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How does a chemical reaction proceed at ultralow temperatures? Can simple quantum mechanical rules such as quantum statistics, single partial-wave scattering, and quantum threshold laws provide a clear understanding of the molecular reactivity under a vanishing collision energy? Starting with an optically trapped near-quantum-degenerate gas of polar ⁴⁰K⁸⁷Rb molecules prepared in their absolute ground state, we report experimental evidence for exothermic atom-exchange chemical reactions. When these fermionic molecules were prepared in a single quantum state at a temperature of a few hundred nanokelvin, we observed p-wave-dominated quantum threshold collisions arising from tunneling through an angular momentum barrier followed by a short-range chemical reaction with a probability near unity. When these molecules were prepared in two different internal states or when molecules and atoms were brought together, the reaction rates were enhanced by a factor of 10 to 100 as a result of s-wave scattering, which does not have a centrifugal barrier. The measured rates agree with predicted universal loss rates related to the two-body van der Waals length.

Alkaline-earth atoms have metastable ‘clock’ states with minute-long optical lifetimes, high-spin nuclei and SU( N )-symmetric interactions, making them powerful platforms for atomic clocks 1 , quantum information processing 2 and quantum simulation 3 . Few-particle systems of such atoms provide opportunities to observe the emergence of complex many-body phenomena with increasing system size 4 . Multi-body interactions among particles are emergent phenomena, which cannot be broken down into sums over underlying pairwise interactions. They could potentially be used to create exotic states of quantum matter 5 , 6 , but have yet to be explored in ultracold fermions. Here we create arrays of isolated few-body systems in an optical clock based on a three-dimensional lattice of fermionic 87 Sr atoms. We use high-resolution clock spectroscopy to directly observe the onset of elastic and inelastic multi-body interactions among atoms. We measure the frequency shifts of the clock transition for varying numbers of atoms per lattice site, from n  = 1 to n  = 5, and observe nonlinear interaction shifts characteristic of elastic multi-body effects. These measurements, combined with theory, elucidate an emergence of SU( N )-symmetric multi-body interactions, which are unique to fermionic alkaline-earth atoms. To study inelastic multi-body effects, we use these frequency shifts to isolate n -occupied sites in the lattice and measure the corresponding lifetimes of the clock states. This allows us to access the short-range few-body physics without experiencing the systematic effects that are encountered in a bulk gas. The lifetimes that we measure in the isolated few-body systems agree very well with numerical predictions based on a simple model for the interatomic potential, suggesting a universality in ultracold collisions. By connecting these few-body systems through tunnelling, the favourable energy and timescales of the interactions will allow our system to be used for studies of high-spin quantum magnetism 7 , 8 and the Kondo effect 3 , 9 . Clock spectroscopy of ultracold strontium atoms in a three-dimensional optical lattice is used to observe the onset of multi-body interactions that result from the underlying pairwise interactions between atoms.

A quantum gas of ultracold polar molecules, with long-range and anisotropic interactions, not only would enable explorations of a large class of many-body physics phenomena but also could be used for quantum information processing. We report on the creation of an ultracold dense gas of potassium-rubidium (⁴⁰K⁸⁷Rb) polar molecules. Using a single step of STIRAP (stimulated Raman adiabatic passage) with two-frequency laser irradiation, we coherently transfer extremely weakly bound KRb molecules to the rovibrational ground state of either the triplet or the singlet electronic ground molecular potential. The polar molecular gas has a peak density of 10¹² per cubic centimeter and an expansion-determined translational temperature of 350 nanokelvin. The polar molecules have a permanent electric dipole moment, which we measure with Stark spectroscopy to be 0.052(2) Debye (1 Debye = 3.336 x 10⁻³⁰ coulomb-meters) for the triplet rovibrational ground state and 0.566(17) Debye for the singlet rovibrational ground state.

A rich internal structure and long-range interactions between them make molecules with non-vanishing dipole moments interesting for many applications. An experiment demonstrating the efficient transfer of loosely bound heteronuclear molecules into more deeply bound energy levels indicates a route towards producing dense ensembles of cold polar molecules. Polar molecules have bright prospects for novel quantum gases with long-range and anisotropic interactions 1 , and could find uses in quantum information science 2 and in precision measurements 3 , 4 , 5 . However, high-density clouds of ultracold polar molecules have so far not been produced. Here, we report a key step towards this goal. We start from an ultracold dense gas of loosely bound 40 K 87 Rb Feshbach molecules 6 , 7 with typical binding energies of a few hundred kilohertz, and coherently transfer these molecules in a single transfer step into a vibrational level of the ground-state molecular potential bound by more than 10 GHz. Starting with a single initial state prepared with Feshbach association 8 , we achieve a transfer efficiency of 84%. Given favourable Franck–Condon factors 9 , 10 , the presented technique can be extended to access much more deeply bound vibrational levels and those exhibiting a significant dipole moment.

We study polar molecule scattering in quasi-one-dimensional geometries. Elastic and reactive collision rates are computed as a function of collision energy and electric dipole moment for different confinement strengths. The numerical results are interpreted in terms of first order scattering and of adiabatic models. Universal dipolar scattering is also discussed. Our results are relevant to experiments where control of the collision dynamics through one-dimensional confinement and an applied electric field is envisioned.

The advent of the laser as an intense source of coherent light gave rise to nonlinear optics, which now plays an important role in many areas of science and technology. One of the first applications of nonlinear optics was the multi-wave mixing 1 , 2 of several optical fields in a nonlinear medium (one in which the refractive index depends on the intensity of the field) to produce coherent light of a new frequency. The recent experimental realization of the matter-wave ‘laser’ 3 , 4 —based on the extraction of coherent atoms from a Bose–Einstein condensate 5 —opens the way for analogous experiments with intense sources of matter waves: nonlinear atom optics 6 . Here we report coherent four-wave mixing in which three sodium matter waves of differing momenta mix to produce, by means of nonlinear atom–atom interactions, a fourth wave with new momentum. We find a clear signature of a four-wave mixing process in the dependence of the generated matter wave on the densities of the input waves. Our results may ultimately facilitate the production and investigation of quantum correlations between matter waves.

Fermionic alkaline-earth atoms have unique properties that make them attractive candidates for the realization of atomic clocks and degenerate quantum gases. At the same time, they are attracting considerable theoretical attention in the context of quantum information processing. Here we demonstrate that when such atoms are loaded in optical lattices, they can be used as quantum simulators of unique many-body phenomena. In particular, we show that the decoupling of the nuclear spin from the electronic angular momentum can be used to implement many-body systems with an unprecedented degree of symmetry, characterized by the S U ( N ) group with N as large as 10. Moreover, the interplay of the nuclear spin with the electronic degree of freedom provided by a stable optically excited state should enable the study of physics governed by the spin–orbital interaction. Such systems may provide valuable insights into the physics of strongly correlated transition-metal oxides, heavy-fermion materials and spin-liquid phases. Building on ideas from quantum information science and on recent experimental advances, the use of ultracold alkaline-earth atoms in optical lattices as quantum simulators of many-body phenomena is proposed. The corresponding models possess a high degree of symmetry and may provide fundamental insights into strongly correlated systems.

State of the art photoassociative measurements of bound state energies in the ground state Yb2 molecule are used to establish limits on non-Newtonian gravity at Yukawa ranges of nanometers.

The production of ultracold molecules with their rich internal structure is currently attracting considerable interest 1 , 2 , 3 , 4 . For future experiments, it will be important to efficiently transfer these molecules from their initial internal quantum state at production to other quantum states of interest. Transfer tools such as optical Raman schemes 5 , 6 , radiofrequency transitions (see, for example, ref.  7 ) or magnetic field ramping 8 , 9 exist, but are either technically involved or limited in their applicability. Here, we demonstrate a simple, highly efficient hybrid transfer method that overcomes a number of the previous limitations. The scheme is based on magnetically tuned mixing of two neighbouring molecular levels, which enables otherwise forbidden radiofrequency transitions between them. By repeating this process at various magnetic fields, molecules can be successively transported through a large manifold of quantum states. Applying nine transfers, we convert very weakly bound Feshbach molecules to a much more deeply bound level with a binding energy corresponding to 3.6 GHz. As an important spin-off of our experiments, we demonstrate a high-precision spectroscopy method for investigating level crossings.