Long-Lived Ultracold Molecules with Electric and Magnetic Dipole Moments

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.

Highly efficient creation and detection of deeply bound molecules via invariant-based inverse engineering with feasible modified drivings

Stimulated Raman Adiabatic Passage (STIRAP) and its variants, such as M-type chainwise-STIRAP, allow for efficiently transferring the populations in a multilevel system and have widely been used to prepare molecules in their rovibrational ground state. However, their transfer efficiencies are generally imperfect. The main obstacle is the presence of losses and the requirement to make the dynamics adiabatic. To this end, in the present paper, a new theoretical method is proposed for the efficient and robust creation and detection of deeply bound molecules in three-level Λ-type and five-level M-type systems via "Invariant-based shortcut-to-adiabaticity." In the regime of large detunings, we first reduce the dynamics of three- and five-level molecular systems to those of effective two- and three-level counterparts. By doing so, the major molecular losses from the excited states can be well suppressed. Consequently, the effective two-level counterpart can be directly compatible with two different "Invariant-based Inverse Engineering" protocols; the results show that both protocols give a comparable performance and have a good experimental feasibility. For the effective three-level counterpart, by considering a relation among the four incident pulses, we show that this model can be further generalized to an effective Λ-type one with the simplest resonant coupling. This generalized model permits us to borrow the "Invariant-based Inverse Engineering" protocol from a standard three-level Λ-type system to a five-level M-type system. Numerical calculations show that the weakly bound molecules can be efficiently transferred to their deeply bound states without strong laser pulses, and the stability against parameter variations is well preserved. Finally, the detection of ultracold deeply bound molecules is discussed.

General Classification of Qubit Encodings in Ultracold Diatomic Molecules

Owing to their rich internal structure and significant long-range interactions, ultracold molecules have been widely explored as carriers of quantum information. Several different schemes for encoding qubits into molecular states, both bare and field-dressed, have been proposed. At the same time, the rich internal structure of molecules leaves many unexplored possibilities for qubit encodings. We show that all molecular qubit encodings can be classified into four classes by the type of the effective interaction between the qubits. In the case of polar molecules, the four classes are determined by the relative magnitudes of matrix elements of the dipole moment operator in the single-molecule basis. We exemplify our classification scheme by considering the encoding of the effective spin-1/2 system into nonadjacent rotational states (e.g., N = 0 and 2) of polar and nonpolar molecules with the same nuclear spin projection. Our classification scheme is designed to inform the optimal choice of molecular qubit encoding for quantum information storage and processing applications, as well as for dynamical generation of many-body entangled states and for quantum annealing.

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

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

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.

Effective Potential and Superfluidity of Microwave-Shielded Polar Molecules

We analytically show that the effective interaction potential between microwave-shielded polar molecules consists of an anisotropic van der Waals-like shielding core and a modified dipolar interaction. This effective potential is validated by comparing its scattering cross sections with those calculated using intermolecular potential involving all interaction channels. It is shown that a scattering resonance can be induced under microwave fields reachable in current experiments. With the effective potential, we further study the Bardeen-Cooper-Schrieffer pairing in the microwave-shielded NaK gas. We show that the superfluid critical temperature is drastically enhanced near the resonance. As the effective potential is suitable for exploring the many-body physics of molecular gases, our results pave the way for studies of the ultracold gases of microwave-shielded molecular gases.

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

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

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

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

Ultracold Gas of Dipolar NaCs Ground State Molecules

We report on the creation of bosonic NaCs molecules in their absolute rovibrational ground state via stimulated Raman adiabatic passage. We create ultracold gases with up to 22 000 dipolar NaCs molecules at a temperature of 300(50) nK and a peak density of 1.0(4)×10^{12}  cm^{-3}. We demonstrate comprehensive quantum state control by preparing the molecules in a specific electronic, vibrational, rotational, and hyperfine state. We measure the ground state ac polarizability at 1064 nm along with the two-body loss rate, which we find to be universal. Employing the tunability and strength of the permanent electric dipole moment of NaCs, we induce dipole moments of up to 2.6 D at a dc electric field of 2.1(2)  kV/cm and demonstrate strong microwave coupling between the two lowest rotational states with a Rabi frequency of 2π×45  MHz. A large electric dipole moment, accessible at relatively small electric fields, makes ultracold gases of NaCs molecules well suited for the exploration of strongly interacting phases of dipolar quantum matter.

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.

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.

Dipolar physics: a review of experiments with magnetic quantum gases

Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.

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.

Seconds-Scale Coherence on Nuclear Spin Transitions of Ultracold Polar Molecules in 3D Optical Lattices

Ultracold polar molecules (UPMs) are emerging as a novel and powerful platform for fundamental applications in quantum science. Here, we report characterization of the coherence between nuclear spin levels of ultracold ground-state sodium-rubidium molecules loaded into a 3D optical lattice with a nearly photon scattering limited trapping lifetime of 9(1) seconds. After identifying and compensating the main sources of decoherence, we achieve a maximum nuclear spin coherence time of T_{2}^{*}=3.3(6)  s with two-photon Ramsey spectroscopy. Furthermore, based on the understanding of the main factor limiting the coherence of the two-photon Rabi transition, we obtain a Rabi line shape with linewidth below 0.8 Hz. The simultaneous realization of long lifetime and coherence time, and ultrahigh spectroscopic resolution in our system unveils the great potentials of Ultracold polar molecules in quantum simulation, computation, and metrology.

Low-temperature reaction dynamics of paramagnetic species in the gas phase

Radicals are abundant in a range of important gas-phase environments. They are prevalent in the atmosphere, in interstellar space, and in combustion processes. As such, understanding how radicals react is essential for the development of accurate models of the complex chemistry occurring in these gas-phase environments. By controlling the properties of the colliding reactants, we can also gain insights into how radical reactions occur on a fundamental level. Recent years have seen remarkable advances in the breadth of experimental methods successfully applied to the study of reaction dynamics involving paramagnetic species-from improvements to the well-known crossed molecular beams approach to newer techniques involving magnetically guided and decelerated beams. Coupled with ever-improving theoretical methods, quantum features are being observed and interesting insights into reaction dynamics are being uncovered in an increasingly diverse range of systems. In this highlight article, we explore some of the exciting recent developments in the study of chemical dynamics involving paramagnetic species. We focus on low-energy reactive collisions involving neutral radical species, where the reaction parameters are controlled. We conclude by identifying some of the limitations of current methods and exploring possible new directions for the field.

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.

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

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

Bimolecular Chemistry in the Ultracold Regime

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

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.

Rotational Coherence Times of Polar Molecules in Optical Tweezers

Qubit coherence times are critical to the performance of any robust quantum computing platform. For quantum information processing using arrays of polar molecules, a key performance parameter is the molecular rotational coherence time. We report a 93(7) ms coherence time for rotational state qubits of laser cooled CaF molecules in optical tweezer traps, over an order of magnitude longer than previous systems. Inhomogeneous broadening due to the differential polarizability between the qubit states is suppressed by tuning the tweezer polarization and applied magnetic field to a "magic" angle. The coherence time is limited by the residual differential polarizability, implying improvement with further cooling. A single spin-echo pulse is able to extend the coherence time to nearly half a second. The measured coherence times demonstrate the potential of polar molecules as high fidelity qubits.

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.

Observation of microwave shielding of ultracold molecules

Harnessing the potential wide-ranging quantum science applications of molecules will require control of their interactions. Here, we used microwave radiation to directly engineer and tune the interaction potentials between ultracold calcium monofluoride (CaF) molecules. By merging two optical tweezers, each containing a single molecule, we probed collisions in three dimensions. The correct combination of microwave frequency and power created an effective repulsive shield, which suppressed the inelastic loss rate by a factor of six, in agreement with theoretical calculations. The demonstrated microwave shielding shows a general route to the creation of long-lived, dense samples of ultracold polar molecules and evaporative cooling.

Quantum-State Control and Manipulation of Paramagnetic Molecules with Magnetic Fields

Since external magnetic fields were first employed to deflect paramagnetic atoms in 1921, a range of magnetic field-based methods have been introduced to state-selectively manipulate paramagnetic species. These methods include magnetic guides, which selectively filter paramagnetic species from all other components of a beam, and magnetic traps, where paramagnetic species can be spatially confined for extended periods of time. However, many of these techniques were developed for atomic-rather than molecular-paramagnetic species. It has proven challenging to apply some of these experimental methods developed for atoms to paramagnetic molecules. Thanks to the emergence of new experimental approaches and new combinations of existing techniques, the past decade has seen significant progress toward the manipulation and control of paramagnetic molecules. This review identifies the key methods that have been implemented for the state-selective manipulation of paramagnetic molecules-discussing the motivation, state of the art, and future prospects of the field. Key applications include the ability to control chemical interactions, undertake precise spectroscopic measurements, and challenge our understanding of chemical reactivity at a fundamental level.

Quantum reactive scattering calculations for the cold and ultracold Li + LiNa → Li2 + Na reaction

A first-principles based quantum dynamics study of the Li + LiNa(v = 0, j = 0) → Li₂(v^', j') + Na reaction is reported for collision energies spanning the ultracold (1 nK) to cold (1 K) regimes. A full-dimensional ab initio potential energy surface for the ground electronic state of Li₂Na is utilized that includes an accurate treatment of the long-range interactions. The Li + LiNa reaction is barrierless and exoergic and exhibits a deep attractive potential well that supports complex formation. Thus, significant reactivity occurs even for collision temperatures approaching absolute zero. The reactive scattering calculations are based on a numerically exact time-independent quantum dynamics methodology in hyperspherical coordinates. Total and rotationally resolved rate coefficients are reported at 56 collision energies and include all contributing partial waves. Several shape resonances are observed in many of the rotationally resolved rate coefficients and a small resonance feature is also reported in the total rate coefficient near 50 mK. Of particular interest, the angular distributions or differential cross sections are reported as a function of both the collision energy and scattering angle. Unique quantum fingerprints (bumps, channels, and ripples) are observed in the angular distributions for each product rotational state due to quantum interference and shape resonance contributions. The Li + LiNa reaction is under active experimental investigation so that these intriguing features could be verified experimentally when sufficient product state resolution becomes feasible for collision energies below 1 K.

Non-adiabatic quantum interference in the ultracold Li + LiNa → Li2 + Na reaction

Electronically non-adiabatic effects play an important role in many chemical reactions. However, how these effects manifest in cold and ultracold chemistry remains largely unexplored. Here for the first time we present from first principles the non-adiabatic quantum dynamics of the reactive scattering between ultracold alkali-metal LiNa molecules and Li atoms. We show that non-adiabatic dynamics induces quantum interference effects that dramatically alter the ultracold rotationally resolved reaction rate coefficients. The interference effect arises from the conical intersection between the ground and an excited electronic state that is energetically accessible even for ultracold collisions. These unique interference effects might be exploited for quantum control applications such as a quantum molecular switch. The non-adiabatic dynamics are based on full-dimensional ab initio potential energy surfaces for the two electronic states that includes the non-adiabatic couplings and an accurate treatment of the long-range interactions. A statistical analysis of rotational populations of the Li2 product reveals a Poisson distribution implying the underlying classical dynamics are chaotic. The Poisson distribution is robust and amenable to experimental verification and appears to be a universal property of ultracold reactions involving alkali metal dimers.

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.

Measurement of the permanent electric dipole moment of ultracold ground state 85Rb133Cs molecules by microwave coherent spectroscopy

We demonstrate measurement of the permanent electric dipole moment (EDM) of ⁸⁵Rb¹³³Cs molecules in the absolute vibrational ground state by microwave (MW) coherent spectroscopy. The rotational states of the considered molecules, which are formed from short-range photoassociation of mixed cold atoms, are nondegenerated under external electric field. To measure the EDM based on electric-field-induced shifts of the sublevels of X¹Σ⁺(v = 0, J = 1) rotational state, we utilized a MW coherent spectroscopy, which has a higher resolution than depletion spectroscopy and one-photon MW spectroscopy and can also eliminate the influence from Stark shift of the excited state existing in both spectroscopies above. In order to acquire accurate electric intensity, electromagnetic induced transparency spectroscopy of ⁸⁵Rb Rydberg atoms is used to implement the calibration. The permanent EDM of ⁸⁵Rb¹³³Cs molecules is finally determined to be 1.266(15) D, which agrees with the theoretical calculations and is comparable with the value of its isotopic molecule.

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.

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.

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.

Enhancing Dipolar Interactions between Molecules Using State-Dependent Optical Tweezer Traps

We show how state-dependent optical potentials can be used to trap a pair of molecules in different internal states at a separation much smaller than the wavelength of the trapping light. This close spacing greatly enhances the dipole-dipole interaction and we show how it can be used to implement two-qubit gates between molecules that are 100 times faster than existing protocols and than rotational coherence times already demonstrated. We analyze complications due to hyperfine structure, tensor light shifts, photon scattering, and collisional loss, and conclude that none is a barrier to implementing the scheme.

Electron Electric Dipole Moment Searches Using Clock Transitions in Ultracold Molecules

Permanent electric dipole moments (EDMs) of fundamental particles such as the electron are signatures of parity and time-reversal violation occurring in physics beyond the standard model. EDM measurements probe new physics at energy scales well beyond the reach of present-day colliders. Recent advances in assembling molecules from ultracold atoms have opened up new opportunities for improving the reach of EDM experiments. However, the magnetic field sensitivity of such ultracold molecules means that new measurement techniques are needed before these opportunities can be fully exploited. We present a technique that takes advantage of magnetically insensitive hyperfine clock transitions in polar molecules, offering a way to improve both the precision and accuracy of EDM searches with ultracold assembled molecules.

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.

Observation of Collisions between Two Ultracold Ground-State CaF Molecules

We measure inelastic collisions between ultracold CaF molecules by combining two optical tweezers, each containing a single molecule. We observe collisions between ^{2}Σ CaF molecules in the absolute ground state |X,v=0,N=0,F=0⟩, and in excited hyperfine and rotational states. In the absolute ground state, we find a two-body loss rate of 7(4)×10^{-11}  cm^{3}/s, which is below, but close to, the predicted universal loss rate.

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.

Microwave coherent control of ultracold ground-state molecules formed by short-range photoassociation

We report the observation of microwave coherent control of rotational states of ultracold ⁸⁵Rb¹³³Cs molecules formed in their vibronic ground state by short-range photoassociation. Molecules are formed in the single rotational state X(v = 0, J = 1) by exciting pairs of atoms to the short-range state (2)³Π_0^-(v = 11, J = 0), followed by spontaneous decay. We use depletion spectroscopy to record the dynamic evolution of the population distribution and observe clear Rabi oscillations while irradiating on a microwave transition between coupled neighbouring rotational levels. A density-matrix formalism that accounts for longitudinal and transverse decay times reproduces both the dynamic evolution during the coherent process and the equilibrium population. The coherent control reported here is valuable both for investigating coherent quantum effects and for applications of cold polar molecules produced by continuous short-range photoassociation.

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.

A Global Full-Dimensional Potential Energy Surface for the K2Rb2 Complex and Its Lifetime

A full-dimensional global potential energy surface for the KRb + KRb → K₂ + Rb₂ reaction is developed from 20 759 ab initio points calculated using a coupled cluster singles, doubles, and perturbative triples (CCSD(T)) method with effective core potentials, extrapolated to the complete basis set limit. The ab initio points are represented with high fidelity (root-mean-square error of 1.86 cm^-1) using the permutation-invariant polynomial-neural network method, which enforces the permutation invariance of the potential with respect to exchange of identical nuclei. The potential energy surface features two D_2h minima and one C_s minimum connected by the isomerization saddle points. The Rice-Ramsperger-Kassel-Marcus lifetime of the K₂Rb₂ reaction intermediate estimated using the potential energy surface is 227 ns, in reasonable agreement with the latest experimental measurement.

Self-Bound Doubly Dipolar Bose-Einstein Condensates

We analyze the physics of self-bound droplets in a doubly dipolar Bose-Einstein condensate composed by particles with both electric and magnetic dipole moments. Using the particularly relevant case of dysprosium, we show that the anisotropy of the doubly dipolar interaction potential is highly versatile and nontrivial, depending critically on the relative orientation and strength between the two dipole moments. This opens novel possibilities for exploring intriguing quantum many-body physics. Interestingly, by varying the angle between the two dipoles we find a dimensional crossover from quasi-one-dimensional to quasi-two-dimensional self-bound droplets. This opens a so far unique scenario in condensate physics, in which a dimensional crossover is solely driven by interactions in the absence of any confinement.

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.

Feshbach Resonances in p-Wave Three-Body Recombination within Fermi-Fermi Mixtures of Open-Shell 6Li and Closed-Shell 173Yb Atoms

We report on the observation of magnetic Feshbach resonances in a Fermi-Fermi mixture of ultracold atoms with extreme mass imbalance and on their unique p-wave dominated three-body recombination processes. Our system consists of open-shell alkali-metal 6Li and closed-shell 173Yb atoms, both spin polarized and held at various temperatures between 1 and 20 μK. We confirm that Feshbach resonances in this system are solely the result of a weak separation-dependent hyperfine coupling between the electronic spin of 6Li and the nuclear spin of 173Yb. Our analysis also shows that three-body recombination rates are controlled by the identical fermion nature of the mixture, even in the presence of s-wave collisions between the two species and with recombination rate coefficients outside the Wigner threshold regime at our lowest temperature. Specifically, a comparison of experimental and theoretical line shapes of the recombination process indicates that the characteristic asymmetric line shape as a function of applied magnetic field and a maximum recombination rate coefficient that is independent of temperature can only be explained by triatomic collisions with nonzero, p-wave total orbital angular momentum. The resonances can be used to form ultracold doublet ground-state molecules and to simulate quantum superfluidity in mass-imbalanced mixtures.