Opportunities for fundamental physics research with radioactive molecules

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

Efficient Creation of Ultracold Ground State ^{6}Li^{40}K Polar Molecules

We report the creation of ultracold ground state ^{6}Li^{40}K polar molecules with high efficiency. Starting from weakly bound molecules, stimulated Raman adiabatic passage is adopted to coherently transfer the molecules to their singlet rovibrational ground state |X^{1}Σ^{+},v=0,J=0⟩. By employing a singlet stimulated Raman adiabatic passage pathway and low-phase-noise narrow-linewidth lasers, we observed a one-way transfer efficiency of 96(4)%. Held in an optical dipole trap, the lifetime of the ground state molecules is measured to be 5.0(3) ms. The large permanent dipole moment of LiK is confirmed by applying a dc electric field on the molecules and performing Stark shift spectroscopy of the ground state. With recent advances in the quantum control of collisions, our work paves the way for exploring quantum many-body physics with strongly interacting ^{6}Li^{40}K molecules.

Observation of Photoassociation Resonances in Ultracold Atom-Molecule Collisions

We report on the observation of photoassociation resonances in ultracold collisions between ^{23}Na^{40}K molecules and ^{40}K atoms. We perform photoassociation in a long-wavelength optical dipole trap to form deeply bound triatomic molecules in electronically excited states. The atom-molecule Feshbach resonance is used to enhance the free-bound Franck-Condon overlap. The photoassociation into well-defined quantum states of excited triatomic molecules is identified by observing resonantly enhanced loss features. These loss features depend on the polarization of the photoassociation lasers, allowing us to assign rotational quantum numbers. The observation of ultracold atom-molecule photoassociation resonances paves the way toward preparing ground-state triatomic molecules, provides a new high-resolution spectroscopy technique for polyatomic molecules, and is also important to atom-molecule Feshbach resonances.

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.

Electroassociation of Ultracold Dipolar Molecules into Tetramer Field-Linked States

The presence of electric or microwave fields can modify the long-range forces between ultracold dipolar molecules in such a way as to engineer weakly bound states of molecule pairs. These so-called field-linked states [A. V. Avdeenkov and J. L. Bohn, Phys. Rev. Lett. 90, 043006 (2003).PRLTAO0031-900710.1103/PhysRevLett.90.043006; L. Lassablière and G. Quéméner, Phys. Rev. Lett. 121, 163402 (2018).PRLTAO0031-900710.1103/PhysRevLett.121.163402], in which the separation between the two bound molecules can be orders of magnitude larger than the molecules themselves, have been observed as resonances in scattering experiments [X.-Y. Chen et al., Nature (London) 614, 59 (2023).NATUAS0028-083610.1038/s41586-022-05651-8]. Here, we propose to use them as tools for the assembly of weakly bound tetramer molecules, by means of ramping an electric field, the electric-field analog of magnetoassociation in atoms. This ability would present new possibilities for constructing ultracold polyatomic molecules.

Ultra-low noise bipolar current source for ultracold atom magnetic system

We report the development of an ultralow-noise bipolar current source based on the configuration of H-bridge current switching. The measured relative current noise fluctuation reaches 4 × 10-9 Hz-1/2, which enables an ultra-stable magnetic system for cold atom experiments. We avoid the influence of the AC leakage currents induced by the large parasitic capacitance of the H-bridge. First, the current sensor is placed as close as possible to the magnetic coils so that the systematic errors from these leakage currents are minimized. Second, the large parasitic capacitance, which parallels the magnetic coils and forms an LC oscillator, is removed from the feedback loop in our setup to maintain a large self-resonance frequency of the feedback control loop. These two improvements lead to a current source that is more precise and less noisy. Remarkably, the lowest current noise density produced by the proposed method is only 500 nA Hz-1/2 at a current of 100 A, which is about ten fold smaller than the case with leakage current. To optimize the feedback control, a numerical simulation is implemented by using Matlab Simulink, and the numerical simulation results are entirely consistent with the experimental results.

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.

Tomography of Feshbach resonance states

Feshbach resonances are fundamental to interparticle interactions and become particularly important in cold collisions with atoms, ions, and molecules. In this work, we present the detection of Feshbach resonances in a benchmark system for strongly interacting and highly anisotropic collisions: molecular hydrogen ions colliding with noble gas atoms. The collisions are launched by cold Penning ionization, which exclusively populates Feshbach resonances that span both short- and long-range parts of the interaction potential. We resolved all final molecular channels in a tomographic manner using ion-electron coincidence detection. We demonstrate the nonstatistical nature of the final-state distribution. By performing quantum scattering calculations on ab initio potential energy surfaces, we show that the isolation of the Feshbach resonance pathways reveals their distinctive fingerprints in the collision outcome.

Resonances in Non-universal Dipolar Collisions

Scattering resonances due to the dipole-dipole interaction between ultracold molecules, induced by static or microwave fields, are studied theoretically. We develop a method for coupled-channel calculations that can efficiently impose many short-range boundary conditions, defined by a short-range phase shift and loss probability as in quantum defect theory. We study how resonances appear as the short-range loss probability is lowered below the universal unit probability. This may become realizable for nonreactive ultracold molecules in blue-detuned box potentials.

Coherent Control of Ultracold Molecular Collisions: The Role of Resonances

We consider the coherent control of ultracold molecule-molecule scattering, impacted by a dense set of rovibrational resonances. To characterize the resonance spectrum, a rudimentary model based on multichannel quantum defect theory has been used to study the control of the scattering cross section and the reaction rate. Complete control around resonance energies is shown to be possible, but thermal averaging over a large number of resonances significantly reduces the extent of control of reaction rates related to the random distribution of optimal control parameters between resonances. We show that measuring the extent of coherent control could be used to extract meaningful information about the relative contribution of direct scattering versus collision complex formation, as well as about the statistical regime.

Field-linked resonances of polar molecules

Scattering resonances are an essential tool for controlling the interactions of ultracold atoms and molecules. However, conventional Feshbach scattering resonances¹, which have been extensively studied in various platforms^1-7, are not expected to exist in most ultracold polar molecules because of the fast loss that occurs when two molecules approach at a close distance^8-10. Here we demonstrate a new type of scattering resonance that is universal for a wide range of polar molecules. The so-called field-linked resonances^11-14 occur in the scattering of microwave-dressed molecules because of stable macroscopic tetramer states in the intermolecular potential. We identify two resonances between ultracold ground-state sodium-potassium molecules and use the microwave frequencies and polarizations to tune the inelastic collision rate by three orders of magnitude, from the unitary limit to well below the universal regime. The field-linked resonance provides a tuning knob to independently control the elastic contact interaction and the dipole-dipole interaction, which we observe as a modification in the thermalization rate. Our result provides a general strategy for resonant scattering between ultracold polar molecules, which paves the way for realizing dipolar superfluids¹⁵ and molecular supersolids¹⁶, as well as assembling ultracold polyatomic molecules.

A Feshbach resonance in collisions between triplet ground-state molecules

Collisional resonances are important tools that have been used to modify interactions in ultracold gases, for realizing previously unknown Hamiltonians in quantum simulations¹, for creating molecules from atomic gases² and for controlling chemical reactions. So far, such resonances have been observed for atom-atom collisions, atom-molecule collisions^3-7 and collisions between Feshbach molecules, which are very weakly bound^8-10. Whether such resonances exist for ultracold ground-state molecules has been debated owing to the possibly high density of states and/or rapid decay of the resonant complex^11-15. Here we report a very pronounced and narrow (25 mG) Feshbach resonance in collisions between two triplet ground-state NaLi molecules. This molecular Feshbach resonance has two special characteristics. First, the collisional loss rate is enhanced by more than two orders of magnitude above the background loss rate, which is saturated at the p-wave universal value, owing to strong chemical reactivity. Second, the resonance is located at a magnetic field where two open channels become nearly degenerate. This implies that the intermediate complex predominantly decays to the second open channel. We describe the resonant loss feature using a model with coupled modes that is analogous to a Fabry-Pérot cavity. Our observations provide strong evidence for the existence of long-lived coherent intermediate complexes even in systems without reaction barriers and open up the possibility of coherent control of chemical reactions.

Ultracold Sticky Collisions: Theoretical and Experimental Status

Collisional complexes, which are formed as intermediate states in molecular collisions, are typically short-lived and decay within picoseconds. However, in ultracold collisions involving bialkali molecules, complexes can live for milliseconds, completely changing the collision dynamics. This can lead to unexpected two-body loss in samples of nonreactive molecules. During the past decade, such "sticky" collisions have been a major hindrance in the preparation of dense and stable molecular samples, especially in the quantum-degenerate regime. Currently, the behavior of the complexes is not fully understood. For example, in some cases, their lifetime has been measured to be many orders of magnitude longer than recent models predict. This is not only an intriguing problem in itself but also practically relevant, since understanding molecular complexes may help to mitigate their detrimental effects. Here, we review the recent experimental and theoretical progress in this field. We treat the case of molecule-molecule as well as molecule-atom collisions.

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.

Creation of an ultracold gas of triatomic molecules from an atom–diatomic molecule mixture

In recent years, there has been notable progress in the preparation and control of ultracold gases of diatomic molecules. The next experimental challenge is the production of ultracold polyatomic molecular gases. Here, we report the creation of an ultracold gas of 23 Na 40 K 2 triatomic molecules from a mixture of ground-state sodium-23–potassium-40 ( 23 Na 40 K) molecules and potassium-40 ( 40 K) atoms. The triatomic molecules were created by adiabatic magneto-association through an atom–diatomic molecule Feshbach resonance. We obtained clear evidence for the creation of triatomic molecules by directly detecting them using radio-frequency dissociation. Approximately 4000 triatomic molecules with a high-peak phase-space density of 0.05 could be created. The ultracold triatomic molecules can serve as a launchpad to probe the three-body potential energy surface and may be used to prepare quantum degenerate triatomic molecular gases.

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.

Chemistry of a Light Impurity in a Bose-Einstein Condensate

Similar to an electron in a solid, an impurity in an atomic Bose-Einstein condensate (BEC) is dressed by excitations from the medium, forming a polaron quasiparticle with modified properties. This impurity can also undergo chemical recombination with atoms from the BEC, a process resonantly enhanced when universal three-body Efimov bound states cross the continuum. To study the interplay between these phenomena, we use a Gaussian state variational method able to describe both Efimov physics and arbitrarily many excitations of the BEC. We show that the polaron cloud contributes to bound state formation, leading to a shift of the Efimov resonance to smaller interaction strengths. This shifted scattering resonance marks the onset of a polaronic instability towards the decay into large Efimov clusters and fast recombination, offering a remarkable example of chemistry in a quantum medium.

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.

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.

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.

Empirical LiK excited state potentials: connecting short range and near dissociation expansions

We report on a high-resolution spectroscopic survey of ⁶Li⁴⁰K molecules near the 2S + 4P dissociation threshold and produce a fully empirical representation for the B¹Π potential by connecting available short- and long-range data. The purpose is to identify a suitable intermediate state for a coherent Raman transfer to the absolute ground state, and the creation of a molecular gas with dipolar interactions. Starting from weakly bound ultracold Feshbach molecules, the transition frequencies to twenty-six vibrational states are determined. Our data are combined with long-range measurements [Ridinger et al., EPL, 2011, 96, 33001], and near-dissociation expansions for the spin-orbit coupled potentials are fitted to extract the van der Waals C₆ dispersion coefficients. A suitable vibrational level is identified by resolving its Zeeman structure and by comparing the experimentally attained g-factor to our theoretical prediction. Using mass-scaling of the short-range data for the B¹Π [Pashov et al., Chem. Phys. Lett., 1998, 292, 615620] and an updated value for its depth, we model the short- and the long-range data simultaneously and produce a Rydberg-Klein-Rees curve covering the entire range.

High resolution laser excitation spectra and Franck-Condon factors of A2Π−X2Σ+ electronic transition of MgF

Magnesium monofluoride (MgF) is proposed as an ideal candidate radical for direct laser cooling. Here, the rotationally resolved laser spectra of MgF for the A2Π− X2Σ+ electronic transition system were recorded by using laser induced fluorescence technique. The MgF radicals were produced by discharging SF6/Ar gas mixtures between the tips of two magnesium needles in a supersonic jet expansion. We recorded a total of 19 vibrational bands belonging to three sequences of Δ v=0, ±1 in the region of 348-370 nm. Accurate spectroscopic constants for both X2Σ+ and A2Π states are determined from rotational analysis of the experimental spectra. Spectroscopic parameters, including the Franck-Condon factors (FCFs), are determined from the experimental results and the Rydberg-Klein-Rees (RKR) calculations. Significant discrepancies between the experimentally measured and RKR-calculated FCFs are found, indicating that the FCFs are nearly independent of the spin-orbit coupling in the A2Π state. Potential energy curves (PECs) and FCFs determined here provide necessary data for the theoretical simulation of the laser-cooling scheme of MgF.

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.

Observation of Feshbach resonances between a single ion and ultracold atoms

The control of physical systems and their dynamics on the level of individual quanta underpins both fundamental science and quantum technologies. Trapped atomic and molecular systems, neutral¹ and charged², are at the forefront of quantum science. Their extraordinary level of control is evidenced by numerous applications in quantum information processing^3,4 and quantum metrology^5,6. Studies of the long-range interactions between these systems when combined in a hybrid atom-ion trap^7,8 have led to landmark results^9-19. However, reaching the ultracold regime-where quantum mechanics dominates the interaction, for example, giving access to controllable scattering resonances^20,21-has so far been elusive. Here we demonstrate Feshbach resonances between ions and atoms, using magnetically tunable interactions between ¹³⁸Ba⁺ ions and ⁶Li atoms. We tune the experimental parameters to probe different interaction processes-first, enhancing three-body reactions^22,23 and the related losses to identify the resonances and then making two-body interactions dominant to investigate the ion's sympathetic cooling¹⁹ in the ultracold atomic bath. Our results provide deeper insights into atom-ion interactions, giving access to complex many-body systems^24-27 and applications in experimental quantum simulation^28-30.

Quantum Spin State Selectivity and Magnetic Tuning of Ultracold Chemical Reactions of Triplet Alkali-Metal Dimers with Alkali-Metal Atoms

We demonstrate that it is possible to efficiently control ultracold chemical reactions of alkali-metal atoms colliding with open-shell alkali-metal dimers in their metastable triplet states by choosing the internal hyperfine and rovibrational states of the reactants as well as by inducing magnetic Feshbach resonances with an external magnetic field. We base these conclusions on coupled-channel statistical calculations that include the effects of hyperfine contact and magnetic-field-induced Zeeman interactions on ultracold chemical reactions of hyperfine-resolved ground-state Na and the triplet NaLi(a^{3}Σ^{+}) producing singlet Na_{2}(^{1}Σ_{g}^{+}) and a Li atom. We find that the reaction rates are sensitive to the initial hyperfine states of the reactants. The chemical reaction of fully spin-polarized, high-spin states of rotationless NaLi(a^{3}Σ^{+},v=0,N=0) molecules with fully spin-polarized Na is suppressed by a factor of 10-100 compared to that of unpolarized reactants. We interpret these findings within the adiabatic state model, which treats the reaction as a sequence of nonadiabatic transitions between the initial nonreactive high-spin state and the final low-spin states of the reaction complex. In addition, we show that magnetic Feshbach resonances can similarly change reaction rate coefficients by several orders of magnitude. Some of these resonances are due to resonant trimer bound states dissociating to the N=2 rotational state of NaLi(a^{3}Σ^{+},v=0) and would thus exist in systems without hyperfine interactions.

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.

Resonant collisional shielding of reactive molecules using electric fields

Full control of molecular interactions, including reactive losses, would open new frontiers in quantum science. We demonstrate extreme tunability of ultracold chemical reaction rates by inducing resonant dipolar interactions by means of an external electric field. We prepared fermionic potassium-rubidium molecules in their first excited rotational state and observed a modulation of the chemical reaction rate by three orders of magnitude as we tuned the electric field strength by a few percent across resonance. In a quasi-two-dimensional geometry, we accurately determined the contributions from the three dominant angular momentum projections of the collisions. Using the resonant features, we shielded the molecules from loss and suppressed the reaction rate by an order of magnitude below the background value, thereby realizing a long-lived sample of polar molecules in large electric fields.

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.

Coherent manipulation of the internal state of ultracold 87Rb133Cs molecules with multiple microwave fields

We explore coherent multi-photon processes in 87Rb133Cs molecules using 3-level lambda and ladder configurations of rotational and hyperfine states, and discuss their relevance to future applications in quantum computation and quantum simulation. In the lambda configuration, we demonstrate the driving of population between two hyperfine levels of the rotational ground state via a two-photon Raman transition. Such pairs of states may be used in the future as a quantum memory, and we measure a Ramsey coherence time for a superposition of these states of 58(9) ms. In the ladder configuration, we show that we can generate and coherently populate microwave dressed states via the observation of an Autler-Townes doublet. We demonstrate that we can control the strength of this dressing by varying the intensity of the microwave coupling field. Finally, we perform spectroscopy of the rotational states of 87Rb133Cs up to N = 6, highlighting the potential of ultracold molecules for quantum simulation in synthetic dimensions. By fitting the measured transition frequencies we determine a new value of the centrifugal distortion coefficient Dv = h × 207.3(2) Hz.

Determining the nature of quantum resonances by probing elastic and reactive scattering in cold collisions

Scattering resonances play a central role in collision processes in physics and chemistry. They help build an intuitive understanding of the collision dynamics due to the spatial localization of the scattering wavefunctions. For resonances that are localized in the reaction region, located at short separation behind the centrifugal barrier, sharp peaks in the reaction rates are the characteristic signature, observed recently with state-of-the-art experiments in low-energy collisions. If, however, the localization occurs outside of the reaction region, mostly the elastic scattering is modified. This may occur due to above-barrier resonances, the quantum analogue of classical orbiting. By probing both elastic and inelastic scattering of metastable helium with deuterium molecules in merged-beam experiments, we differentiate between the nature of quantum resonances-tunnelling resonances versus above-barrier resonances-and corroborate our findings by calculating the corresponding scattering wavefunctions.

Dipolar evaporation of reactive molecules to below the Fermi temperature

The control of molecules is key to the investigation of quantum phases, in which rich degrees of freedom can be used to encode information and strong interactions can be precisely tuned1. Inelastic losses in molecular collisions2-5, however, have greatly hampered the engineering of low-entropy molecular systems6. So far, the only quantum degenerate gas of molecules has been created via association of two highly degenerate atomic gases7,8. Here we use an external electric field along with optical lattice confinement to create a two-dimensional Fermi gas of spin-polarized potassium-rubidium (KRb) polar molecules, in which elastic, tunable dipolar interactions dominate over all inelastic processes. Direct thermalization among the molecules in the trap leads to efficient dipolar evaporative cooling, yielding a rapid increase in phase-space density. At the onset of quantum degeneracy, we observe the effects of Fermi statistics on the thermodynamics of the molecular gas. These results demonstrate a general strategy for achieving quantum degeneracy in dipolar molecular gases in which strong, long-range and anisotropic dipolar interactions can drive the emergence of exotic many-body phases, such as interlayer pairing and p-wave superfluidity.

Coherently forming a single molecule in an optical trap

Ultracold single molecules have wide-ranging potential applications, such as ultracold chemistry, precision measurements, quantum simulation, and quantum computation. However, given the difficulty of achieving full control of a complex atom-molecule system, the coherent formation of single molecules remains a challenge. Here, we report an alternative route to coherently bind two atoms into a weakly bound molecule at megahertz levels by coupling atomic spins to their two-body relative motion in a strongly focused laser with inherent polarization gradients. The coherent nature is demonstrated by long-lived atom-molecule Rabi oscillations. We further manipulate the motional levels of the molecules and measure the binding energy precisely. This work opens the door to full control of all degrees of freedom in atom-molecule systems.

A joint data and model driven method for study diatomic vibrational spectra including dissociation behavior

The details of quantum multi-body interactions are so rich and subtle which make it difficult to accurately model for some situations such as the behavior of diatomic long-range vibrations. In recent years, data-driven machine learning has made remarkable achievements in capturing complex relationships that are subtle. Combining the characteristics of these two fields, we propose a joint machine learning method to obtain reliable diatomic vibrational spectra including dissociation energy by using accessible heterogeneous micro/macro information such as low lying vibrational energy levels and heat capacity. Applications of this method to CO and Br₂ in the ground state yield their state of the art of vibrational spectra including dissociation limit. The strategy introduced here is an exploration of combining the model-driven and data-driven method to cover subtle physical details that are difficult to study in a single way.

Bichromatic Photoassociation Spectroscopy for the Determination of Rotational Constants of Cs2 0 u + Long-Range State below the 6S1/2 + 6P1/2 Asymptote

This article demonstrates new observation of the high-resolution ro-vibrational bichromatic photoassociation spectra (BPAS) of Cs₂ in the 0u+ long-range state below the asymptotes 6S_1/2 + 6P_1/2. By combining with a modulation spectroscopic technique, precise references of the frequency differences have been engineered through the BPAS, with which the rotational constants of low-lying vibrational levels of the Cs₂0u+ long-range state have been accurately determined by fitting the frequency differences to the non-rigid-rotor model. The rotational constants for the newly observed seven ro-vibrational levels are summarized and disagreement for the level ῦ = 498 is clarified. The rotational constants of different vibrational levels demonstrate strong perturbations of the related energy structures. A simple analysis is performed and shows good agreement with experimental results.

Ultracold Gas of Bosonic ^{23}Na^{39}K Ground-State Molecules

We report the creation of ultracold bosonic dipolar ^{23}Na^{39}K molecules in their absolute rovibrational ground state. Starting from weakly bound molecules immersed in an ultracold atomic mixture, we coherently transfer the dimers to the rovibrational ground state using an adiabatic Raman passage. We analyze the two-body decay in a pure molecular sample and in molecule-atom mixtures and find an unexpectedly low two-body decay coefficient for collisions between molecules and ^{39}K atoms in a selected hyperfine state. The preparation of bosonic ^{23}Na^{39}K molecules opens the way for future comparisons between fermionic and bosonic ultracold ground-state molecules of the same chemical species.

Resonant Dipolar Collisions of Ultracold Molecules Induced by Microwave Dressing

We demonstrate microwave dressing on ultracold, fermionic ^{23}Na^{40}K ground-state molecules and observe resonant dipolar collisions with cross sections exceeding 3 times the s-wave unitarity limit. The origin of these interactions is the resonant alignment of the approaching molecules' dipoles along the intermolecular axis, which leads to strong attraction. We explain our observations with a conceptually simple two-state picture based on the Condon approximation. Furthermore, we perform coupled-channel calculations that agree well with the experimentally observed collision rates. The resonant microwave-induced collisions found here enable controlled, strong interactions between molecules, of immediate use for experiments in optical lattices.

Tune-Out and Magic Wavelengths for Ground-State ^{23}Na^{40}K Molecules

We demonstrate a versatile, state-dependent trapping scheme for the ground and first excited rotational states of ^{23}Na^{40}K molecules. Close to the rotational manifold of a narrow electronic transition, we determine tune-out frequencies where the polarizability of one state vanishes while the other remains finite, and a magic frequency where both states experience equal polarizability. The proximity of these frequencies of only 10 GHz allows for dynamic switching between different trap configurations in a single experiment, while still maintaining sufficiently low scattering rates.

Quantum resonances near absolute zero

Ultralow-energy atom-molecule collisions reveal quasi-bound state quantum resonances

Loss of Ultracold ^{87}Rb^{133}Cs Molecules via Optical Excitation of Long-Lived Two-Body Collision Complexes

We show that the lifetime of ultracold ground-state ^{87}Rb^{133}Cs molecules in an optical trap is limited by fast optical excitation of long-lived two-body collision complexes. We partially suppress this loss mechanism by applying square-wave modulation to the trap intensity, such that the molecules spend 75% of each modulation cycle in the dark. By varying the modulation frequency, we show that the lifetime of the collision complex is 0.53±0.06  ms in the dark. We find that the rate of optical excitation of the collision complex is 3_{-2}^{+4}×10^{3}  W^{-1} cm^{2} s^{-1} for λ=1550  nm, leading to a lifetime of <100  ns for typical trap intensities. These results explain the two-body loss observed in experiments on nonreactive bialkali molecules.

Thermalization and Sub-Poissonian Density Fluctuations in a Degenerate Molecular Fermi Gas

We observe thermalization in the production of a degenerate Fermi gas of polar ^{40}K^{87}Rb molecules. By measuring the atom-dimer elastic scattering cross section near the Feshbach resonance, we show that Feshbach molecules rapidly reach thermal equilibrium with both parent atomic species. Equilibrium is essentially maintained through coherent transfer to the ground state. Sub-Poissonian density fluctuations in Feshbach and ground-state molecules are measured, giving an independent characterization of degeneracy and directly probing the molecular Fermi-Dirac distribution.

Probing ultracold chemistry using ion spectrometry

Reactions between KRb molecules at sub-microkelvin temperatures were probed using ion spectrometry.

Direct observation of bimolecular reactions of ultracold KRb molecules

Femtochemistry techniques have been instrumental in accessing the short time scales necessary to probe transient intermediates in chemical reactions. In this study, we took the contrasting approach of prolonging the lifetime of an intermediate by preparing reactant molecules in their lowest rovibronic quantum state at ultralow temperatures, thereby markedly reducing the number of exit channels accessible upon their mutual collision. Using ionization spectroscopy and velocity-map imaging of a trapped gas of potassium-rubidium (KRb) molecules at a temperature of 500 nanokelvin, we directly observed reactants, intermediates, and products of the reaction 40K87Rb + 40K87Rb → K2Rb2* → K2 + Rb2. Beyond observation of a long-lived, energy-rich intermediate complex, this technique opens the door to further studies of quantum-state–resolved reaction dynamics in the ultracold regime.

Observation of Interference between Resonant and Detuned stirap in the Adiabatic Creation of ^{23}Na^{40}K Molecules

Stimulated Raman adiabatic passage (stirap) allows efficiently transferring the populations between two discrete quantum states and has been used to prepare molecules in their rovibrational ground state. In realistic molecules, a well-resolved intermediate state is usually selected to implement the resonant stirap. Because of the complex molecular level structures, the detuned stirap always coexists with the resonant stirap and may cause unexpected interference phenomenon. However, it is generally accepted that the detuned stirap can be neglected if compared with the resonant stirap. Here we report on the first observation of interference between the resonant and detuned stirap in the adiabatic creation of ^{23}Na^{40}K ground-state molecules. The interference is identified by observing that the number of Feshbach molecules after a round-trip stirap oscillates as a function of the hold time, with a visibility of about 90%. This occurs even if the intermediate excited states are well resolved, and the single-photon detuning of the detuned stirap is about 1 order of magnitude larger than the linewidth of the excited state and the Rabi frequencies of the stirap lasers. Moreover, the observed interference indicates that if more than one hyperfine level of the ground state is populated, the stirap prepares a coherent superposition state among them, but not an incoherent mixed state. Further, the purity of the hyperfine levels of the created ground state can be quantitatively determined by the visibility of the oscillation.

Universal Scattering of Ultracold Atoms and Molecules in Optical Potentials

Universal collisions describe the reaction of molecules and atoms as dominated by long-range interparticle interactions. Here, we calculate the universal inelastic rate coefficients for a large group of ultracold polar molecules in their lower ro-vibrational states colliding with one of their constituent atoms. The rate coefficients are solely determined by values of the dispersion coefficient and reduced mass of the collisional system. We use the ab initio coupled-cluster linear response method to compute dynamic molecular polarizabilities and obtain the dispersion coefficients for some of the collisional partners and use values from the literature for others. Our polarizability calculations agree well with available experimental measurements. Comparison of our inelastic rate coefficients with results of numerically exact quantum-mechanical calculations leads us to conjecture that collisions with heavier atoms can be expected to be more universal.