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 collisions3-7 and collisions between Feshbach molecules, which are very weakly bound8-10. 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 complex11-15. 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.

Collisional cooling of ultracold molecules.

Since the original work on Bose-Einstein condensation1,2, the use of quantum degenerate gases of atoms has enabled the quantum emulation of important systems in condensed matter and nuclear physics, as well as the study of many-body states that have no analogue in other fields of physics3. Ultracold molecules in the micro- and nanokelvin regimes are expected to bring powerful capabilities to quantum emulation4 and quantum computing5, owing to their rich internal degrees of freedom compared to atoms, and to facilitate precision measurement and the study of quantum chemistry6. Quantum gases of ultracold atoms can be created using collision-based cooling schemes such as evaporative cooling, but thermalization and collisional cooling have not yet been realized for ultracold molecules. Other techniques, such as the use of supersonic jets and cryogenic buffer gases, have reached temperatures limited to above 10 millikelvin7,8. Here we show cooling of NaLi molecules to micro- and nanokelvin temperatures through collisions with ultracold Na atoms, with both molecules and atoms prepared in their stretched hyperfine spin states. We find a lower bound on the ratio of elastic to inelastic molecule-atom collisions that is greater than 50-large enough to support sustained collisional cooling. By employing two stages of evaporation, we increase the phase-space density of the molecules by a factor of 20, achieving temperatures as low as 220 nanokelvin. The favourable collisional properties of the Na-NaLi system could enable the creation of deeply quantum degenerate dipolar molecules and raises the possibility of using stretched spin states in the cooling of other molecules.

Spin transport in a tunable Heisenberg model realized with ultracold atoms.

Simple models of interacting spins have an important role in physics. They capture the properties of many magnetic materials, but also extend to other systems, such as bosons and fermions in a lattice, gauge theories, high-temperature superconductors, quantum spin liquids, and systems with exotic particles such as anyons and Majorana fermions1,2. To study and compare these models, a versatile platform is needed. Realizing such systems has been a long-standing goal in the field of ultracold atoms. So far, spin transport has only been studied in systems with isotropic spin-spin interactions3-12. Here we realize the Heisenberg model describing spins on a lattice, with fully adjustable anisotropy of the nearest-neighbour spin-spin couplings (called the XXZ model). In this model we study spin transport far from equilibrium after quantum quenches from imprinted spin-helix patterns. When spins are coupled only along two of three possible orientations (the XX model), we find ballistic behaviour of spin dynamics, whereas for isotropic interactions (the XXX model), we find diffusive behaviour. More generally, for positive anisotropies, the dynamics ranges from anomalous superdiffusion to subdiffusion, whereas for negative anisotropies, we observe a crossover in the time domain from ballistic to diffusive transport. This behaviour is in contrast with expectations from the linear-response regime and raises new questions in understanding quantum many-body dynamics far away from equilibrium.

Spin Dynamics Dominated by Resonant Tunneling into Molecular States.

Optical lattices and Feshbach resonances are two of the most ubiquitously used tools in atomic physics, allowing for the precise control, discrete confinement, and broad tunability of interacting atomic systems. Using a quantum simulator of lithium-7 atoms in an optical lattice, we investigate Heisenberg spin dynamics near a Feshbach resonance. We find novel resonance features in spin-spin interactions that can be explained only by lattice-induced resonances, which have never been observed before. We use these resonances to adiabatically convert atoms into molecules in excited bands. Lattice-induced resonances should be of general importance for studying strongly interacting quantum many-body systems in optical lattices.

Dynamics of Stripe Patterns in Supersolid Spin-Orbit-Coupled Bose Gases.

Despite ground-breaking observations of supersolidity in spin-orbit-coupled Bose-Einstein condensates, until now the dynamics of the emerging spatially periodic density modulations has been vastly unexplored. Here, we demonstrate the nonrigidity of the density stripes in such a supersolid condensate and explore their dynamic behavior subject to spin perturbations. We show both analytically in infinite systems and numerically in the presence of a harmonic trap how spin waves affect the supersolid's density profile in the form of crystal waves, inducing oscillations of the periodicity as well as the orientation of the fringes. Both these features are well within reach of present-day experiments. Our results show that this system is a paradigmatic supersolid, featuring superfluidity in conjunction with a fully dynamic crystalline structure.

A stripe phase with supersolid properties in spin-orbit-coupled Bose-Einstein condensates.

Supersolidity combines superfluid flow with long-range spatial periodicity of solids, two properties that are often mutually exclusive. The original discussion of quantum crystals and supersolidity focused on solid 4He and triggered extensive experimental efforts that, instead of supersolidity, revealed exotic phenomena including quantum plasticity and mass supertransport. The concept of supersolidity was then generalized from quantum crystals to other superfluid systems that break continuous translational symmetry. Bose-Einstein condensates with spin-orbit coupling are predicted to possess a stripe phase with supersolid properties. Despite several recent studies of the miscibility of the spin components of such a condensate, the presence of stripes has not been detected. Here we observe the predicted density modulation of this stripe phase using Bragg reflection (which provides evidence for spontaneous long-range order in one direction) while maintaining a sharp momentum distribution (the hallmark of superfluid Bose-Einstein condensates). Our work thus establishes a system with continuous symmetry-breaking properties, associated collective excitations and superfluid behaviour.

Preparation of the Spin-Mott State: A Spinful Mott Insulator of Repulsively Bound Pairs.

We observe and study a special ground state of bosons with two spin states in an optical lattice: the spin-Mott insulator, a state that consists of repulsively bound pairs that is insulating for both spin and charge transport. Because of the pairing gap created by the interaction anisotropy, it can be prepared with low entropy and can serve as a starting point for adiabatic state preparation. We find that the stability of the spin-Mott state depends on the pairing energy, and observe two qualitatively different decay regimes, one of which exhibits protection by the gap.

Tunable Single-Ion Anisotropy in Spin-1 Models Realized with Ultracold Atoms.

Mott insulator plateaus in optical lattices are a versatile platform to study spin physics. Using sites occupied by two bosons with an internal degree of freedom, we realize a uniaxial single-ion anisotropy term proportional to (S^{z})^{2} that plays an important role in stabilizing magnetism for low-dimensional magnetic materials. Here we explore nonequilibrium spin dynamics and observe a resonant effect in the spin alignment as a function of lattice depth when exchange coupling and on-site anisotropy are similar. Our results are supported by many-body numerical simulations and are captured by the analytical solution of a two-site model.

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.

Enhanced Superexchange in a Tilted Mott Insulator.

In an optical lattice, entropy and mass transport by first-order tunneling are much faster than spin transport via superexchange. Here we show that adding a constant force (tilt) suppresses first-order tunneling, but not spin transport, realizing new features for spin Hamiltonians. Suppression of the superfluid transition can stabilize larger systems with faster spin dynamics. For the first time in a many-body spin system, we vary superexchange rates by over a factor of 100 and tune spin-spin interactions via the tilt. In a tilted lattice, defects are immobile and pure spin dynamics can be studied.

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.

How to Dress Radio-Frequency Photons with Tunable Momentum.

We demonstrate how the combination of oscillating magnetic forces and radio-frequency (rf) pulses endows rf photons with tunable momentum. We observe velocity-selective spin-flip transitions and the associated Doppler shift. Recoil-dressed photons are a promising tool for measurements and quantum simulations, including the realization of gauge potentials and spin-orbit coupling schemes which do not involve optical transitions.

Λ-Enhanced Imaging of Molecules in an Optical Trap.

We report on nondestructive imaging of optically trapped calcium monofluoride molecules using in situ Λ-enhanced gray molasses cooling. 200 times more fluorescence is obtained compared to destructive on-resonance imaging, and the trapped molecules remain at a temperature of 20 µK. The achieved number of scattered photons makes possible nondestructive single-shot detection of single molecules with high fidelity.

Two-photon spectroscopy of the NaLi triplet ground state.

We employ two-photon spectroscopy to study the vibrational states of the triplet ground state potential (a3Σ+) of the 23Na6Li molecule. Pairs of Na and Li atoms in an ultracold mixture are photoassociated into an excited triplet molecular state, which in turn is coupled to vibrational states of the triplet ground potential. Vibrational state binding energies, line strengths, and potential fitting parameters for the triplet ground a3Σ+ potential are reported. We also observe rotational splitting in the lowest vibrational state.

Photoassociation of ultracold NaLi.

We perform photoassociation spectroscopy in an ultracold 23Na-6Li mixture to study the c3Σ+ excited triplet molecular potential. We observe 50 vibrational states and their substructure to an accuracy of 20 MHz, and provide line strength data from photoassociation loss measurements. An analysis of the vibrational line positions using near-dissociation expansions and a full potential fit is presented. This is the first observation of the c3Σ+ potential, as well as photoassociation in the NaLi system.

Long-Lived Ultracold Molecules with Electric and Magnetic Dipole Moments.

We create fermionic dipolar ^{23}Na^{6}Li molecules in their triplet ground state from an ultracold mixture of ^{23}Na and ^{6}Li. Using magnetoassociation across a narrow Feshbach resonance followed by a two-photon stimulated Raman adiabatic passage to the triplet ground state, we produce 3×10^{4} ground state molecules in a spin-polarized state. We observe a lifetime of 4.6 s in an isolated molecular sample, approaching the p-wave universal rate limit. Electron spin resonance spectroscopy of the triplet state was used to determine the hyperfine structure of this previously unobserved molecular state.

Radio Frequency Magneto-Optical Trapping of CaF with High Density.

We demonstrate significantly improved magneto-optical trapping of molecules using a very slow cryogenic beam source and either rf modulated or dc magnetic fields. The rf magneto-optical trap (MOT) confines 1.0(3)×10^{5} CaF molecules at a density of 7(3)×10^{6} cm^{-3}, which is an order of magnitude greater than previous molecular MOTs. Near Doppler-limited temperatures of 340(20) µK are attained. The achieved density enables future work to directly load optical tweezers and create optical arrays for quantum simulation.

Coherence Times of Bose-Einstein Condensates beyond the Shot-Noise Limit via Superfluid Shielding.

We demonstrate a new way to extend the coherence time of separated Bose-Einstein condensates that involves immersion into a superfluid bath. When both the system and the bath have similar scattering lengths, immersion in a superfluid bath cancels out inhomogeneous potentials either imposed by external fields or inherent in density fluctuations due to atomic shot noise. This effect, which we call superfluid shielding, allows for coherence lifetimes beyond the projection noise limit. We probe the coherence between separated condensates in different sites of an optical lattice by monitoring the contrast and decay of Bloch oscillations. Our technique demonstrates a new way that interactions can improve the performance of quantum devices.

Spin-Orbit Coupling and Spin Textures in Optical Superlattices.

We propose and demonstrate a new approach for realizing spin-orbit coupling with ultracold atoms. We use orbital levels in a double-well potential as pseudospin states. Two-photon Raman transitions between left and right wells induce spin-orbit coupling. This scheme does not require near resonant light, features adjustable interactions by shaping the double-well potential, and does not depend on special properties of the atoms. A pseudospinor Bose-Einstein condensate spontaneously acquires an antiferromagnetic pseudospin texture, which breaks the lattice symmetry similar to a supersolid.

Weyl Points in Three-Dimensional Optical Lattices: Synthetic Magnetic Monopoles in Momentum Space.

We show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three-dimensional optical lattices. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl fermions, which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in condensed matter physics due to their unusual properties such as the topologically protected "Fermi arc" surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is well within experimental reach with an extension of techniques recently used in ultracold gases.