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arXiv:cond-mat/0501636 · Physical Review Letters

Ultracold Collisions Involving Heteronuclear Alkali Metal Dimers

Marko T. Cvitaš, Pavel Soldán, Jeremy M. Hutson, Pascal Honvault, Jean–Michel Launay

Published May 26, 2005• 82 citations
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Abstract

We carry out the first quantum dynamics calculations on ultracold atom-diatom collisions in isotopic mixtures. The systems studied are spin-polarized $^{7}\mathrm{Li}+^{6}\mathrm{Li}^{7}\mathrm{Li}$, $^{7}\mathrm{Li}+^{6}\mathrm{Li}_{2}$, $^{6}\mathrm{Li}+^{6}\mathrm{Li}^{7}\mathrm{Li}$, and $^{6}\mathrm{Li}+^{7}\mathrm{Li}_{2}$. Reactive scattering can occur for the first two systems even when the molecules are in their ground rovibrational states, but is slower than vibrational relaxation in homonuclear systems. Implications for sympathetic cooling of heteronuclear molecules are discussed.

DOI
10.1103/physrevlett.94.200402

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We carry out the first quantum dynamics calculations on ultracold atom-diatom collisions in isotopic mixtures. The systems studied are spin-polarized 7Li+6Li7Li^{7}\mathrm{Li}+^{6}\mathrm{Li}^{7}\mathrm{Li}7Li+6Li7Li, 7Li+6Li2^{7}\mathrm{Li}+^{6}\mathrm{Li}_{2}7Li+6Li2​, 6Li+6Li7Li^{6}\mathrm{Li}+^{6}\mathrm{Li}^{7}\mathrm{Li}6Li+6Li7Li, and 6Li+7Li2^{6}\mathrm{Li}+^{7}\mathrm{Li}_{2}6Li+7Li2​. Reactive scattering can occur for the first two systems even when the molecules are in their ground rovibrational states, but is slower than vibrational relaxation in homonuclear systems. Implications for sympathetic cooling of heteronuclear molecules are discussed.
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 vibrational state v = 0 and for vibrational quenching of non-reactive dimers with v ≥ 1. Using the known dipole moments and estimated van der Waals coefficients of each species, we calculate electric field dependent loss rate constants for collisions of molecules tightly confined to quasi-two-dimensional geometry by a one-dimensional optical lattice. A simple scaling relation of the quasi-two-dimensional loss rate constants with dipole strength, trap frequency and collision energy is given for like bosons or like fermions. It should be possible to stabilize ultracold dimers of any of these species against destructive collisions by confining them in a lattice and orienting them with an electric field of less than 20 kV cm(-1).
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-polarized Li + Li2, Na + Na2 and K + K2 are described. All these systems have potential energy surfaces on which barrierless atom exchange reactions can occur, and both inelastic and reactive rates are very fast (typically k inel > 10-10 cm3 s−1 in the Wigner regime).
We investigate the energetics of reactions involving pairs of alkali-metal dimers. Atom exchange reactions to form homonuclear dimers are energetically allowed for some but not all of the heteronuclear dimers. We carry out high-level electronic structure calculations on the potential energy surfaces of all the heteronuclear alkali-metal trimers and show that trimer formation reactions are always energetically forbidden for low-lying singlet states of the dimers. The results have important implications for the stability of quantum gases of alkali-metal dimers.
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( a 3 Σ + ) and Li( 2 S) to form Li 2 ( a 3 Σ u + ) and Na( 2 S). 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 Li 2 Na interaction at short range, which we attribute to a relatively small number of open Li 2 ( a 3 Σ 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.
There is at present great interest in the properties of ultracold molecules. Molecules are created in traps in excited rovibrational states and any vibrational relaxation results in the trap loss. This thesis provides a theoretical study of interactions and collisions in the spin-polarized lithium -b lithium dimer system at ultralow energies. Potential energy surface of the electronic quartet ground state of lithium trimer is generated ab initio using the CCSD(T) method and represented by an IMLS/Shepard fit. Long-range nonadditive interactions are modelled using a symmetric global form with coefficients taken from a fit to the atom-molecule dispersion coefficients. The surface allows barrierless atom-exchange reactions. It has a global minimum of ≈ 4000 cm(^-1) at equilateral geometries with r(_e) = 3.1 Å. The nonadditive interactions are very strong near equilibrium. They increase the well depth by a factor of 4 and reduce the interatomic distance by ≈ 1 Å. Another surface of À symmetry in C(_s) meets the ground state surface at linear geometries at short range. Part of the seam, near D(_ooh) geometries, is in an energetically accessible region for cold collisions. Inside the seam, the lowest À surface correlates with (^4)II rather than (^4)Σ state. Inelastic and reactive collisions are investigated using a quantum mechanical coupled channel method in hyperspherical coordinates. Bosonic and fermionic systems in the spin-stretched states are considered. The inelastic rate coefficients from the rovibrationally excited states of dimer at ultralow collision energies are large, often above 10-(^-10) cm(^3)s(^-1) The elastic cross sections are ≈ 3 orders of magnitude lower at 1 nK. Atom-molecule mixtures, at the densities found in Bose-Einstein condensates of alkali metal atoms that were recently produced, would last only a fraction of a second. Classical Langevin model describes semi-quantitatively the energy dependence of inelastic cross sections above ≈ 50 mK. No systematic differences between the bosonic and fermionic systems were found. Sensitivity of the results on potential was investigated. Reactions in isotopic mixtures of lithium may be exothermic even from the molecular ground state. The reactive rate coefficients are 1 - 2 orders of magnitude smaller than those in systems involving an initially vibrationally excited dimer.
The prospects of sympathetic cooling of polar molecules with magnetically cotrapped alkali-metal atoms are generally considered poor due to strongly anisotropic atom-molecule interactions leading to large spin relaxation rates. Using rigorous quantum scattering calculations based on ab initio interaction potentials, we show that inelastic spin relaxation in low-temperature collisions of CaH(${}^{2}\ensuremath{\Sigma}$) molecules with Li and Mg atoms occurs at a slow rate despite the strongly anisotropic interactions. This unexpected result, which we rationalize using multichannel quantum-defect theory, opens up the possibility of sympathetic cooling of polar ${}^{2}\ensuremath{\Sigma}$ molecules with alkali-metal atoms in a magnetic trap and with alkaline-earth-metal atoms in an optical dipole trap.