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.

Nuclear spin conservation enables state-to-state control of ultracold molecular reactions.

Quantum-state control of reactive systems has enabled microscopic probes of underlying interaction potentials and the alteration of reaction rates using quantum statistics. However, extending such control to the quantum states of reaction outcomes remains challenging. Here, we realize this goal by utilizing the conservation of nuclear spins throughout the reaction. Using resonance-enhanced multiphoton ionization spectroscopy to investigate the products formed in bimolecular reactions between ultracold KRb molecules we find that the system retains a near-perfect memory of the reactants' nuclear spins, manifested as a strong parity preference for the rotational states of the products. We leverage this effect to alter the occupation of these product states by changing the coherent superposition of initial nuclear spin states with an external magnetic field. In this way, we are able to control both the inputs and outputs of a reaction with quantum-state resolution. The techniques demonstrated here open up the possibilities to study quantum entanglement between reaction products and ultracold reaction dynamics at the state-to-state level.

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.

Controlling the Scattering Length of Ultracold Dipolar Molecules.

By applying a circularly polarized and slightly blue-detuned microwave field with respect to the first excited rotational state of a dipolar molecule, one can engineer a long-range, shallow potential well in the entrance channel of the two colliding partners. As the applied microwave ac field is increased, the long-range well becomes deeper and can support a certain number of bound states, which in turn bring the value of the molecule-molecule scattering length from a large negative value to a large positive one. We adopt an adimensional approach where the molecules are described by a rescaled rotational constant B[over ˜]=B/s_{E_{3}} where s_{E_{3}} is a characteristic dipolar energy. We found that molecules with B[over ˜]>10^{8} are immune to any quenching losses when a sufficient ac field is applied, the ratio elastic to quenching processes can reach values above 10^{3}, and that the value and sign of the scattering length can be tuned. The ability to control the molecular scattering length opens the door for a rich, strongly correlated, many-body physics for ultracold molecules, similar to that for ultracold atoms.

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.

Collisions of ultracold 23Na87Rb molecules with controlled chemical reactivities.

The collision of molecules at ultracold temperatures is of great importance to understand the chemical interactions at the quantum regime. Although much theoretical work has been devoted to this, experimental data are only sparsely available, mainly because of the difficulty in producing ground-state molecules at ultracold temperatures. We report here the creation of optically trapped samples of ground-state bosonic sodium-rubidium molecules with precisely controlled internal states and, enabled by this, a detailed study on the inelastic loss with and without the NaRb + NaRb → Na2 + Rb2 chemical reaction. Contrary to intuitive expectations, we observed very similar loss and heating, regardless of the chemical reactivities. In addition, as evidenced by the reducing loss rate constants with increasing temperatures, we found that these collisions are already outside the Wigner region although the sample temperatures are sub-microkelvin. Our measurement agrees semiquantitatively with models based on long-range interactions but calls for a deeper understanding on the short-range physics for a more complete interpretation.

Creation of an Ultracold Gas of Ground-State Dipolar

We report the successful production of an ultracold sample of absolute ground-state ^{23}Na^{87}Rb molecules. Starting from weakly bound Feshbach molecules formed via magnetoassociation, the lowest rovibrational and hyperfine level of the electronic ground state is populated following a high-efficiency and high-resolution two-photon Raman process. The high-purity absolute ground-state samples have up to 8000 molecules and densities of over 10^{11} cm^{-3}. By measuring the Stark shifts induced by external electric fields, we determined the permanent electric dipole moment of the absolute ground-state ^{23}Na^{87}Rb and demonstrated the capability of inducing an effective dipole moment over 1 D. Bimolecular reaction between ground-state ^{23}Na^{87}Rb molecules is endothermic, but we still observed a rather fast decay of the molecular sample. Our results pave the way toward investigation of ultracold molecular collisions in a fully controlled manner and possibly to quantum gases of ultracold bosonic molecules with strong dipolar interactions.

Evaporative cooling of the dipolar hydroxyl radical.

Atomic physics was revolutionized by the development of forced evaporative cooling, which led directly to the observation of Bose-Einstein condensation, quantum-degenerate Fermi gases and ultracold optical lattice simulations of condensed-matter phenomena. More recently, substantial progress has been made in the production of cold molecular gases. Their permanent electric dipole moment is expected to generate systems with varied and controllable phases, dynamics and chemistry. However, although advances have been made in both direct cooling and cold-association techniques, evaporative cooling has not been achieved so far. This is due to unfavourable ratios of elastic to inelastic scattering and impractically slow thermalization rates in the available trapped species. Here we report the observation of microwave-forced evaporative cooling of neutral hydroxyl (OH(•)) molecules loaded from a Stark-decelerated beam into an extremely high-gradient magnetic quadrupole trap. We demonstrate cooling by at least one order of magnitude in temperature, and a corresponding increase in phase-space density by three orders of magnitude, limited only by the low-temperature sensitivity of our spectroscopic thermometry technique. With evaporative cooling and a sufficiently large initial population, much colder temperatures are possible; even a quantum-degenerate gas of this dipolar radical (or anything else it can sympathetically cool) may be within reach.

Ultracold collisions and reactions of vibrationally excited OH radicals with oxygen atoms.

We report a quantum dynamics study of O + OH (v = 1, j = 0) collisions on its ground electronic state, employing two different potential energy surfaces: the DIMKP surface by Kendrick and Pack, and the XXZLG surface by Xu et al. A time-independent quantum mechanical method based on hyperspherical coordinates has been adopted for the dynamics calculations. Energy-dependent probabilities and rate coefficients are computed for the elastic, inelastic, and reactive channels over the collision energy range E(coll) = 10(-10)-0.35 eV, for J = 0 total angular momentum. Initial state-selected reaction rate coefficients are also calculated from the J = 0 reaction probabilities by applying a J-shifting approximation, for temperatures in the range T = 10(-6)-700 K. Our results show that the dynamics of the collisional process and its outcome are strongly influenced by long-range forces, and chemical reactivity is found to be sensitive to the choice of the potential energy surface. For O + OH (v = 1, j = 0) collisions at low temperatures, vibrational relaxation of OH competes with reactive scattering. Since long-range interactions can facilitate vibrational relaxation processes, we find that the DIMKP potential (which explicitly includes van der Waals dispersion terms) favours vibrational relaxation over chemical reaction at low temperatures. On the DIMKP potential in the ultracold regime, the reaction rate coefficient for O + OH (v = 1, j = 0) is found to be a factor of thirteen lower than that for O + OH (v = 0, j = 0). This significantly high reactivity of OH (v = 0, j = 0), compared to that of OH (v = 1, j = 0), is attributed to enhancement caused by the presence of a HO(2) quasibound state (scattering resonance) with energy near the O + OH (v = 0, j = 0) dissociation threshold. In contrast, the XXZLG potential does not contain explicit van der Waals terms, being just an extrapolation by a nearly constant function at large O-OH distances. Therefore, long-range potential couplings are absent in calculations using the XXZLG surface, which does not induce vibrational relaxation as efficiently as the DIMKP potential. The XXZLG potential leads to a slightly higher reactivity (a factor of 1.4 higher) for O + OH (v = 1, j = 0) compared to that for O + OH (v = 0, j = 0) at ultracold temperatures. Overall, both potential surfaces yield comparable values of reaction rate coefficients at low temperatures for the O + OH (v = 1, j = 0) reaction.

Quantum dynamics of the H+O(2)-->O+OH reaction.

Quantum scattering calculations of the H+O(2)-->O+OH reaction are presented using two different representations of the electronically adiabatic potential energy surface of the HO(2) system. The calculations have been performed using a three-dimensional time-independent quantum reactive scattering program based on hyperspherical coordinates. The effect of vibrational and rotational excitations of the O(2) molecule on the reactivity is investigated by carrying out calculations for vibrational quantum numbers v=0-8 and rotational quantum numbers j=1-9 for both potential surfaces. While the energy threshold for the reaction is lowered with increase in vibrational or rotational excitation of the molecule the overall energy dependence of the reaction probability remained largely unaffected with rovibrational excitations. Vibrational excitation was found to wash out resonances in the reaction probabilities. The sensitivity of the rate coefficients to the initial vibrational level of the O(2) molecule is investigated and it is found that the rate coefficient is a strong function of the vibrational quantum number of the O(2) molecule. The effect is more pronounced at low temperatures with the rate coefficient at 400 K increasing by about eight orders of magnitude when the vibrational level of O(2) is increased from 0 to 6. Thermal rate coefficients of the reaction calculated using cumulative reaction probabilities within a J-shifting approximation have been found to be in reasonable agreement with experimental results. Results show that vibrational excitation of the O(2) molecule needs to be considered in evaluating thermal rate coefficients of the reaction.

Quantum calculations of H2-H2 collisions: from ultracold to thermal energies.

We present quantum dynamics of collisions between two para-H(2) molecules from low (10(-3) K) to high collision energies (1 eV). The calculations are carried out using a quantum scattering code that solves the time-independent Schrodinger equation in its full dimensionality without any decoupling approximations. The six-dimensional potential energy surface for the H(4) system developed by Boothroyd et al. [J. Chem. Phys. 116, 666 (2002)] is used in the calculations. Elastic, inelastic, and state-to-state cross sections as well as rate coefficients from T=1 K to 400 K obtained from our calculations are compared with available experimental and theoretical results. Overall, good agreement is obtained with previous studies.

Quantum dynamics of the O + OH --> H + O2 reaction at low temperatures.

We report quantum dynamics calculations of the O + OH --> H + O(2) reaction on two different representations of the electronic ground state potential energy surface (PES) using a time-independent quantum formalism based on hyperspherical coordinates. Calculations show that several excited vibrational levels of the product O(2) molecule are populated in the reaction. Rate coefficients evaluated using both PESs were found to be very sensitive to the energy resolution of the reaction probability, especially at temperatures lower than 100 K. It is found that the rate coefficient remains largely constant in the temperature range of 10-39 K, in agreement with the conclusions of a recent experimental study [Carty et al., J. Phys. Chem. A 110, 3101 (2006)]. This is in contrast with the time-independent quantum calculations of Xu et al. [J. Chem. Phys. 127, 024304 (2007)] which, using the same PES, predicted nearly two orders of magnitude drop in the rate coefficient value from 39 to 10 K. Implications of our findings to oxygen chemistry in the interstellar medium are discussed.

Cold and ultracold chemical reactions of F+HCl and F+DCl.

We report quantum dynamics calculations of F((2)P)+HCl(v,j)-->HF(v('),j('))+Cl((2)P) and F+DCl(v,j)-->DF(v('),j('))+Cl reactions at cold and ultracold temperatures. The effect of rotational and vibrational excitations of the HCl molecule on the reactivity is investigated. It is found that, in the ultracold regime, vibrational excitation of the HCl molecule from v=0 to v=2 enhances the reactivity by four orders of magnitude. The rotational excitation from j=0 to j=1 decreases the reactivity while the rotational excitation from j=0 to j=2 increases the reactivity. The overall effect of rotational excitation was found to be much smaller than vibrational excitation. The reactivity of the F+DCl system is significantly lower than that of the F+HCl case indicating the importance of quantum tunneling at low energies. For both reactions, Feshbach resonances corresponding to Fcdots, three dots, centered HCl or Fcdots, three dots, centeredDCl triatomic states occur at low energies. We also explored the validity of the coupled-states approximation for cold collisions taking the F+HCl(v=0,j=0) reaction as an illustrative example. It is found that the coupled-states approximation is generally valid for the background scattering even at low energies but it is inadequate to accurately describe the rich resonances in the energy dependence of the cross section resulting from the decay of van der Waals complexes. It is further shown that the coupled-states approximation cannot be used for scattering in the Wigner threshold regime when the molecule is initially in a rotationally excited level.