The Buffer Gas Beam: An Intense, Cold, and Slow Source for Atoms and Molecules

Blue-Detuned Magneto-optical Trap of CaF Molecules

A key method to produce trapped and laser-cooled molecules is the magneto-optical trap (MOT), which is conventionally created using light red detuned from an optical transition. In this work, we report a MOT for CaF molecules created using blue-detuned light. The blue-detuned MOT (BDM) achieves temperatures well below the Doppler limit and provides the highest densities and phase-space densities reported to date in CaF MOTs. Our results suggest that BDMs are likely achievable in many relatively light molecules including polyatomic ones, but our measurements suggest that BDMs will be challenging to realize in substantially heavier molecules due to sub-mK trap depths. In addition to record temperatures and densities, we find that the BDM substantially simplifies and enhances the loading of molecules into optical tweezer arrays, which are a promising platform for quantum simulation and quantum information processing. Notably, the BDM reduces molecular number requirements ninefold compared to a conventional red-detuned MOT, while not requiring additional hardware. Our work therefore substantially simplifies preparing large-scale molecular tweezer arrays, which are a novel platform for simulation of quantum many-body dynamics and quantum information processing with molecular qubits.

Direct Laser Cooling of Rydberg Atoms with an Isolated-Core Transition

We propose a scheme to directly laser cool Rydberg atoms by laser cooling the residual ion core within the Rydberg-electron orbit. The scheme is detailed for alkaline-earth-metal Rydberg atoms, whose ions can be easily laser cooled. We demonstrate that a closed optical cooling cycle can be found despite the perturbations caused by the Rydberg electron and that this cycle can be driven over more than 100  μs to achieve laser cooling. The cooling dynamics with and without the presence of magnetic fields are discussed in detail.

Ultracold field-linked tetratomic molecules

Ultracold polyatomic molecules offer opportunities1 in cold chemistry2,3, precision measurements4 and quantum information processing5,6, because of their rich internal structure. However, their increased complexity compared with diatomic molecules presents a challenge in using conventional cooling techniques. Here we demonstrate an approach to create weakly bound ultracold polyatomic molecules by electroassociation7 (F.D. et al., manuscript in preparation) in a degenerate Fermi gas of microwave-dressed polar molecules through a field-linked resonance8-11. Starting from ground-state NaK molecules, we create around 1.1 × 103 weakly bound tetratomic (NaK)2 molecules, with a phase space density of 0.040(3) at a temperature of 134(3) nK, more than 3,000 times colder than previously realized tetratomic molecules12. We observe a maximum tetramer lifetime of 8(2) ms in free space without a notable change in the presence of an optical dipole trap, indicating that these tetramers are collisionally stable. Moreover, we directly image the dissociated tetramers through microwave-field modulation to probe the anisotropy of their wavefunction in momentum space. Our result demonstrates a universal tool for assembling weakly bound ultracold polyatomic molecules from smaller polar molecules, which is a crucial step towards Bose-Einstein condensation of polyatomic molecules and towards a new crossover from a dipolar Bardeen-Cooper-Schrieffer superfluid13-15 to a Bose-Einstein condensation of tetramers. Moreover, the long-lived field-linked state provides an ideal starting point for deterministic optical transfer to deeply bound tetramer states16-18.

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.

Sympathetic Cooling and Slowing of Molecules with Rydberg Atoms

We propose to sympathetically slow and cool polar molecules in a cold, low-density beam using laser-cooled Rydberg atoms. The elastic collision cross sections between molecules and Rydberg atoms are large enough to efficiently thermalize the molecules even in a low-density environment. Molecules traveling at 100  m/s can be stopped in under 30 collisions with little inelastic loss. Our method does not require photon scattering from the molecules and can be generically applied to complex species for applications in precision measurement, quantum information science, and controlled chemistry.

Relativistic coupled-cluster calculations of RaOH pertinent to spectroscopic detection and laser cooling

A relativistic coupled-cluster study of the low-lying electronic states in the radium monohydroxide molecule (RaOH), a radioactive polyatomic molecule of interest to laser cooling and to the search of new physics beyond the Standard Model, is reported. The level positions of the A2Π1/2 and C2Σ states have been computed with an accuracy of around 200 cm-1 to facilitate spectroscopic observation of RaOH using laser induced fluorescence spectroscopy, thereby exploiting the systematic convergence of electron-correlation and basis-set effects in relativistic coupled-cluster calculations. The energy level for the B2Δ3/2 state has also been calculated accurately to conclude that the B2Δ3/2 state lies above the A2Π1/2 state. This confirms X2Σ ↔ A2Π1/2 as a promising optical cycling transition for laser cooling RaOH.

Chiral molecule candidates for trapped ion spectroscopy by ab initio calculations: From state preparation to parity violation

Parity non-conservation (PNC) due to the weak interaction is predicted to give rise to enantiomer dependent vibrational constants in chiral molecules, but the phenomenon has so far eluded experimental observation. The enhanced sensitivity of molecules to physics beyond the Standard Model (BSM) has led to substantial advances in molecular precision spectroscopy, and these may be applied to PNC searches as well. Specifically, trapped molecular ion experiments leverage the universality of trapping charged particles to optimize the molecular ion species studied toward BSM searches, but in searches for PNC, only a few chiral molecular ion candidates have been proposed so far. Importantly, viable candidates need to be internally cold, and their internal state populations should be detectable with high quantum efficiency. To this end, we focus on molecular ions that can be created by near threshold resonant two-photon ionization and detected via state-selective photo-dissociation. Such candidates need to be stable in both charged and neutral chiral versions to be amenable to these methods. Here, we present a collection of suitable chiral molecular ion candidates we have found, including CHDBrI+ and CHCaBrI+, that fulfill these conditions according to our ab initio calculations. We find that organo-metallic species have low ionization energy as neutrals and relatively high dissociation thresholds. Finally, we compute the magnitude of the PNC values for vibrational transitions for some of these candidates. An experimental demonstration of state preparation and readout for these candidates will be an important milestone toward measuring PNC in chiral molecules for the first time.

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.

Bichromatic Imaging of Single Molecules in an Optical Tweezer Array

We report on a novel bichromatic fluorescent imaging scheme for background-free detection of single CaF molecules trapped in an optical tweezer array. By collecting fluorescence on one optical transition while using another for laser cooling, we achieve an imaging fidelity of 97.7(2)% and a nondestructive detection fidelity of 95.5(6)%. Notably, these fidelities are achieved with a modest photon budget, suggesting that the method could be extended to more complex laser-coolable molecules with less favorable optical cycling properties. We also report on a framework and new methods to characterize various loss mechanisms that occur generally during fluorescent detection of trapped molecules, including two-photon decay and admixtures of higher excited states that are induced by the trapping light. In particular, we develop a novel method to dispersively measure transition matrix elements between electronically excited states. The method could also be used to measure arbitrarily small Franck-Condon factors between electronically excited states, which could significantly aid in ongoing efforts to laser cool complex polyatomic molecules.

Nonresonant cavity for multipass laser intensity buildup

A nonresonant cavity to build up laser intensity is modeled, developed, and tested. It can be used for overlapping multiple lasers of different wavelengths, increasing their intensities by more than an order of magnitude while maintaining good uniformity. It is simple to set up, has flexible optical characteristics, and is robust against perturbations. The intensity buildup requires no resonances, and the wavelength dependence of the performance is limited only by the mirror coatings. The cavity can be used, for example, in applications requiring a spatially constrained intensity buildup, such as in atomic and molecular traps.

Low-Temperature Gas-Phase Kinetics of Ethanol-Methanol Heterodimer Formation

The structures of gas-phase noncovalently bound clusters have long been studied in supersonic expansions. This method of study, while providing a wealth of information about the nature of noncovalent bonds, precludes observation of the formation of the cluster, as the clusters form just after the orifice of the pulsed valve. Here, we directly observe formation of ethanol-methanol dimers via microwave spectroscopy in a controlled cryogenic environment. Time profiles of the concentration of reagents in the cell yielded gas-phase reaction rate constants of k_Me-g = (2.8 ± 1.4) × 10^-13 cm³ molecule^-1 s^-1 and k_Me-t = (1.6 ± 0.8) × 10^-13 cm³ molecule^-1 s^-1 for the pseudo-second-order ethanol-methanol dimerization reaction at 8 K. The relaxation cross section between the gauche and trans conformers of ethanol was also measured using the same technique. In addition, thermodynamic relaxation between conformers of ethanol over time allowed for selection of conformer stoichiometry in the ethanol-methanol dimerization reaction, but no change in the ratio of dimer conformers was observed with changing ethanol monomer stoichiometry.

Optical Trapping of a Polyatomic Molecule in an ℓ-Type Parity Doublet State

We report optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). CaOH molecules from a magneto-optical trap are sub-Doppler laser cooled to 20(3)  μK in free space and loaded into an optical dipole trap. We attain an in-trap molecule number density of 3(1)×10^{9}  cm^{-3} at a temperature of 57(8)  μK. Trapped CaOH molecules are optically pumped into an excited vibrational bending mode, whose ℓ-type parity doublet structure is a potential resource for a wide range of proposed quantum science applications with polyatomic molecules. We measure the spontaneous, radiative lifetime of this bending mode state to be ∼0.7  s.

High-sensitivity low-noise photodetector using a large-area silicon photomultiplier

The application of silicon photomultiplier (SiPM) technology for weak-light detection at a single photon level has expanded thanks to its better photon detection efficiency in comparison to a conventional photomultiplier tube (PMT). SiPMs with large detection area have recently become commercially available, enabling applications where the photon flux is low both temporarily and spatially. On the other hand, several drawbacks exist in the usage of SiPMs such as a higher dark count rate, many readout channels, slow response time, and optical crosstalk; therefore, users need to carefully consider the trade-offs. This work presents a SiPM-embedded compact large-area photon detection module. Various techniques are adopted to overcome the disadvantages of SiPMs so that it can be generally utilized as an upgrade from a PMT. A simple cooling component and recently developed optical crosstalk suppression method are adopted to reduce the noise which is more serious for larger-area SiPMs. A dedicated readout circuit increases the response frequency and reduces the number of readout channels. We favorably compare this design with a conventional PMT and obtain both higher photon detection efficiency and larger-area acceptance.

Laser Spectroscopy of Aromatic Molecules with Optical Cycling Centers: Strontium(I) Phenoxides

We report the production and spectroscopic characterization of strontium(I) phenoxide (SrOC₆H₅ or SrOPh) and variants featuring electron-withdrawing groups designed to suppress vibrational excitation during spontaneous emission from the electronically excited state. Optical cycling closure of these species, which is the decoupling of the vibrational state changes from spontaneous optical decay, is found by dispersed laser-induced fluorescence spectroscopy to be high, in accordance with theoretical predictions. A high-resolution, rotationally resolved laser excitation spectrum is recorded for SrOPh, allowing the estimation of spectroscopic constants and identification of candidate optical cycling transitions for future work. The results confirm the promise of strontium phenoxides for laser cooling and quantum state detection at the single-molecule level.

High-resolution spectroscopy of buffer-gas-cooled phthalocyanine

For over five decades, studies in the field of chemical physics and physical chemistry have primarily aimed to understand the quantum properties of molecules. However, high-resolution rovibronic spectroscopy has been limited to relatively small and simple systems because translationally and rotationally cold samples have not been prepared in sufficiently large quantities for large and complex systems. In this study, we present high-resolution rovibronic spectroscopy results for large gas-phase molecules, namely, free-base phthalocya-nine (FBPc). The findings suggest that buffer-gas cooling may be effective for large molecules introduced via laser ablation. High-resolution electronic spectroscopy, combined with other experimental and theoretical studies, will be useful in understanding the quantum properties of molecules. These findings also serve as a guide for quantum chemical calculations of large molecules.

Absolute frequency metrology of buffer-gas-cooled molecular spectra at 1 kHz accuracy level

By reducing both the internal and translational temperature of any species down to a few kelvins, the buffer-gas-cooling (BGC) technique has the potential to dramatically improve the quality of ro-vibrational molecular spectra, thus offering unique opportunities for transition frequency measurements with unprecedented accuracy. However, the difficulty in integrating metrological-grade spectroscopic tools into bulky cryogenic equipment has hitherto prevented from approaching the kHz level even in the best cases. Here, we overcome this drawback by an original opto-mechanical scheme which, effectively coupling a Lamb-dip saturated-absorption cavity ring-down spectrometer to a BGC source, allows us to determine the absolute frequency of the acetylene (ν1 + ν3) R(1)e transition at 6561.0941 cm−1 with a fractional uncertainty as low as 6 × 10−12. By improving the previous record with buffer-gas-cooled molecules by one order of magnitude, our approach paves the way for a number of ultra-precise low-temperature spectroscopic studies, aimed at both fundamental Physics tests and optimized laser cooling strategies.

The chemistry of AlF and CaF production in buffer gas sources

In this work, we explore the role of chemical reactions on the properties of buffer gas cooled molecular beams. In particular, we focus on scenarios relevant to the formation of AlF and CaF via chemical reactions between the Ca and Al atoms ablated from a solid target in an atmosphere of a fluorine-containing gas, in this case, SF6 and NF3. Reactions are studied following an ab initio molecular dynamics approach, and the results are rationalized following a tree-shaped reaction model based on Bayesian inference. We find that NF3 reacts more efficiently with hot metal atoms to form monofluoride molecules than SF6. In addition, when using NF3, the reaction products have lower kinetic energy, requiring fewer collisions to thermalize with the cryogenic helium. Furthermore, we find that the reaction probability for AlF formation is much higher than for CaF across a broad range of temperatures.

Functionalizing aromatic compounds with optical cycling centres

Molecular design principles provide guidelines for augmenting a molecule with a smaller group of atoms to realize a desired property or function. We demonstrate that these concepts can be used to create an optical cycling centre, the Ca(I)-O unit, that can be attached to a number of aromatic ligands, enabling the scattering of many photons from the resulting molecules without changing the molecular vibrational state. Such capability plays a central role in quantum state preparation and measurement, as well as laser cooling and trapping, and is therefore a prerequisite for many quantum science and technology applications. We provide further molecular design principles that indicate the ability to optimize and expand this work to an even broader class of molecules. This represents a great step towards a quantum functional group, which may serve as a generic qubit moiety that can be attached to a wide range of molecular structures and surfaces.

Rotational Cooling Effect on the Rate Constant in the CH3F + Ca+ Reaction at Low Collision Energies

The rotational cooling effect on the reaction rate constant of the gas-phase ion-polar-molecule reaction CH₃F + Ca⁺ → CH₃ + CaF⁺ was experimentally studied at low collision energies. Fluoromethane molecules showed higher reactivity as the rotational temperature decreased. The experimental rate constants were compared with the capture rate constants which were obtained by the Perturbed Rotational State (PRS) theory assuming the rotational level distribution corresponding to the experimental conditions. The PRS result shows a strong dependence of the capture rate constants on the rotational level distribution in accordance with the experimental findings. However, the PRS capture rate constants deviate from the measurement values as the average collision energy increases especially when the fluoromethane molecules are rotationally cooled far below room temperature. The present paper suggests that the rotational state distribution significantly affects the rate constants of ion-polar-molecule reactions and is one of the important issues to be considered in the study of molecular synthesis in the interstellar medium, where the thermal equilibrium is not necessarily established.

Single-Color Isomer-Resolved Spectroscopy

Structural isomers, such as conformers or tautomers, are of significant importance across chemistry and biology, as they can have different functionalities. In gas-phase experiments using molecular beams, formation of many different isomers cannot be prevented, and their presence significantly complicates the assignment of spectral lines. Current isomer-resolved spectroscopic techniques heavily rely on theoretical calculations or make use of elaborate double-resonance schemes. We show here that isomer-resolved spectroscopy can also be performed using a single tunable laser. In particular, we demonstrate single-color isomer-resolved spectroscopy by utilizing electrostatic deflection to spatially separate the isomers. We show that for 3-aminophenol we can spatially separate the syn and anti conformers and use these pure samples to perform high-resolution REMPI spectroscopy, making the assignment of transitions to a particular isomer trivial, without any additional a priori information. This approach allows one to add isomer specificity to any molecular-beam-based experiment.

Magneto-optical trapping and sub-Doppler cooling of a polyatomic molecule

Laser cooling and trapping^1,2, and magneto-optical trapping methods in particular², have enabled groundbreaking advances in science, including Bose-Einstein condensation^3-5, quantum computation with neutral atoms^6,7 and high-precision optical clocks⁸. Recently, magneto-optical traps (MOTs) of diatomic molecules have been demonstrated^9-12, providing access to research in quantum simulation¹³ and searches for physics beyond the standard model¹⁴. Compared with diatomic molecules, polyatomic molecules have distinct rotational and vibrational degrees of freedom that promise a variety of transformational possibilities. For example, ultracold polyatomic molecules would be uniquely suited to applications in quantum computation and simulation^15-17, ultracold collisions¹⁸, quantum chemistry¹⁹ and beyond-the-standard-model searches^20,21. However, the complexity of these molecules has so far precluded the realization of MOTs for polyatomic species. Here we demonstrate magneto-optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). After trapping, the molecules are laser cooled in a blue-detuned optical molasses to a temperature of 110 μK, which is below the Doppler cooling limit. The temperatures and densities achieved here make CaOH a viable candidate for a wide variety of quantum science applications, including quantum simulation and computation using optical tweezer arrays^15,17,22,23. This work also suggests that laser cooling and magneto-optical trapping of many other polyatomic species^24-27 will be both feasible and practical.

Molecular Laser Cooling in a Dynamically Tunable Repulsive Optical Trap

Recent work with laser-cooled molecules in attractive optical traps has shown that the differential ac Stark shifts arising from the trap light itself can become problematic, limiting collisional shielding efficiencies, rotational coherence times, and laser-cooling temperatures. In this Letter, we explore trapping and laser cooling of CaF molecules in a ring-shaped repulsive optical trap. The observed dependences of loss rates on temperature and barrier height show characteristic behavior of repulsive traps and indicate strongly suppressed average ac Stark shifts. Within the trap, we find that Λ-enhanced gray molasses cooling is effective, producing similar minimum temperatures as those obtained in free space. By combining in-trap laser cooling with dynamical reshaping of the trap, we also present a method that allows highly efficient and rapid transfer from molecular magneto-optical traps into conventional attractive optical traps, which has been an outstanding challenge for experiments to date. Notably, our method could allow nearly lossless transfer over millisecond timescales.

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 theoretical study on laser cooling feasibility of XH (X = As, Sb and Bi): effects of intersystem crossings and spin-orbit couplings

We investigate the low-lying electronic states and feasibility of direct laser cooling of AsH, SbH and BiH by means of the highly accurate ab initio and dynamical methods with the inclusion of the spin-orbit coupling effects. Twelve low-lying Ω states for each of them are computed using the internally contracted multireference configuration interaction method. Our computed spectroscopic constants are in excellent agreement with the available experimental data. The calculated spin-orbit matrix elements are large enough, and thus the intersystem crossings from the A³Π state and the transitions to the a¹Δ₂ state should be considered in laser cooling. We find that, from AsH to BiH, the location of the crossing point between the A³Π and ⁵Σ^- states moves down towards the ground vibrational level of A³Π along with enhanced spin-orbit coupling effects, which increases the difficulty of laser cooling heavier hydrides. An empirical law of "crossing point shifting down" down a group in the periodic table is generalized, which may become a helpful caveat when cooling diatomic molecules containing heavier elements. By choosing specific spin-orbit states, we construct feasible laser cooling schemes for AsH and SbH based on the A³Π₂ → X³Σ-1 transitions, which feature very large vibrational branching ratios R₀₀ (AsH: 0.9662; SbH: 0.9248) and short radiative lifetimes (AsH: 914 ns; SbH: 883 ns). In particular, a constructed laser cooling scheme for AsH is able to scatter 1.24 × 10⁴ photons, whereas that for SbH can scatter 8.60 × 10³ photons, which are enough to cool AsH and SbH to the ultracold regime. The present work demonstrates the importance of intersystem crossings and spin-orbit couplings in molecular laser cooling.

A variable time step self-consistent mean field DSMC model for three-dimensional environments

A self-consistent mean field direct simulation Monte Carlo (SCMFD) algorithm was recently proposed for simulating collision environments for a range of one-dimensional model systems. This work extends the one-dimensional SCMFD approach to three dimensions and introduces a variable time step (3D-vt-SCMFD), enabling the modeling of a considerably wider range of different collision environments. We demonstrate the performance of the augmented method by modeling a varied set of test systems: ideal gas mixtures, Poiseuille flow of argon, and expansion of gas into high vacuum. For the gas mixtures, the 3D-vt-SCMFD method reproduces the properties (mean free path, mean free time, collision frequency, and temperature) in excellent agreement with theoretical predictions. From the Poiseuille flow simulations, we extract flow profiles that agree with the solution to the Navier-Stokes equations in the high-density limit and resemble free molecular flow at low densities, as expected. The measured viscosity from 3D-vt-SCMF is ∼15% lower than the theoretical prediction from Chapman-Enskog theory. The expansion of gas into vacuum is examined in the effusive regime and at the hydrodynamic limit. In both cases, 3D-vt-SCMDF simulations produce gas beam density, velocity, and temperature profiles in excellent agreement with analytical models. In summary, our tests show that 3D-vt-SCMFD is robust and computationally efficient, while also illustrating the diversity of systems the SCMFD model can be successfully applied to.

Sub-Hz Differential Rotational Spectroscopy of Enantiomers

We demonstrate for the first time high-precision differential microwave spectroscopy, achieving sub-Hz precision by coupling a cryogenic buffer gas cell with a tunable microwave Fabry–Perot cavity. We report statistically limited sub-Hz precision of (0.08 ± 0.72) Hz, observed between enantiopure samples of (R)-1,2-propanediol and (S)-1,2-propanediol at frequencies near 15 GHz. We confirm highly repeatable spectroscopic measurements compared to traditional pulsed-jet methods, opening up new capabilities in probing subtle molecular structural effects at the 10−10 level and providing a platform for exploring sources of systematic error in parity-violation searches. We discuss dominant systematic effects at this level and propose possible extensions of the technique for higher precision.

Zeeman-Sisyphus Deceleration of Molecular Beams

We present a robust, continuous molecular decelerator that employs high magnetic fields and few optical pumping steps. CaOH molecules are slowed, accumulating at low velocities in a range sufficient for loading both magnetic and magneto-optical traps. During the slowing, the molecules scatter only seven photons, removing around 8 K of energy. Because large energies can be removed with only a few spontaneous radiative decays, this method can in principle be applied to nearly any paramagnetic atomic or molecular species, opening a general path to trapping of complex molecules.

On the Feasibility of Rovibrational Laser Cooling of Radioactive RaF+ and RaH+ Cations

Polar radioactive molecules have been suggested to be exceptionally sensitive systems in the search for signatures of symmetry-violating effects in their structure. Radium monofluoride (RaF) possesses an especially attractive electronic structure for such searches, as the diagonality of its Franck-Condon matrix enables the implementation of direct laser cooling for precision experiments. To maximize the sensitivity of experiments with short-lived RaF isotopologues, the molecular beam needs to be cooled to the rovibrational ground state. Due to the high kinetic energies and internal temperature of extracted beams at radioactive ion beam (RIB) facilities, in-flight rovibrational cooling would be restricted by a limited interaction timescale. Instead, cooling techniques implemented on ions trapped within a radiofrequency quadrupole cooler-buncher can be highly efficient due to the much longer interaction times (up to seconds). In this work, the feasibility of rovibrationally cooling trapped RaF+ and RaH+ cations with repeated laser excitation is investigated. Due to the highly diagonal nature between the ionic ground state and states in the neutral system, any reduction of the internal temperature of the molecular ions would largely persist through charge-exchange without requiring the use of cryogenic buffer gas cooling. Quasirelativistic X2C and scalar-relativistic ECP calculations were performed to calculate the transition energies to excited electronic states and to study the nature of chemical bonding for both RaF+ and RaH+. The results indicate that optical manipulation of the rovibrational distribution of trapped RaF+ and RaH+ is unfeasible due to the high electronic transition energies, which lie beyond the capabilities of modern laser technology. However, more detailed calculations of the structure of RaH+ might reveal possible laser-cooling pathways.

Deceleration and Trapping of SrF Molecules

We report on the electrostatic trapping of neutral SrF molecules. The molecules are captured from a cryogenic buffer-gas beam source into the moving traps of a 4.5-m-long traveling-wave Stark decelerator. The SrF molecules in X^{2}Σ^{+}(v=0,N=1) state are brought to rest as the velocity of the moving traps is gradually reduced from 190  m/s to zero. The molecules are held for up to 50 ms in multiple electric traps of the decelerator. The trapped packets have a volume (FWHM) of 1  mm^{3} and a velocity spread of 5(1)  m/s, which corresponds to a temperature of 60(20) mK. Our result demonstrates a factor 3 increase in the molecular mass that has been Stark decelerated and trapped. Heavy molecules (mass>100  amu) offer a highly increased sensitivity to probe physics beyond the standard model. This work significantly extends the species of neutral molecules of which slow beams can be created for collision studies, precision measurement, and trapping experiments.

Polarization Enhanced Deep Optical Dipole Trapping of Λ-Cooled Polar Molecules

We demonstrate loading of SrF molecules into an optical dipole trap (ODT) via in-trap Λ-enhanced gray molasses cooling. We find that this cooling can be optimized by a proper choice of relative ODT and cooling beam polarizations. In this optimized configuration, we observe molecules with temperatures as low as 14(1)  μK in traps with depths up to 570  μK. With optimized parameters, we transfer ∼5% of molecules from our radio-frequency magneto-optical trap into the ODT, at a density of ∼2×10^{9}  cm^{-3}, a phase space density of ∼2×10^{-7}, and with a trap lifetime of ∼1  s.

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.

Entanglement-Assisted Quantum Chiral Spectroscopy

The most important problem of spectroscopic chiral analysis is the enantioselective effects of the light-molecule interactions are inherently weak and severely reduced by the environment noises. Enormous efforts had been spent to overcome this problem by enhancing the symmetry break in the light-molecule interactions or reducing the environment noises. Here, we propose an alternative way to solve this problem by using frequency-entangled two-photon pairs as probe signals and detecting them in coincidence, i.e., using quantum chiral spectroscopy. For this purpose, we develop the theory of entanglement-assisted quantum chiral spectroscopy. Our results show that the quantum spectra of the left- and right-handed molecules are always distinguishable by suitably configuring the frequency-entangled two-photon pairs. In contrast, the classical spectra of the two enantiomers, where the broadband signal photon is frequency-uncorrelated with the idle one, become indistinguishable in the strong dissipation region. This offers our quantum chiral spectroscopy a great advantage over the classical chiral spectroscopy. Our work opens up an exciting area that exploring profound advantages of the quantum spectroscopy in chiral analysis.

Fine and hyperfine interactions in 171YbOH and 173YbOH

The odd isotopologues of ytterbium monohydroxide, ^171,173YbOH, have been identified as promising molecules to measure parity (P) and time reversal (T) violating physics. Here, we characterize the òΠ_1/2(0,0,0)-X̃²Σ⁺(0,0,0) band near 577 nm for these odd isotopologues. Both laser-induced fluorescence excitation spectra of a supersonic molecular beam sample and absorption spectra of a cryogenic buffer-gas cooled sample were recorded. In addition, a novel spectroscopic technique based on laser-enhanced chemical reactions is demonstrated and used in absorption measurements. This technique is especially powerful for disentangling congested spectra. An effective Hamiltonian model is used to extract the fine and hyperfine parameters for the òΠ_1/2(0,0,0) and X̃²Σ⁺(0,0,0) states. A comparison of the determined X̃²Σ⁺(0,0,0) hyperfine parameters with recently predicted values [Denis et al., J. Chem. Phys. 152, 084303 (2020); K. Gaul and R. Berger, Phys. Rev. A 101, 012508 (2020); and Liu et al., J. Chem. Phys. 154,064110 (2021)] is made. The measured hyperfine parameters provide experimental confirmation of the computational methods used to compute the P,T-violating coupling constants W_d and W_M, which correlate P,T-violating physics to P,T-violating energy shifts in the molecule. The dependence of the fine and hyperfine parameters of the òΠ_1/2(0,0,0) and X̃²Σ⁺(0,0,0) states for all isotopologues of YbOH are discussed, and a comparison to isoelectronic YbF is made.

Frequency-doubled Nd:YAG MOPA laser system with programmable rectangular pulses up to 200 microseconds

A compact frequency-doubled diode-pumped Nd:YAG master-oscillator power-amplifier laser system with programmable microsecond pulse length has been developed. Analog pulse shaping of the output from a single-frequency continuous-wave Nd:YAG oscillator, and subsequent amplification, allowed the generation of rectangular pulses with pulse lengths on the order of the Nd:YAG fluorescence lifetime. Temporally flat-top pulses of 1064 nm light with 520 mJ pulse energy, 2.6 kW peak power, and 200 μs duration, with linewidth below 10 kHz, were obtained at a repetition rate of 2 Hz. Second harmonic generation in a LBO crystal yielded pulses of 262 mJ and 1.3 kW peak power at 532 nm. The peak power can be maintained within 2.9% over the duration of the laser pulse, and long-term intensity stability of 1.1% was observed. The spatially flat-top beam at 1064 nm used in the amplifier is converted to a Gaussian beam at 532 nm with beam quality factor M² = 1.41(14) during the second harmonic generation. This system has potential as a pump source for Ti:sapphire, dye, or optical parametric amplifiers to generate tunable high-power single-frequency radiation for applications in precision measurements and laser slowing.

Mechanistic Insights into Ultracold Chemical Reactions under the Control of the Geometric Phase

Ultracold chemical reactions involve collision temperatures approaching absolute zero, and for molecular systems that exhibit a barrierless and exoergic reaction path significant reactivity can occur. In addition, many molecules contain a conical intersection, and the associated geometric phase has been shown to significantly alter the outcome of ultracold reactions. Here we report a quantum dynamics study for the ultracold O + OH → H + O₂ reaction. An analysis of the scattering wave functions reveals explicitly the nature of the quantum interference between the direct and looping reaction pathways around the conical intersection and thus illustrates how the reaction proceeds under the control of the geometric phase for the first time. The wave function analysis should generalize to other ultracold reactions that contain a conical intersection. Our findings indicate that quantum control techniques such as an optical lattice trap or the initial state orientation may be effective in controlling the reactivity.

A supersonic laser ablation beam source with narrow velocity spreads

A supersonic beam source for SrF and BaF molecules is constructed by combining the expansion of carrier gas (a mixture of 2% SF₆ and 98% argon) from an Even-Lavie valve with laser ablation of a barium/strontium metal target at a repetition rate of 10 Hz. Molecular beams with a narrow translational velocity spread are produced at relative values of Δv/v = 0.053(11) and 0.054(9) for SrF and BaF, respectively. The relative velocity spread of the beams produced in our source is lower in comparison with the results from other metal fluoride beams produced in supersonic laser ablation sources. The rotational temperature of BaF is measured to be 3.5 K. The source produces 6 × 10⁸ and 10⁷ molecules per steradian per pulse in the X²Σ⁺ (ν = 0, N = 1) state of BaF and SrF molecules, respectively, a state amenable to Stark deceleration and laser cooling.

Study of HgOH to Assess Its Suitability for Electron Electric Dipole Moment Searches

In search of suitable molecular candidates for probing the electric dipole moment (EDM) of the electron (de), a property that arises due to parity and time-reversal violating (P,T-odd) interactions, we consider the triatomic mercury hydroxide (HgOH) molecule. The impetus for this proposal is based on previous works on two systems: the recently proposed ytterbium hydroxide (YbOH) experiment that demonstrates the advantages of polyatomics for such EDM searches, and the finding that mercury halides provide the highest enhancement due to de compared to other diatomic molecules. We identify the ground state of HgOH as being in a bent geometry, and show that its intrinsic EDM sensitivity is comparable to the corresponding value for YbOH. Along with the theoretical results, we discuss plausible experimental schemes for an EDM measurement in HgOH. Furthermore, we provide pilot calculations of the EDM sensitivity for de for HgCH3 and HgCF3, that are natural extensions of HgOH.

Towards chemistry at absolute zero

The prospect of cooling matter down to temperatures that are close to absolute zero raises intriguing questions about how chemical reactivity changes under these extreme conditions. Although some types of chemical reaction still occur at 1 μK, they can no longer adhere to the conventional picture of reactants passing over an activation energy barrier to become products. Indeed, at ultracold temperatures, the system enters a fully quantum regime, and quantum mechanics replaces the classical picture of colliding particles. In this Review, we discuss recent experimental and theoretical developments that allow us to explore chemical reactions at temperatures that range from 100 K to 500 nK. Although the field is still in its infancy, exceptional control has already been demonstrated over reactivity at low temperatures.

Isomer-specific kinetics of the C+ + H2O reaction at the temperature of interstellar clouds

The reaction C⁺ + H₂O → HCO⁺/HOC⁺ + H is one of the most important astrophysical sources of HOC⁺ ions, considered a marker for interstellar molecular clouds exposed to intense ultraviolet or x-ray radiation. Despite much study, there is no consensus on rate constants for formation of the formyl ion isomers in this reaction. This is largely due to difficulties in laboratory study of ion-molecule reactions under relevant conditions. Here, we use a novel experimental platform combining a cryogenic buffer-gas beam with an integrated, laser-cooled ion trap and high-resolution time-of-flight mass spectrometer to probe this reaction at the temperature of cold interstellar clouds. We report a reaction rate constant of k = 7.7(6) × 10^-9 cm³ s^-1 and a branching ratio of formation η = HOC⁺/HCO⁺ = 2.1(4). Theoretical calculations suggest that this branching ratio is due to the predominant formation of HOC⁺ followed by isomerization of products with internal energy over the isomerization barrier.

Infrared Comb Spectroscopy of Buffer-Gas-Cooled Molecules: Toward Absolute Frequency Metrology of Cold Acetylene

We review the recent developments in precision ro-vibrational spectroscopy of buffer-gas-cooled neutral molecules, obtained using infrared frequency combs either as direct probe sources or as ultra-accurate optical rulers. In particular, we show how coherent broadband spectroscopy of complex molecules especially benefits from drastic simplification of the spectra brought about by cooling of internal temperatures. Moreover, cooling the translational motion allows longer light-molecule interaction times and hence reduced transit-time broadening effects, crucial for high-precision spectroscopy on simple molecules. In this respect, we report on the progress of absolute frequency metrology experiments with buffer-gas-cooled molecules, focusing on the advanced technologies that led to record measurements with acetylene. Finally, we briefly discuss the prospects for further improving the ultimate accuracy of the spectroscopic frequency measurement.

Magnetic properties and quench dynamics of two interacting ultracold molecules in a trap

We theoretically investigate the magnetic properties and nonequilibrium dynamics of two interacting ultracold polar and paramagnetic molecules in a one-dimensional harmonic trap in external electric and magnetic fields. The molecules interact via a multichannel two-body contact potential, incorporating the short-range anisotropy of intermolecular interactions. We show that various magnetization states arise from the interplay of the molecular interactions, electronic spins, dipole moments, rotational structures, external fields, and spin-rotation coupling. The rich magnetization diagrams depend primarily on the anisotropy of the intermolecular interaction and the spin-rotation coupling. These specific molecular properties are challenging to calculate or measure. Therefore, we propose the quench dynamics experiments for extracting them from observing the time evolution of the analyzed system. Our results indicate the possibility of controlling the molecular few-body magnetization with the external electric field and pave the way towards studying the magnetization of ultracold molecules trapped in optical tweezers or optical lattices and their application in quantum simulation of molecular multichannel many-body Hamiltonians and quantum information storing.

Towards accurate prediction for laser-coolable molecules: relativistic coupled-cluster calculations for yttrium monoxide and prospects for improving its laser cooling efficiencies

Benchmark relativistic coupled-cluster calculations for yttrium monoxide (YO) with accurate treatment of relativistic and electron correlation effects are reported. The spin-orbit mixing of 2Π and 2Δ is found to be an order of magnitude smaller than previously reported in the literature. Together with the measurement of the lifetime of the A'2Δ3/2 state, it implies an enhanced capability of a narrow-line cooling scheme to bring YO to sub-recoil temperature. The computed electronic transition properties also support a four-photon scheme to close the leakage of the A2Π1/2 ↔ X2Σ1/2+ cycle through the A'2Δ3/2 state by repumping the A'2Δ3/2 state to the B2Σ1/2+ state, which subsequently decays back to X2Σ1/2+. Relativistic coupled-cluster methods, capable of providing accurate spectroscopic parameters that characterize the local potential curves and hence of providing accurate Franck-Condon factors, appear to be promising candidates for accurate calculation of properties for laser-coolable molecules.

Manipulating beams of paramagnetic atoms and molecules using inhomogeneous magnetic fields

We review methods to manipulate the motion of pulsed supersonic atomic and molecular beams using time-independent and -dependent inhomogeneous magnetic fields. In addition, we discuss current and possible future applications and research directions.

A study of the translational temperature dependence of the reaction rate constant between CH3CN and Ne+ at low temperatures

We have measured the translational temperature dependence of the reaction rate constant for CH₃CN + Ne⁺ → products at low temperatures. A cold Ne⁺ ensemble was embedded in Ca⁺ Coulomb crystals by a sympathetic laser cooling technique, while cold acetonitrile (CH₃CN) molecules were produced by two types of Stark velocity filters to widely change the translational temperatures. The measured reaction rate constant gradually increases with the decrease in the translational temperature of the velocity-selected CH₃CN molecules from 60 K down to 2 K, and thereby, a steep increase was observed at temperatures lower than 5 K. A comparison between experimental rate constants and the ion-dipole capture rate constants by the Perturbed Rotational State (PRS) theory was performed. The PRS capture rate constant reproduces well the reaction rate constant at a few kelvin but not for temperatures higher than 5 K. The result indicates that the reaction probability is small compared to typical ion-polar molecule reactions at temperatures above 5 K.

Direct laser cooling of a symmetric top molecule

Ultracold polyatomic molecules have potentially wide-ranging applications in quantum simulation and computation, particle physics, and quantum chemistry. For atoms and small molecules, direct laser cooling has proven to be a powerful tool for quantum science in the ultracold regime. However, the feasibility of laser-cooling larger, nonlinear polyatomic molecules has remained unknown because of their complex structure. We laser-cooled the symmetric top molecule calcium monomethoxide (CaOCH3), reducing the temperature of ~104 molecules from 22 ± 1 millikelvin to 1.8 ± 0.7 millikelvin in one dimension and state-selectively cooling two nuclear spin isomers. These results demonstrate that the use of proper ro-vibronic transitions enables laser cooling of nonlinear molecules, thereby opening a path to efficient cooling of chiral molecules and, eventually, optical tweezer arrays of complex polyatomic species.