Reactions of H2, HD, and D2 with H2+, HD+, and D2+: Product-Channel Branching Ratios and Simple Models.

We present measurements of the product-channel branching ratios of the reactions (i) HD+ + HD forming H2D+ + D (38.1(30)%) and HD2+ + H (61.9(30)%), (ii) HD+ + D2 forming HD2+ + D (61.4(35)%) and D3+ + H (38.6(35)%), and (iii) D2+ + HD forming HD2++ D (60.5(20)%) and D3+ + H (39.5(20)%) at collision energies Ecoll near zero, i.e., below kB × 1 K. These branching ratios are compared with branching ratios predicted using three simple models: a combinatorial model (M1), a model (M2) describing the reactions as H-, H+-, D-, and D+-transfer processes, and a statistical model (M3) that relates the reaction rate coefficients to the translational and rovibrational state densities of the HnD3-n+ + H/D (n = 0, 1, 2 or 3) product channels. The experimental data are incompatible with the predictions of models M1 and M2 and reveal that the branching ratios exhibit clear correlations with the product state densities.

Heteronuclear Long-Range Rydberg Molecules.

We present the formation of homonuclear Cs_{2}, K_{2}, and heteronuclear CsK long-range Rydberg molecules in a dual-species magneto-optical trap for ^{39}K and ^{133}Cs by one-photon UV photoassociation. The different ground-state-density dependence of homo- and heteronuclear photoassociation rates and the detection of stable molecular ions resulting from autoionization provide an unambiguous assignment. We perform bound-bound millimeter-wave spectroscopy of long-range Rydberg molecules to access molecular states not accessible by one-photon photoassociation. Calculations based on the most recent theoretical model and atomic parameters do not reproduce the full set of data from homo- and heteronuclear long-range Rydberg molecules consistently. This shows that photoassociation and millimeter-wave spectroscopy of heteronuclear long-range Rydberg molecules provide a benchmark for the development of theoretical models.

The H2+ + HD reaction at low collision energies: H3+/H2D+ branching ratio and product-kinetic-energy distributions.

The fully state-selected reactions between H2+ molecules in the X+ 2Σg+(v+ = 0, N+ = 0) state and HD molecules in the X 1Σg+(v = 0, J = 0) state forming H3+ + D and H2D+ + H have been studied at collision energies Ecoll between 0 and kB·30 K with a resolution of about 75 mK at the lowest energies. H2 molecules in a supersonic beam were prepared in Rydberg-Stark states with principal quantum number n = 27 and merged with a supersonic beam of ground-state HD molecules using a curved surface-electrode Rydberg-Stark decelerator and deflector. The reaction between H2+ and HD was studied within the orbit of the Rydberg electron to avoid heating of the ions by stray electric fields. The reaction was observed for well-defined and adjustable time intervals, called reaction-observation windows, between two electric-field pulses. The first pulse swept all ions away from the reaction volume and its falling edge defined the beginning of the reaction-observation window. The second pulse extracted the product ions toward a charged-particle detector located at the end of a time-of-flight tube and its rising edge defined the end of the reaction-observation window. Monitoring and analysing the time-of-flight distributions of the H3+ and H2D+ products in dependence of the duration of the reaction-observation window enabled us to obtain information on the kinetic-energy distribution of the product ions and determine branching ratios of the H3+ + D and H2D+ + H reaction channels. The mean product-kinetic-energy release is 0.46(5) eV, representing 27(3)% of the available energy, and the H3+ + D product branching ratio is 0.225(20). The relative reaction rates correspond closely to Langevin capture rates down to the lowest energies probed experimentally (≈kB·50 mK).

New Method to Study Ion-Molecule Reactions at Low Temperatures and Application to the H2++H2→H3++H Reaction.

Studies of ion-molecule reactions at low temperatures are difficult because stray electric fields in the reaction volume affect the kinetic energy of charged reaction partners. We describe a new experimental approach to study ion-molecule reactions at low temperatures and present, as example, a measurement of the H2++H2→H3++H reaction with the H2+ ion prepared in a single rovibrational state at collision energies in the range Ecol /kB =5-60 K. To reach such low-collision energies, we use a merged-beam approach and observe the reaction within the orbit of a Rydberg electron, which shields the ions from stray fields. The first beam is a supersonic beam of pure ground-state H2 molecules and the second is a supersonic beam of H2 molecules excited to Rydberg-Stark states of principal quantum number n selected in the range 20-40. Initially, the two beams propagate along axes separated by an angle of 10°. To merge the two beams, the Rydberg molecules in the latter beam are deflected using a surface-electrode Rydberg-Stark deflector. The collision energies of the merged beams are determined by measuring the velocity distributions of the two beams and they are adjusted by changing the temperature of the pulsed valve used to generate the ground-state H2 beam and by adapting the electric-potential functions applied to the electrodes of the deflector. The collision energy is varied down to below Ecol /kB =10 K, that is, below Ecol ≈1 meV, with an energy resolution of 100 µeV. We demonstrate that the Rydberg electron acts as a spectator and does not affect the cross sections, which are found to closely follow a classical Langevin-capture model in the collision energy range investigated. Because all neutral atoms and molecules can be excited to Rydberg states, this method of studying ion-molecule reactions is applicable to other reactions involving singly charged cations.

Observation of Rydberg-Atom Macrodimers: Micrometer-Sized Diatomic Molecules.

Long-range metastable molecules consisting of two cesium atoms in high Rydberg states have been observed in an ultracold gas. A sequential three-photon two-color photoassociation scheme is employed to form these molecules in states, which correlate to np(n+1)s dissociation asymptotes. Spectral signatures of bound molecular states are clearly resolved at the positions of avoided crossings between long-range van der Waals potential curves. The experimental results are in agreement with simulations based on a detailed model of the long-range multipole-multipole interactions of Rydberg-atom pair states. We show that a full model is required to accurately predict the occurrence of bound Rydberg macrodimers. The macrodimers are distinguished from repulsive molecular states by their behavior with respect to spontaneous ionization and possible decay channels are discussed.

Exotic Chemistry with Ultracold Rydberg Atoms.

We review recent experiments carried out with dense (10(12) cm(-3)) ultracold (T = 40 µK) samples of Cs atoms which have the goal to characterize, by high-resolution spectroscopy, the interactions between Cs atoms, Cs(+) ions and electrons that lead to the formation of metastable long-range molecules. The types of molecules observed in these experiments and the mechanisms leading to the aggregation of atoms in weakly bound molecules are very different from those encountered in warmer samples. In particular, we present results on molecules with binding energies of less than 0.05 J/mol and discuss their properties in the context of a new category of molecular states arising from slow-electron-atom scattering and their relation to atomic and molecular Rydberg states. One of the astonishing aspects of these types of molecules is that they can still be treated in good approximation in the realm of the Born-Oppenheimer approximation despite a huge electronic-state density. Non-Born-Oppenheimer effects are revealed by the decay of the molecules into neutral and charged fragments.

Observation of enhanced rate coefficients in the H2++H2→H3++H reaction at low collision energies.

The energy dependence of the rate coefficient of the H2++H2→H3++H reaction has been measured in the range of collision energies between kB⋅10K and kB⋅300mK. A clear deviation of the rate coefficient from the value expected on the basis of the classical Langevin-capture behavior has been observed at collision energies below kB⋅1K, which is attributed to the joint effects of the ion-quadrupole and Coriolis interactions in collisions involving ortho-H2 molecules in the j = 1 rotational level, which make up 75% of the population of the neutral H2 molecules in the experiments. The experimental results are compared to very recent predictions by Dashevskaya et al. [J. Chem. Phys. 145, 244315 (2016)], with which they are in agreement.

Experimental characterization of singlet scattering channels in long-range Rydberg molecules.

We observe the formation of long-range Cs2 Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near 6s1/2(F=3,4)→np3/2 resonances (n=26-34). The spectra reveal two types of molecular states recently predicted by D. A. Anderson, S. A. Miller, and G. Raithel [Phys. Rev. A 90, 062518 (2014)]: states bound purely by triplet s-wave scattering with binding energies ranging from 400 MHz at n=26 to 80 MHz at n=34, and states bound by mixed singlet-triplet s-wave scattering with smaller and F-dependent binding energies. The experimental observations are accounted for by an effective Hamiltonian including s-wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom. The analysis enables the characterization of the role of singlet scattering in the formation of long-range Rydberg molecules and the determination of an effective singlet s-wave scattering length for low-energy-electron-Cs collisions.

Observation of dipole-quadrupole interaction in an ultracold gas of Rydberg atoms.

We observe the direct excitation of pairs of Cs atoms from the ground state to molecular states correlating asymptotically to nsn'f asymptotes. The molecular resonances are interpreted as originating from the dipole-quadrupole interaction between the nsn'f pair states and close-by npnp asymptotes (22≤n≤32). This interpretation is supported by Stark spectroscopy of the pair states and a detailed modeling of the interaction potentials. The dipole-quadrupole interaction mixes electronic states of opposite parity and, thus, requires a coupling between electronic and nuclear motion to conserve the total parity of the system. This non-Born-Oppenheimer coupling is facilitated by the near-degeneracy of even- and odd-L partial waves in the atom-atom scattering which have opposite parity.

Inelastic collisions of ultracold polar LiCs molecules with caesium atoms in an optical dipole trap.

We investigate collisions of ultracold polar LiCs molecules and ultracold caesium atoms. LiCs molecules are formed in an optical dipole trap by photoassociation of caesium and lithium atoms via the B(1)Π excited state followed by spontaneous emission to the X(1)Σ(+) ground state and the lowest triplet state a(3)Σ(+). The molecules are then stored together with caesium atoms in the same optical trap. Rate coefficients for the loss of molecules induced by collisions with surrounding Cs atoms are measured for molecular ensembles produced via different photoassociation resonances. The results are analyzed in terms of the unitarity limit for the inelastic rates and predictions from the universal model of Idziaszek and Julienne (Phys. Rev. Lett., 2010, 104, 113202).

Calculations of static dipole polarizabilities of alkali dimers: prospects for alignment of ultracold molecules.

The rapid development of experimental techniques to produce ultracold alkali molecules opens the ways to manipulate them and to control their dynamics using external electric fields. A prerequisite quantity for such studies is the knowledge of their static dipole polarizability. In this paper, we computed the variations with internuclear distance and with vibrational index of the static dipole polarizability components of all homonuclear alkali dimers including Fr(2), and of all heteronuclear alkali dimers involving Li to Cs, in their electronic ground state and in their lowest triplet state. We use the same quantum chemistry approach as in our work on dipole moments [Aymar and Dulieu, J. Chem. Phys. 122, 204302 (2005)], based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective potentials for core polarization. Polarizabilities are extracted from electronic energies using the finite-field method. For the heaviest species Rb(2), Cs(2), and Fr(2) and for all heteronuclear alkali dimers, such results are presented for the first time. The accuracy of our results on atomic and molecular static dipole polarizabilities is discussed by comparing our values with the few available experimental data and elaborate calculations. We found that for all alkali pairs, the parallel and perpendicular components of the ground state polarizabilities at the equilibrium distance R(e) scale as (R(e))(3), which can be related to a simple electrostatic model of an ellipsoidal charge distribution. Prospects for possible alignment and orientation effects with these molecules in forthcoming experiments are discussed.