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We investigate the effects of static electric and magnetic fields on the differential ac Stark shifts for microwave transitions in ultracold bosonic $^{87}$Rb$^{133}$Cs molecules, for light of wavelength $\lambda = 1064~\mathrm{nm}$. Near this wavelength we observe unexpected two-photon transitions that may cause trap loss. We measure the ac Stark effect in external magnetic and electric fields, using microwave spectroscopy of the first rotational transition. We quantify the isotropic and anisotropic parts of the molecular polarizability at this wavelength. We demonstrate that a modest electric field can decouple the nuclear spins from the rotational angular momentum, greatly simplifying the ac Stark effect. We use this simplification to control the ac Stark shift using the polarization angle of the trapping laser.

We have characterized the stereodynamics of the H + LiH (v = 0, j = 0–1) reactive collisions leading to H2 formation through the quantum mechanical analysis of the k–j and k′–j′ vector correlations that describe the polarization of the reactants and products, respectively. Our results, which cover the collision energy interval between 10–4 and 1 eV, are unexpectedly complex given the apparent simplicity and featureless nature of the potential energy surface for the LiH2 system and point toward the existence of a dynamical barrier connected to the centrifugal barrier. Both reactants and products, in particular the second ones, display strong directional preferences in the cold region that indicate a bias for collinear approaching and departing geometries and are independent of the final state of the products. As more energy is available for the reaction, the polarization of reactants and products becomes weaker and strongly dependent on the final state. While stereodynamical control is feasible and signifi...

The dynamics of inelastic collisions between HF and H has been investigated in detail by means of time-independent quantum mechanical calculations on the LWA-78 potential energy surface ( Li , G. ; et al. J. Chem. Phys. 2007 , 127 , 174302 ). Reaction probabilities, differential cross sections, and three-vector correlations have been calculated and analyzed. Our results show that there are two competing collision mechanisms that correlate with low and high impact parameters and show very different stereodynamical preferences. The mechanism promoted by high impact parameters is the only one present at low collision energies. We also observe the presence of an apparent threshold in the inelastic cross section for relatively high initial HF rotational quantum numbers, which is associated with the larger energy difference between adjacent rotational quantum states with increasing rotation.

We investigate magnetically tunable Feshbach resonances in ultracold collisions between ground-state Yb and Cs atoms, using coupled-channel calculations based on an interaction potential recently determined from photoassociation spectroscopy. We predict resonance positions and widths for all stable isotopes of Yb, together with resonance decay parameters where appropriate. The resonance patterns are richer and more complicated for fermionic Yb than for spin-zero isotopes, because there are additional level splittings and couplings due to scalar and tensorial Yb hyperfine interactions. We examine collisions involving Cs atoms in a variety of hyperfine states, and identify resonances that appear most promising for experimental observation and for magnetoassociation to form ultracold CsYb molecules.

Polar molecules in superpositions of rotational states exhibit long-range dipolar interactions, but maintaining their coherence in a trapped sample is a challenge. We present calculations that show many laser-coolable molecules have convenient rotational transitions that are exceptionally insensitive to magnetic fields. We verify this experimentally for CaF where we find a transition with sensitivity below $5\text{ }\text{ }\mathrm{Hz}\text{ }{\mathrm{G}}^{\ensuremath{-}1}$ and use it to demonstrate a rotational coherence time of 6.4(8) ms in a magnetic trap. Simulations suggest it is feasible to extend this to more than 1 s using a smaller cloud in a biased magnetic trap.

Ultracold molecules with both electron spin and an electric dipole moment offer new possibilities in quantum science. We use density-functional theory to calculate hyperfine coupling constants for a selection of molecules important in this area, including RbSr, LiYb, RbYb, CaF, and SrF. We find substantial hyperfine coupling constants for the fermionic isotopes of the alkaline-earth-metal and Yb atoms. We discuss the hyperfine level patterns and Zeeman splittings expected for these molecules. The results will be important both to experiments aimed at forming ultracold open-shell molecules and to their applications.

10 págs.; 10 figs.; 1 tab.; Special Issue: Dynamics of Molecular Collisions XXV: Fifty Years of Chemical Reaction Dynamics, We have analyzed the influence of the rotational excitation on the H + D(v = 0, j) reaction through quantum mechanical (QM) and quasiclassical trajectories (QCT) calculations at a wide range of total energies. The agreement between both types of calculations is excellent. We have found that the rotational excitation largely increases the reactivity at large values of the total energy. Such an increase cannot be attributed to a stereodynamical effect but to the existence of recrossing trajectories that become reactive as the target molecule gets rotationally excited. At low total energies, however, recrossing is not significant and the reactivity evolution is dominated by changes in the collision energy; the reactivity decreases with the collision energy as it shrinks the acceptance cone. When state-to-state results are considered, rotational excitation leads to cold products rovibrational distributions, so that most of the energy is released as recoil energy., The authors acknowledge funding by the Spanish Ministry of Science and Innovation (grant Consolider Ingenio 2010 CSD2009-00038). J.A., F.J.A. and P.G.J. acknowledge also funding by the Spanish Ministry of Economy and Competitiveness (grant CTQ2012-37404-C02), and V.J.H. acknowledges additional funding by the Spanish Ministry of Science and Innovation (FIS2013-48087-C2-1P) and by the European Research Council (ERC-2013-Syg-610256).

We present calculations of the hyperfine coupling constants for all the heteronuclear alkali-metal diatomic molecules at the equilibrium geometry of the electronic ground state. These constants are important in developing methods to control ultracold polar molecules. The results are based on electronic structure calculations using density-functional theory, and are in good agreement with experiment for the limited set of molecules for which experiments are so far available.

We investigate the effect of far-off-resonant trapping light on ultracold bosonic 87Rb133Cs molecules. We use kHz-precision microwave spectroscopy to measure the differential AC~Stark shifts between the ground and first excited rotational levels of the molecule with hyperfine-state resolution. We demonstrate through both experiment and theory that coupling between neighboring hyperfine states manifests in rich structure with many avoided crossings. This coupling may be tuned by rotating the polarization of the linearly polarized trapping light. A combination of spectroscopic and parametric heating measurements allows complete characterization of the molecule polarizability at a wavelength of 1550~nm in both the ground and first excited rotational states.

Time-independent quantum mechanical calculations have been performed in order to characterize the dynamics and stereodynamics of Cl + HD reactive collisions. Calculations have been carried out at two different total energy values and for various initial states using the adiabatic potential energy surface by Bian and Werner [J. Chem. Phys. 2000, 112, 220]. Special attention has been paid to the reaction with HD(v = 1) for which integral and differential cross-sections have been calculated and the effect of vibrational vs translational energy on the reactivity has been examined. In addition, the reactant polarization parameters and polarization-dependent differential cross-sections have been determined. From these results, the spatial preferences of the reaction and the extent of the control of the cross sections achievable through a suitable preparation of the reactants have been also studied. The directional requirements are tighter for the HCl channel than for the DCl one. Formation of the products takes place preferentially when the rotational angular momentum of the HD molecule is perpendicular to the reactants approach direction. Cross-sections and polarization moments computed from the scattering calculations have been compared with experimental results by Kandel et al. [J. Chem. Phys. 2000, 112, 670] for the reaction with HD(v = 1) produced by stimulated Raman pumping. The agreement so obtained is good, and it improves the accordance found in previous calculations with other methodologies and potential energy surfaces.

We demonstrate coherent control of the rotational and hyperfine state of ultracold, chemically stable $^{87}\mathrm{Rb}^{133}\mathrm{Cs}$ molecules with external microwave fields. We create a sample of $\ensuremath{\sim}2000$ molecules in the lowest hyperfine level of the rovibronic ground state $N=0$. We measure the transition frequencies to eight different hyperfine levels of the $N=1$ state at two magnetic fields $\ensuremath{\sim}23$ G apart. We determine accurate values of rotational and hyperfine coupling constants that agree well with previous calculations. We observe Rabi oscillations on each transition, allowing complete population transfer to a selected hyperfine level of $N=1$. Subsequent application of a second microwave pulse allows the transfer of molecules back to a different hyperfine level of $N=0$.

We report the binding energy of $^{87}\mathrm{Rb}^{133}\mathrm{Cs}$ molecules in their rovibrational ground state measured using an offset-free optical frequency comb based on difference frequency generation technology. We create molecules in the absolute ground state using stimulated Raman adiabatic passage (STIRAP) with a transfer efficiency of 88%. By measuring the absolute frequencies of our STIRAP lasers, we find the energy-level difference from an initial weakly bound Feshbach state to the rovibrational ground state with a resolution of $\ensuremath{\sim}5$ kHz over an energy-level difference of more than $114\phantom{\rule{0.28em}{0ex}}\mathrm{T}\mathrm{Hz}$; this lets us discern the hyperfine splitting of the ground state. Combined with theoretical models of the Feshbach-state binding energies and ground-state hyperfine structure, we determine a zero-field binding energy of $h\ifmmode\times\else\texttimes\fi{}114\phantom{\rule{0.16em}{0ex}}268\phantom{\rule{0.16em}{0ex}}135.24(4)(3)\phantom{\rule{0.28em}{0ex}}\mathrm{M}\mathrm{Hz}$. To our knowledge, this is the most accurate determination to date of the dissociation energy of a molecule.

[EN] Differential cross sections (DSCs) of the HD(v0 , j0) product for the reaction of H atoms with supersonically cooled D2 molecules in a small number of initial rotational states have been measured at a collision energy of 1.97 eV. These DCSs show an oscillatory pattern that results from interferences caused by different dynamical scattering mechanisms leading to products scattered into the same solid angle. The interferences depend on the initial rotational state j of the D2(v ¼ 0, j) reagent and diminish in strength with increasing rotation. We present here a detailed explanation for this behavior and how each dynamical scattering mechanism has a dependence on the helicity U, the projection of the initial rotational angular momentum j of the D2 reagent on the approach direction. Each helicity corresponds to a different internuclear axis distribution, with the consequence that the dependence on U reveals the preference of the different quasiclassical mechanisms as a function of approach direction. We believe that these results are general and will appear in any reaction for which several mechanisms are operative.

This article presents theoretical methods for the description of the directional effect of reactant rotation on the reactivity of atom-diatom systems and suggests an experiment that could be used to test theoretical predictions. The theory can be used in conjunction with both quantum reactive scattering and quasiclassical trajectory calculations, and is stated in general terms, which allows it to deal with arbitrary reactant polarizations. The illustrative results obtained for the benchmark H + D 2 reaction are also presented and show that under experimentally achievable conditions one can largely control reactive cross sections and product state distributions, while at the same time gaining valuable and at times surprising information on the reaction mechanism.

The dynamics of the asymmetric D + MuH (Mu = Muonium) reaction leading to Mu exchange, DMu + H, and H abstraction, DH + Mu, channels has been investigated using time-independent quantum mechanical (QM) calculations. Reaction probabilities, cross sections, cumulative reaction probabilities, and rate coefficients were determined for the two exit channels of the reaction. Quasiclassical trajectory (QCT) calculations were also performed in order to check the reliability of the method for this reaction and to discern the genuine quantum effects. Overall, the Mu exchange channel exhibits more structured reaction probabilities and cross sections with much larger rate coefficients than the H abstraction counterpart. Over the 100-1000 K temperature interval considered in this study, the QM rate coefficients for the Mu exchange vary between ≈5 × 10-15 and 2 × 10-11 cm 3 s-1 and those for the generation of DH + Mu between 2 × 10-18 and 3.5 × 10-12 cm3 s -1. In common with the rest of the isotopologues of the H + H 2 system, the height of the respective barriers in the collinear (symmetric stretch) vibrationally adiabatic potential energy curves matches the classical total energy threshold very accurately. Indeed, the lower and narrower vibrationally adiabatic collinear barrier as compared with that for the DH + Mu formation determines the preponderance of the DMu + H channel. Comparison of QM and QCT results and their analysis show that tunneling accounts for the reactivity at energies below the height of these barriers and that its effect on the rate coefficients becomes appreciable below 300 K. As expected, with growing temperature the contribution of tunneling to the global reactivity decreases markedly, but the rate coefficients are still much higher for the Mu exchange channel due to the effect of MuH rotational excitation that boosts the formation of DMu while diminishing the H abstraction channel that leads to DH formation. The analysis of the thermal cumulative reaction probabilities of the two channels indicates that at the lowest energies/temperatures the reaction into the DH + Mu channel takes place via 'leakage' from collisions proceeding along the DMu + H reaction path. © the Partner Organisations 2014., This work has been funded by the Spanish Ministry of Science and Innovation under grants CTQ2008-02578/BQU, CTQ2012-37404-C02, FIS2010-16455, and CSD2009-00038. JA acknowledges funding by the Junta de Castilla y León (grant SA244B12-1).

We investigate the interactions between ultracold alkali metal atoms and closed-shell atoms using electronic structure calculations on the prototype system Rb+Sr. There are molecular bound states that can be tuned across atomic thresholds with magnetic field, and there are previously neglected terms in the collision Hamiltonian that can produce zero-energy Feshbach resonances with significant widths. The largest effect comes from the interaction-induced variation of the Rb hyperfine coupling. The resonances may be used to form paramagnetic polar molecules if the magnetic field can be controlled precisely enough., 5 pages, 2 figures

Control over all internal and external degrees of freedom of molecules at the level of single quantum states will enable a series of fundamental studies in physics and chemistry. In particular, samples of ground-state molecules at ultralow temperatures and high number densities will facilitate new quantum-gas studies and future applications in quantum information science. However, high phase-space densities for molecular samples are not readily attainable because efficient cooling techniques such as laser cooling are lacking. Here we produce an ultracold and dense sample of molecules in a single hyperfine level of the rovibronic ground state with each molecule individually trapped in the motional ground state of an optical lattice well. Starting from a zero-temperature atomic Mott-insulator state with optimized double-site occupancy, weakly bound dimer molecules are efficiently associated on a Feshbach resonance and subsequently transferred to the rovibronic ground state by a stimulated four-photon process with >50% efficiency. The molecules are trapped in the lattice and have a lifetime of 8 s. Our results present a crucial step towards Bose–Einstein condensation of ground-state molecules and, when suitably generalized to polar heteronuclear molecules, the realization of dipolar quantum-gas phases in optical lattices.

We investigate the microwave spectra of ultracold alkali metal dimers in magnetic, electric and combined fields taking into account the hyperfine structure due to nuclear spins. We consider the molecules 41K87Rb and 7Li133Cs, which are the targets of current experiments, and demonstrate two extremes of large and small nuclear quadrupole couplings. We calculate the frequencies and intensities of transitions that may be used to transfer ultracold molecules between hyperfine states in a magnetic field, employing different polarizations of microwave radiation. In an electric field, the hyperfine levels display narrow avoided crossings at specific fields that we explain in terms of molecular alignment. The hyperfine splittings that arise in electric fields may hinder individual addressing in schemes that use ultracold molecules in quantum computation, but the structure of the spectra is suppressed in combined fields.

A detailed comparison of quantum mechanical (QM) and quasiclassical trajectory (QCT) integral and differential cross sections (DCSs) as well as opacity functions is presented in this work for the vibrationally inelastic collisions of H+D(2)(v=0,j=0)--H+D(2)(v(')=3,j(')) at 1.72 eV collision energy. These results are also compared with the experimental differential cross sections by Greaves et al. [Nature (London) 454, 88 (2008)]. The agreement between QCT and QM results is fairly good but some differences are appreciable, and it is shown that the experimental results are in a somewhat better agreement with the calculated QM DCS. The present results and their analysis confirm that the vibrational excitation takes place by elongation of the D-D bond in a "tug-of-war" mechanism, where the incoming H atom and one of the D atoms compete for the formation of a bond with the other D atom, as proposed by Greaves et al. It is also found that these collisions may give rise to the formation of short-lived collision complexes (tau(coll)=35-50 fs) that can be traced back to the presence of relatively deep wells in the potential surface when the original D-D bond is stretched. The analysis of the trajectories into v(')=3 reveals that most of them cross at least twice the reaction barrier via a recrossing mechanism.

We calculate the microwave spectra of ultracold $^{40}\text{K}^{87}\text{R}\text{b}$ alkali-metal dimers, including hyperfine interactions and in the presence of electric and magnetic fields. We show that microwave transitions may be used to transfer molecules between different hyperfine states, but only because of the presence of nuclear quadrupole interactions. Hyperfine splittings may also complicate the use of ultracold molecules for quantum computing. The spectrum of molecules oriented in electric fields may be simplified dramatically by applying a simultaneous magnetic field.

We investigate the energy levels of heteronuclear alkali metal dimers in levels correlating with the lowest rotational level of the ground electronic state, which are important in efforts to produce ground-state ultracold molecules. We use density-functional theory to calculate nuclear quadrupole and magnetic coupling constants for RbK and RbCs and explore the hyperfine structure in the presence of electric and magnetic fields. For nonrotating states, the zero-field splittings are dominated by the electron-mediated part of the nuclear spin-spin coupling. They are a few kHz for RbK isotopologs and a few tens of kHz for RbCs isotopologs., 8 pages, 6 figures

We investigate the hyperfine energy levels and Zeeman splittings for homonuclear alkali-metal dimers in low-lying rotational and vibrational states, which are important for experiments designed to produce quantum gases of deeply bound molecules. We carry out density-functional theory (DFT) calculations of the nuclear hyperfine coupling constants. For nonrotating states, the zero-field splittings are determined almost entirely by the scalar nuclear spin-spin coupling constant. By contrast with the heteronuclear case, the total nuclear spin remains a good quantum number in a magnetic field. We also investigate levels with rotational quantum number N = 1, which have long-range anisotropic quadrupole-quadrupole interactions and may be collisionally stable. For these states the splitting is dominated by nuclear quadrupole coupling for most of the alkali-metal dimers and the Zeeman splittings are considerably more complicated.

The explicit consideration of the vector correlations is an essential step when it comes to determining the mechanism of chemical reactions. Usual vector correlations involve initial and final relative velocity vectors and rotational angular momenta. However, the correlation between the orbital, ℓ, and rotational, j, angular momenta has seldom received any attention. In this article, we present a semiclassical methodology capable of describing the ℓ-j correlation that may serve as a connection between the quantum and quasiclassical treatments. Using the scattering matrix in the orbital angular momentum representation, the ℓ-j correlation is expressed as a probability density function of the angle formed by both vectors. This technique is exemplified through the H + D2 reaction and its accuracy is appraised by comparing with results derived from calculations based on quasiclassical trajectories.