A potential energy surface for the lowest quartet electronic state of lithium trimer is developed and used to study spin-polarized Li + Li_2 collisions at ultralow kinetic energies. The potential energy surface allows barrierless atom exchange reactions. Elastic and inelastic cross sections are calculated for collisions involving a variety of rovibrational states of Li_2. Inelastic collisions are responsible for trap loss in molecule production experiments. Isotope effects and the sensitivity of the results to details of the potential energy surface are investigated. It is found that for vibrationally excited states the cross sections are only quite weakly dependent on details of the potential energy surface.
We study collisions of para-H$_2$ with five rare gas atomic species (He, Ne, Ar, Kr and Xe) over the range from 1 K to 1 $μ$ K and evaluate the feasibility of sympathetic cooling H$_2$ with ultracold ground state rare gas atoms co-trapped within a deep optical trap. Collision cross-sections over this large temperature range show that all of these species could be used to cool H$_2$ to ultracold temperatures and that argon and helium are the most promising species for future experiments.
It is demonstrated that elastic collisions of ultracold atoms forming a heteronuclear collision complex can be manipulated by laboratory practicable dc electric fields. The mechanism of electric field control is based on the interaction of the instantaneous dipole moment of the collision pair with external electric fields. It is shown that this interaction is dramatically enhanced in the presence of a p-wave shape or Feshbach scattering resonance near the collision threshold, which leads to novel electric-field-induced Feshbach resonances.
A scattering model is developed for ultracold molecular collisions, which allows inelastic processes, chemical reactions, and complex formation to be treated in a unified way. All these scattering processes and various combinations of them are possible in ultracold molecular gases, and as such this model will allow the rigorous parametrization of experimental results. In addition we show how, once extracted, these parameters can be related to the physical properties of the system, shedding light on fundamental aspects of molecular collision dynamics.
Resonances in ultracold collisions involving heavy molecules are difficult to understand, and have proven challenging to detect. Here we report the observation of magnetically tunable Feshbach resonances in ultracold collisions between $^{23}$Na$^{40}$K molecules in the rovibrational ground state and $^{40}$K atoms. We prepare the atoms and molecules in various hyperfine levels of their ground states and observe the loss of molecules as a function of the magnetic field. The atom-molecule Feshbach resonances are identified by observing an enhancement of the loss rate coefficients. We have obser…
It has recently become possible to form molecules in ultracold gases of trapped alkali metal atoms. Once formed, the molecules may undergo elastic, inelastic and reactive collisions. Inelastic and reactive collisions are particularly important because they release kinetic energy and eject atoms and molecules from the trap. The theory needed to handle such collisions is presented and recent quantum dynamics calculations on ultracold atom-diatom collisions of spin-polarised Li + Li_2, Na + Na_2 and K + K_2 are described. All these systems have potential energy surfaces on which barrierless atom …
We present a formalism for rigorous calculations of cross sections for inelastic and reactive collisions of ultracold atoms and molecules confined by laser fields in quasi-2D geometry. Our results show that the elastic-to-inelastic ratios of collision cross sections are enhanced in the presence of a laser confinement and that the threshold energy dependence of the collision cross sections can be tuned by varying the confinement strength and external magnetic fields. The enhancement of the elastic-to-inelastic ratios is inversely proportional to $\sqrt{ε/\hbar ω_0}$, where $ε$ is the kinetic en…
We present a formalism for rigorous calculations of cross sections for inelastic and reactive collisions of ultracold atoms and molecules confined by laser fields in quasi-2D geometry. Our results show that the elastic-to-inelastic ratios of collision cross sections are enhanced in the presence of a laser confinement and that the threshold energy dependence of the collision cross sections can be tuned by varying the confinement strength and external magnetic fields. The enhancement of the elastic-to-inelastic ratios is inversely proportional to $\sqrt{ε/\hbar ω_0}$, where $ε$ is the kinetic en…
In the absence of inelastic scattering, Feshbach resonances produce poles in scattering lengths and very large peaks in elastic cross sections. However, inelastic scattering removes the poles. Whenever the resonant state is coupled comparably to the elastic and inelastic channels, the scattering length exhibits only a small oscillation and peaks in cross sections are dramatically suppressed. A resonant scattering length is defined to characterize the amplitude of the oscillation, and is shown to be small for many collisions of ultracold molecules. The results suggest that cross sections for ul…
Multichannel quantum defect theory (MQDT) has been widely applied to resonant and non-resonant scattering in a variety of atomic collision processes. In recent years, the method has been applied to cold collisions with considerable success, and it has proven to be a computationally viable alternative to full-close coupling (CC) calculations when spin, hyperfine and external field effects are included. In this paper, we describe a hybrid approach for molecule-molecule scattering that includes the simplicity of MQDT while treating the short-range interaction explicitly using CC calculations. Thi…
We show that quantum interference-based coherent control is a highly efficient tool for tuning ultracold molecular collision dynamics, and is free from the limitations of commonly used methods that rely on external electromagnetic fields. By varying {the relative populations and} phases of an initial coherent superpositions of degenerate molecular states, we demonstrate complete coherent control over integral scattering cross sections in the ultracold $s$-wave regime of both the initial and final collision channels. The proposed control methodology is applied to ultracold O$_2$~+~O$_2$ collisi…
We show that low-energy inelastic cross sections can decrease as well as increase in the vicinity of a zero-energy Feshbach resonance. When an external field is used to tune across such a resonance, the real and imaginary parts of the scattering length show asymmetric oscillations, with both peaks and troughs. In favorable circumstances the inelastic collision rate can be reduced almost to zero. This may be important for efforts to achieve evaporative and sympathetic cooling for molecules.
Estimates for the lifetime of collision complexes formed during ultracold molecular collisions based on density-of-states arguments are shown to be consistent with similar estimate based on classical trajectory calculations. In the classical version, these collisions are shown to exhibit chaos, and their fractal dimensions are calculated versus collision energy. From these results, a picture emerges that ultracold collisions are classically ergodic, justifying the density-of-states estimates for lifetimes. These results point the way toward using the techniques of classical and quantum chaos t…
Rigorous quantum scattering calculations on ultracold molecular collisions in external fields present an outstanding computational problem due to strongly anisotropic atom-molecule interactions that depend on the relative orientation of the collision partners, as well as on their vibrational degrees of freedom. Here, we present the first numerically exact three-dimensional quantum scattering calculations on strongly anisotropic atom-molecule (Li+CaH) collisions in an external magnetic field based on the parity-adapted total angular momentum representation and a new three-dimensional potential …
Ultracold collisions between Cs atoms and Cs2 dimers in the electronic ground state are observed in an optically trapped gas of atoms and molecules. The Cs2 molecules are formed in the triplet ground state by cw-photoassociation through the outer well of the 0g-(P3/2) excited electronic state. Inelastic atom-molecule collisions converting internal excitation into kinetic energy lead to a loss of Cs2 molecules from the dipole trap. Rate coefficients are determined for collisions involving Cs atoms in either the F=3 or F=4 hyperfine ground state and Cs2 molecules in either highly vibrationally e…
We present an accurate quantum mechanical study of molecule-molecule collisions in the presence of a magnetic field. The work focusses on the analysis of elastic scattering and spin relaxation in collisions of O2(3Sigma_g) molecules at cold (~0.1 K) and ultracold (~10^{-6} K) temperatures. Our calculations show that magnetic spin relaxation in molecule-molecule collisions is extremely efficient except at magnetic fields below 1 mT. The rate constant for spin relaxation at T=0.1 K and a magnetic field of 0.1 T is found to be as large as 6.1 x 10^{-11} cm3/s. The magnetic field dependence of ela…
Ultracold molecular collisions in magnetic fields: Efficient incorporation of hyperfine structure in the total rotational angular momentum representation
Inspired by Wannier's threshold law, we recognize that collision complex decay meets the requirements of quantum-classical correspondence in sufficiently exothermic ultracold reactions. We make use of this correspondence to elucidate the classical foundations of ultracold reactions and to help bring calculations currently beyond the capabilities of quantum mechanics within reach. A classical method with a simplified model of many-body interactions is provided for determination of the collision complex lifetime and demonstrated for a reduced-dimensional system, as preliminary to the calculation…
We explore the suitability of ultracold collisions between spin-polarized SrF($^2Σ^+$) molecules and Rb($^2$S) atoms as elementary steps for the sympathetic cooling of SrF($^2Σ^+$) molecules in a magnetic trap. To this end, we carry out quantum mechanical scattering calculations on ultracold Rb+SrF collisions in a magnetic field based on an accurate potential energy surface for the triplet electronic state of Rb-SrF developed ab initio using a spin-restricted coupler cluster method with single, double and noniterative triple excitations [RCCSD(T)]. The Rb-SrF interaction has a global minimum w…
This paper summarizes the recent theoretical works on inelastic collisions and chemical reactions at cold and ultracold temperatures involving neutral or ionic systems of atoms and molecules. Tables of zero-temperature rate constants of various molecules are provided.
Ultracold collisions of the polyatomic species CaOH are considered, in internal states where the collisions should be dominated by long-range dipole-dipole interactions. The computed rate constants suggest that evaporative cooling can be quite efficient for these species, provided they start at temperatures achievable by laser cooling. The rate constants are shown to become more favorable for evaporative cooling as the electric field increases. Moreover, long-range dimer states (CaOH)$^*_2$ are predicated to occur, having lifetimes on the order of microseconds.
Ultracold collisions of cold atoms or molecules make the bound states of the collision complex formed from the two colliding species accessible for control and manipulation of the cold species or the complex. Such resonances are best treated by a resonant scattering theory, which in the ultracold domain can take advantage of the properties of the long-range potential and the methods of multichannel quantum defect theory. Coupled channels calculations on the threshold scattering states and bound states of the 40K87Rb molecule illustrate the ideas and methodology of quantum defect theory using t…
Ultracold molecules undergo "sticky collisions" that result in loss even for chemically nonreactive molecules. Sticking times can be enhanced by orders of magnitude by interactions that lead to non-conservation of nuclear spin or total angular momentum. We present a quantitative theory of the required strength of such symmetry-breaking interactions based on classical simulation of collision complexes. We find static electric fields as small as $10$~V/cm can lead to non-conservation of angular momentum, while we find nuclear spin is conserved during collisions. We also compute loss of collision…
We investigate the ultracold reaction dynamics of magnetically trapped NH($X ^3Σ^-$) radicals using rigorous quantum scattering calculations involving three coupled potential energy surfaces. We find that the reactive NH + NH cross section is driven by a short-ranged collisional mechanism, and its magnitude is only weakly dependent on magnetic field strength. Unlike most ultracold reactions observed so far, the NH + NH scattering dynamics is non-universal. Our results indicate that chemical reactions can cause more trap loss than spin-inelastic NH + NH collisions, making molecular evaporative …
Understanding the sources of losses and chemical reactions of ultracold alkali-metal molecules is among the critical elements needed for their application in precision measurements and quantum technologies. Recent experiments with nonreactive systems have reported unexpectedly large loss rates, posing a challenge for theoretical explanation. Here, we examine the dynamics of intermediate four-atom complexes formed in bimolecular collisions. We calculate the nuclear spin--rotation, spin--spin, and quadrupole coupling constants for bialkali tetramers using ab intio quantum-chemical methods. We sh…
Understanding and controlling collisions is crucial to the burgeoning field of ultracold molecules. All experiments so far have observed fast loss of molecules from the trap. However, the dominant mechanism for collisional loss is not well understood when there are no allowed 2-body loss processes. Here we experimentally investigate collisional losses of nonreactive ultracold RbCs molecules, and compare our findings with the sticky collision hypothesis that pairs of molecules form long-lived collision complexes. We demonstrate that loss of molecules occupying their rotational and hyperfine gro…
We demonstrate microwave dressing on ultracold, fermionic ${}^{23}$Na${}^{40}$K ground-state molecules and observe resonant dipolar collisions with cross sections exceeding three times the $s$-wave unitarity limit. The origin of these collisions is the resonant alignment of the approaching molecules' dipoles along the intermolecular axis, which leads to strong attraction. We explain our observations with a conceptually simple two-state picture based on the Condon approximation. Furthermore, we perform coupled-channels calculations that agree well with the experimentally observed collision rate…
We show that products of the isotopic substitution reactions in experimentally accessible molecules such as NaK, RbCs, and SrF are cold according to their translational energy below hundreds of mK. For these chemical reactions, molecular products may occupy only the lowest rotational states. We also discuss the possibility of controlling the chemical reactions by the electric field in ultracold mixtures of molecules and atoms with low kinetic energy release, where one of the constituent atoms of colliding molecule is replaced by its isotope. This letter opens new avenues in investigating the b…
Elastic and spin-changing inelastic collision cross sections are presented for cold and ultracold magnetically trapped NH. The cross sections are obtained from coupled-channel scattering calculations as a function of energy and magnetic field. We specifically investigate the influence of the intramolecular spin-spin, spin-rotation, and intermolecular magnetic dipole coupling on the collision dynamics. It is shown that $^{15}$NH is a very suitable candidate for evaporative cooling experiments. The dominant trap-loss mechanism in the ultracold regime originates from the intermolecular dipolar co…
We investigate collisional loss in an ultracold mixture of $^{40}$K$^{87}$Rb molecules and $^{87}$Rb atoms, where chemical reactions between the two species are energetically forbidden. Through direct detection of the KRb$_{2}^{*}$ intermediate complexes formed from atom-molecule collisions, we show that a $1064$ nm laser source used for optical trapping of the sample can efficiently deplete the complex population via photo-excitation, an effect which can explain the universal two-body loss observed in the mixture. By monitoring the time-evolution of the KRb$_{2}^{*}$ population after a sudden…
We present quantum dynamics of collisions between two para-H2 molecules from low (1 mK) 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 H4 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 ar…
Quantum scattering calculations are reported for the H+HCl(v,j=0) and H+DCl(v,j=0) collisions for vibrational levels v=0-2 of the diatoms. Calculations were performed for incident kinetic energies in the range 10-7 to 10-1 eV, for total angular momentum J=0 and s-wave scattering in the entrance channel of the collisions. Cross sections and rate coefficients are characterized by resonance structures due to quasibound states associated with the formation of the H...HCl and H...DCl van der Waals complexes in the incident channel. For the H+HCl(v,j=0) collision for v=1,2, reactive scattering leadi…
Universal collision rate constants are calculated for ultracold collisions of two like bosonic or fermionic heteronuclear alkali-metal dimers involving the species Li, Na, K, Rb, or Cs. Universal collisions are those for which the short range probability of a reactive or quenching collision is unity such that a collision removes a pair of molecules from the sample. In this case, the collision rates are determined by universal quantum dynamics at very long range compared to the chemical bond length. We calculate the universal rate constants for reaction of the reactive dimers in their ground vi…
Collisional complexes, which are formed as intermediate states in molecular collisions, are typically short-lived and decay within picoseconds. However, in ultracold collisions involving bialkali molecules, complexes can live for milliseconds, completely changing the collision dynamics. This can lead to unexpected two-body loss in samples of nonreactive molecules. During the last decade, such "sticky" collisons have been a major hindrance in the preparation of dense and stable molecular samples, especially in the quantum-degenerate regime. Currently, the behavior of the complexes is not fully …
Because the de Broglie wavelength of ultracold molecules is very large, the cross sections for collisions of molecules at ultracold temperatures are always computed by the time-independent quantum scattering approach. Here, we report the first accurate time-dependent wave packet dynamics calculation for reactive scattering of ultracold molecules. Wave packet dynamics calculations can be applied to molecular systems with more dimensions and provide real-time information on the process of bond-rearrangement and/or energy exchange in molecular collisions. Our work thus makes possible the extensio…
The effect of conical intersections (CIs) on electronic relaxation, transitions from excited states to ground states, is well studied, but their influence on hyperfine quenching in a reactant molecule is not known. Here, we report on ultracold collision dynamics of the hydroxyl free-radical OH with Sr atoms leading to quenching of OH hyperfine states. Our quantum-mechanical calculations of this process reveal that quenching is efficient due to anomalous molecular dynamics in the vicinity of the conical intersection at collinear geometry. We observe wide scattering resonance features in both el…
A close coupling quantum-mechanical calculation is performed for rotational energy transfer in a HD+HD collision at very low energy, down to the ultracold temperatures: $T \sim 10^{-8}$ K. A global six-dimensional H$_2$-H$_2$ potential energy surface is adopted from a previous work [Boothroyd {\it et al.}, J. Chem. Phys., {\bf 116}, 666 (2002).] State-resolved integral cross sections $σ_{ij\rightarrow i'j'}(\varepsilon_{kin})$ of different quantum-mechanical rotational transitions $ij\rightarrow i'j'$ in the HD molecules and corresponding state-resolved thermal rate coefficients $k_{ij\rightar…
We present elastic and inelastic spin-changing cross sections for cold and ultracold NH($X\,^3Σ^-$) + NH($X\,^3Σ^-$) collisions, obtained from full quantum scattering calculations on an accurate \textit{ab initio} quintet potential-energy surface. Although we consider only collisions in zero field, we focus on the cross sections relevant for magnetic trapping experiments. It is shown that evaporative cooling of both fermionic $^{14}$NH and bosonic $^{15}$NH is likely to be successful for hyperfine states that allow for s-wave collisions. The calculated cross sections are very sensitive to the …
