlCl is monitored using absorption spectroscopy in a cryogenic gas. For KCl, the production of Al and K atoms was also monitored. We model the AlCl production in the limits of nonequilibrium recombination dominated by first-encounter events. The non-equilibrium model is in agreement with the data and also reproduces the observed trend with different XCl_n precursors. We find that AlCl production is limited by the solid-state densities of Al and Cl atoms and the recondensation of Al atoms in the ablation plume. We suggest future directions for optimizing the production of cold AlCl molecules using laser ablation.

Nonlinear laser-induced frequency shift in a 23Na spin-1 condensate

Herein, we report on the experimental observations and a quantitative determination of the laser-induced frequency shift (LIFS) in the photoassociation (PA) spectra of spinor Bose-Einstein condensate of sodium. Our investigations revealed a nonlinear dependence of the LIFS on the intensity of PA laser. By developing a model within the quadratic Stark effect, we simulate the experimental results via a theoretical model that confirms the former. The experimental observations and the theoretical analysis can further improve the accuracy of investigations on important molecular properties and on preparation of specific molecular states, with possible applications in various key fields.

Velocity-tunable beam of continuously decelerated polar molecules for cold ion-molecule reaction studies

Producing high densities of molecules is a fundamental challenge for low-temperature, ion-molecule reaction studies. Traveling-wave Stark decelerators promise to deliver high density beams of cold, polar molecules but require non-trivial control of high-voltage potentials. We have overcome this experimental challenge and demonstrate continuous deceleration of ND₃ from 385 to 10 m/s, while driving the decelerator electrodes with a 10 kV amplitude sinewave. In addition, we test an alternative slowing scheme, which increases the time delay between decelerated packets of ND₃ and non-decelerated molecules, allowing for better energy resolution of subsequent reaction studies. We characterize this source of neutral, polar molecules suitable for energy-resolved reaction studies with trapped ions at cold translational temperatures. We also propose a combined apparatus consisting of the traveling-wave decelerator and a linear ion trap with a time-of-flight mass spectrometer and discuss to what extent it may achieve cold, energy-resolved, ion-neutral reactions.

Accurate prediction and measurement of vibronic branching ratios for laser cooling linear polyatomic molecules

We report a generally applicable computational and experimental approach to determine vibronic branching ratios in linear polyatomic molecules to the 10^-5 level, including for nominally symmetry-forbidden transitions. These methods are demonstrated in CaOH and YbOH, showing approximately two orders of magnitude improved sensitivity compared with the previous state of the art. Knowledge of branching ratios at this level is needed for the successful deep laser cooling of a broad range of molecular species.

Visible light photonic integrated Brillouin laser

Narrow linewidth visible light lasers are critical for atomic, molecular and optical (AMO) physics including atomic clocks, quantum computing, atomic and molecular spectroscopy, and sensing. Stimulated Brillouin scattering (SBS) is a promising approach to realize highly coherent on-chip visible light laser emission. Here we report demonstration of a visible light photonic integrated Brillouin laser, with emission at 674 nm, a 14.7 mW optical threshold, corresponding to a threshold density of 4.92 mW μm^-2, and a 269 Hz linewidth. Significant advances in visible light silicon nitride/silica all-waveguide resonators are achieved to overcome barriers to SBS in the visible, including 1 dB/meter waveguide losses, 55.4 million quality factor (Q), and measurement of the 25.110 GHz Stokes frequency shift and 290 MHz gain bandwidth. This advancement in integrated ultra-narrow linewidth visible wavelength SBS lasers opens the door to compact quantum and atomic systems and implementation of increasingly complex AMO based physics and experiments.

Full-Dimensional Global Potential Energy Surface for the KRb + KRb → K2Rb2* → K2 + Rb2 Reaction with Accurate Long-Range Interactions and Quantum Statistical Calculation of the Product State Distribution under Ultracold Conditions

A full-dimensional global potential energy surface (PES) for the KRb + KRb → K₂Rb₂* → K₂ + Rb₂ reaction is reported based on high-level ab initio calculations. The short-range part of the PES is fit with the permutationally invariant polynomial-neural network method, while the long-range parts of the PES in both the reactant and product asymptotes are represented by an asymptotically correct form. The long- and short-range parts are connected with intermediate-range parts to make them smooth. Within a statistical quantum model, this PES reproduces both the measured loss rates of ultracold KRb molecules and the K₂ and Rb₂ product state distributions, underscoring the important role of tunneling in ultracold chemistry. The PES also correctly predicts the lifetime of the K₂Rb₂* intermediate complex within the Rice-Ramsperger-Kassel-Marcus limit. It thus provides a reliable platform for future dynamical studies of the prototypical reaction.

Theoretical investigation of laser cooling for BN- anion by ab inito calculation

A theoretical investigation for the feasibility of laser cooling BN^-anion is presented. An ab initio calculation on the three low-lying states Χ²Σ⁺, Α²Π and Β²Σ⁺ are performed at the CASSCF/MRCI + Q level. The calculated spectroscopic constants are in good agreement with the available theoretical and experimental data. Radiative properties including Franck-Condon factor, Einstein coefficients and radiative lifetimes are determined. The calculation shows that the transition B²Σ⁺(v^')↔X²Σ⁺(v^'') has highly diagonal FCFs, especially f₀₀ = 0.9898, and enough short radiative lifetimes. A cooling scheme by three laser beams is proposed, which requires one main pumping laser(λ₀₀ = 474.67 nm) and two repumping lasers (λ₀₁ = 514.64 nm, λ₁₂= 514.90 nm). The population dynamics of cooling is investigated with the rate equation approach. The simulation demonstrates that the population does not remain trapped within the intermediate Α²Π state. The resultant scattered photons are about2.5×10⁴, which is expected to stop BN^-anion molecule in a cryogenic beam theoretically.

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{23}\hbox {Na}^{87}$$\end{document}23Na87Rb 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Na}_2$$\end{document}Na2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Rb}_2$$\end{document}Rb2 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Na}_2\hbox {Rb}_2$$\end{document}Na2Rb2 complex is quickly destroyed and thus that the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{23}\hbox {Na}^{87}$$\end{document}23Na87Rb molecules are rapidly lost.

Precision test of statistical dynamics with state-to-state ultracold chemistry

Chemical reactions represent a class of quantum problems that challenge both the current theoretical understanding and computational capabilities¹. Reactions that occur at ultralow temperatures provide an ideal testing ground for quantum chemistry and scattering theories, because they can be experimentally studied with unprecedented control², yet display dynamics that are highly complex³. Here we report the full product state distribution for the reaction 2KRb → K₂ + Rb₂. Ultracold preparation of the reactants allows us complete control over their initial quantum degrees of freedom, whereas state-resolved, coincident detection of both products enables the probability of scattering into each of the 57 allowed rotational state-pairs to be measured. Our results show an overall agreement with a state-counting model based on statistical theory^4-6, but also reveal several deviating state-pairs. In particular, we observe a strong suppression of population in the state-pair closest to the exoergicity limit as a result of the long-range potential inhibiting the escape of products. The completeness of our measurements provides a benchmark for quantum dynamics calculations beyond the current state of the art.

Accurate semiempirical potential energy curves for the a3Σ+-state of NaCs, KCs, and RbCs

A five parameter semiempirical Tang-Toennies type model is used to describe the potential curves of the a³Σ⁺-state of the heteronuclear polar molecules NaCs, KCs, and RbCs. These molecules are of current interest in experiments at ultra-cold conditions to explore the effects of the strong dipole-dipole forces on the collective many-body quantum behavior. New quantum phenomena are also anticipated in systems consisting of atomic species with different fermion/boson statistics. The model parameters are obtained by simultaneously fitting all five of the parameters to the extensive LIF-Fourier transform spectroscopy published by Tiemann and collaborators [e.g., Docenko et al. J. Phys. B: At., Mol. Opt. Phys. 39, S929-S943 (2006)], who also report best fit potential curves. Although the new potentials are in good agreement with the earlier potentials, they have the advantage that they are continuous over the entire range of internuclear distances and have the correct long-range behavior. The scattering lengths for all isotope combinations show good agreement with dedicated experiments where available. The new potentials are also in excellent agreement with combining rules based on the potentials of the homonuclear systems.

Collisions between Ultracold Molecules and Atoms in a Magnetic Trap

We prepare mixtures of ultracold CaF molecules and Rb atoms in a magnetic trap and study their inelastic collisions. When the atoms are prepared in the spin-stretched state and the molecules in the spin-stretched component of the first rotationally excited state, they collide inelastically with a rate coefficient k_{2}=(6.6±1.5)×10^{-11}  cm^{3}/s at temperatures near 100  μK. We attribute this to rotation-changing collisions. When the molecules are in the ground rotational state we see no inelastic loss and set an upper bound on the spin-relaxation rate coefficient of k_{2}<5.8×10^{-12}  cm^{3}/s with 95% confidence. We compare these measurements to the results of a single-channel loss model based on quantum defect theory. The comparison suggests a short-range loss parameter close to unity for rotationally excited molecules, but below 0.04 for molecules in the rotational ground state.