Observation of Bose-Einstein condensation of dipolar molecules

Ensembles of particles governed by quantum mechanical laws exhibit intriguing emergent behaviour. Atomic quantum gases1,2, liquid helium3,4 and electrons in quantum materials5-7 all exhibit distinct properties because of their composition and interactions. Quantum degenerate samples of ultracold dipolar molecules promise the realization of new phases of matter and new avenues for quantum simulation8 and quantum computation9. However, rapid losses10, even when reduced through collisional shielding techniques11-13, have so far prevented evaporative cooling to a Bose-Einstein condensate (BEC). Here we report on the realization of a BEC of dipolar molecules. By strongly suppressing two- and three-body losses via enhanced collisional shielding, we evaporatively cool sodium-caesium molecules to quantum degeneracy and cross the phase transition to a BEC. The BEC reveals itself by a bimodal distribution when the phase-space density exceeds 1. BECs with a condensate fraction of 60(10)% and a temperature of 6(2) nK are created and found to be stable with a lifetime close to 2 s. This work opens the door to the exploration of dipolar quantum matter in regimes that have been inaccessible so far, promising the creation of exotic dipolar droplets14, self-organized crystal phases15 and dipolar spin liquids in optical lattices16.

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.

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.

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.

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.

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.

Time-Dependent Wave Packet Dynamics Calculations of Cross Sections for Ultracold Four-Atom Reactions

We report here the first time-dependent wave packet dynamics study for an ultracold four-atom reaction. Our calculations provide accurate integral cross sections and rate constants all the way down to the Bethe-Wigner threshold regime for the benchmark OH + H₂(v = 2, j = 0) → H₂O + H reaction, indicating that the time-dependent wave packet method is a powerful tool for studying ultracold four-atom reactions.

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.

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.

Hyperfine structure of the NaCs b3Π2 state near the dissociation limit 3S1/2 + 6P3/2 observed with ultracold atomic photoassociation

We report new observations of the hyperfine structure in three ro-vibrational levels of the b³Π₂ state of NaCs near the dissociation limit 3S_1/2 + 6P_3/2. The experiment was done via photoassociation of ultracold atoms in a dual-species dark-spot magneto-optical trap, and the spectra were measured as atomic trap losses. The simulation of the hyperfine structure showed that the greater part of the observed structure belongs to almost isolated levels of the b³Π₂ state, but there are other parts of mixed character where the contribution from the ¹Σ symmetry dominates.

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.

Ultracold Rare-Earth Magnetic Atoms with an Electric Dipole Moment

We propose a new method to produce an electric and magnetic dipolar gas of ultracold dysprosium atoms. The pair of nearly degenerate energy levels of opposite parity, at 17513.33  cm^{-1} with electronic angular momentum J=10, and at 17514.50  cm^{-1} with J=9, can be mixed with an external electric field, thus inducing an electric dipole moment in the laboratory frame. For field amplitudes relevant to current-day experiments, i.e., an electric field of 5  kV/cm, we predict a large magnetic dipole moment up to 13 Bohr magnetons, and sizeable electric dipole moment up to 0.22 D. When a magnetic field is present, we show that the induced electric dipole moment is strongly dependent on the angle between the fields. The lifetime of the field-mixed levels is found in the millisecond range, thus allowing for suitable experimental detection and manipulation.

Observation of photoassociation of ultracold sodium and cesium at the asymptote Na (3S1/2) + Cs (6P1/2)

We report on the production of ultracold heteronuclear NaCs* molecules in a dual-species magneto-optical trap through photoassociation. The electronically excited molecules are formed below the Na (3S_1/2) + Cs (6P_1/2) dissociation limit. 12 resonance lines are detected using trap-loss spectroscopy based on a highly sensitive modulation technique. The highest observed rovibrational level exhibits clear hyperfine structure, which is detected for the first time. This structure is simulated within a simplified model consisting of 4 coupled levels belonging to the initially unperturbed Hund's case "a" electronic states, which have been explored in our previous work that dealt with the Na (3S_1/2) + Cs (6P_3/2) asymptote [W. Liu et al., Phys. Rev. A 94, 032518 (2016)].

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.

Molecular collisions and reactive scattering in external fields: Are field-induced couplings important at short range?

We use accurate quantum scattering calculations to elucidate the role of short-range molecule-field interactions in atom-molecule inelastic collisions and abstraction chemical reactions at low temperatures. We consider two examples: elastic and inelastic scattering of NH(Σ3) molecules with Mg(S1) atoms in a magnetic field; reactive scattering LiF + H → Li + HF in an electric field. Our calculations suggest that, for non-reactive collision systems and abstraction chemical reactions, the molecule-field interactions cannot generally be neglected at short range because the atom-molecule potential passes through zero at short range. An important exception occurs for Zeeman transitions in atom-molecule collisions at magnetic fields ≲1000 G, for which the molecule-field couplings need only be included at large ρ outside the range of the atom-molecule interaction. Our results highlight the importance of an accurate description of ρ-dependent molecule-field interactions in quantum scattering calculations on molecular collisions and chemical reactions at low temperatures.

Ultracold Nonreactive Molecules in an Optical Lattice: Connecting Chemistry to Many-Body Physics

We derive effective lattice models for ultracold bosonic or fermionic nonreactive molecules (NRMs) in an optical lattice, analogous to the Hubbard model that describes ultracold atoms in a lattice. In stark contrast to the Hubbard model, which is commonly assumed to accurately describe NRMs, we find that the single on-site interaction parameter U is replaced by a multichannel interaction, whose properties we elucidate. Because this arises from complex short-range collisional physics, it requires no dipolar interactions and thus occurs even in the absence of an electric field or for homonuclear molecules. We find a crossover between coherent few-channel models and fully incoherent single-channel models as the lattice depth is increased. We show that the effective model parameters can be determined in lattice modulation experiments, which, consequently, measure molecular collision dynamics with a vastly sharper energy resolution than experiments in a free-space ultracold gas.

Long-range interactions between polar bialkali ground-state molecules in arbitrary vibrational levels

We have calculated the isotropic C6 coefficients characterizing the long-range van der Waals interaction between two identical heteronuclear alkali-metal diatomic molecules in the same arbitrary vibrational level of their ground electronic state X(1)Σ(+). We consider the ten species made up of (7)Li, (23)Na, (39)K, (87)Rb, and (133)Cs. Following our previous work [Lepers et al., Phys. Rev. A 88, 032709 (2013)], we use the sum-over-state formula inherent to the second-order perturbation theory, composed of the contributions from the transitions within the ground state levels, from the transition between ground-state and excited state levels, and from a crossed term. These calculations involve a combination of experimental and quantum-chemical data for potential energy curves and transition dipole moments. We also investigate the case where the two molecules are in different vibrational levels and we show that the Moelwyn-Hughes approximation is valid provided that it is applied for each of the three contributions to the sum-over-state formula. Our results are particularly relevant in the context of inelastic and reactive collisions between ultracold bialkali molecules in deeply bound or in Feshbach levels.

Spin waves and dielectric softening of polar molecule condensates

We consider an oblate Bose-Einstein condensate of heteronuclear polar molecules in a weak applied electric field. This system supports a rich quasiparticle spectrum that plays a critical role in determining its bulk dielectric properties. In particular, in sufficiently weak fields the system undergoes a polarization wave rotonization, leading to the development of textured electronic structure and a dielectric instability that is characteristic of the onset of a negative static dielectric function.

Deviation from universality in collisions of ultracold 6Li2 molecules

Collisions of 6Li2 molecules with free 6Li atoms reveal a striking deviation from universal predictions based on long-range van der Waals interactions. Li2 closed-channel molecules are formed in the highest vibrational state near a narrow Feshbach resonance and decay via two-body collisions with Li2, Li, and Na. For Li2 + Li2 and Li2 + Na, the decay rates agree with the universal predictions of the quantum Langevin model. In contrast, the rate for Li2 + Li is exceptionally small, with an upper bound 10 times smaller than the universal prediction. This can be explained by the low density of available decay states in systems of light atoms [G. Quéméner, J.-M. Launay, and P. Honvault, Phys. Rev. A 75, 050701 (2007)], for which such collisions have not been studied before.

Optical production of stable ultracold (88)Sr(2) molecules

We have produced large samples of stable ultracold (88)Sr(2) molecules in the electronic ground state in an optical lattice. The fast, all-optical method of molecule creation involves a near-intercombination-line photoassociation pulse followed by spontaneous emission with a near-unity Franck-Condon factor. The detection uses excitation to a weakly bound electronically excited vibrational level corresponding to a very large dimer and yields a high-Q molecular vibronic resonance. This is the first of two steps needed to create deeply bound (88)Sr(2) for frequency metrology and ultracold chemistry.

Resonant control of polar molecules in individual sites of an optical lattice

We study the resonant control of two nonreactive polar molecules in an optical lattice site, focusing on the example of RbCs. Collisional control can be achieved by tuning bound states of the intermolecular dipolar potential by varying the applied electric field or trap frequency. We consider a wide range of electric fields and trapping geometries, showing that a three-dimensional optical lattice allows significantly wider avoided crossings than free space or quasi-two dimensional geometries. Furthermore, we find that dipolar confinement-induced resonances can be created with reasonable trapping frequencies and electric fields, and have widths that will enable useful control in forthcoming experiments.