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Physical Review A

Ultracold collisions between Li atoms and Li2 diatoms in high vibrational states

Goulven Quéméner, Jean–Michel Launay, Pascal Honvault

Published May 25, 2007• 48 citations
Publisher

Abstract

We have performed a quantum-dynamical study of vibrational deexcitation and elastic scattering at ultralow collision energies for the bosonic system $^{7}\mathrm{Li}+^{7}\mathrm{Li}_{2}$ and for the fermionic system $^{6}\mathrm{Li}+^{6}\mathrm{Li}_{2}$ with diatomic molecules in high vibrational states. Inelastic rates show a strong and irregular dependence on the vibrational state of the diatomic molecule. For the highest vibrational state which lies near the dissociation limit, vibrational deexcitation processes are not suppressed, but rather depleted, for both bosonic and fermionic systems.

DOI
10.1103/physreva.75.050701

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•Jan 1, 2004•0 citations
We have performed a quantum-dynamical study of vibrational deexcitation and elastic scattering at ultralow collision energies for the bosonic system 7Li+7Li2^{7}\mathrm{Li}+^{7}\mathrm{Li}_{2}7Li+7Li2​ and for the fermionic system 6Li+6Li2^{6}\mathrm{Li}+^{6}\mathrm{Li}_{2}6Li+6Li2​ with diatomic molecules in high vibrational states. Inelastic rates show a strong and irregular dependence on the vibrational state of the diatomic molecule. For the highest vibrational state which lies near the dissociation limit, vibrational deexcitation processes are not suppressed, but rather depleted, for both bosonic and fermionic systems.
Accurate quantum calculations have been carried out at ultralow energies (from ${10}^{\ensuremath{-}2}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}{10}^{\ensuremath{-}6}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$) for the vibrational deexcitation of ${\mathrm{Li}}_{2}(^{1}\ensuremath{\Sigma}_{g}^{+})$ by collisions with He, starting from a broad range of initial highly excited vibrational levels. The results indicate the clear dominance of a few transitions with the smallest $\ensuremath{\Delta}\ensuremath{\nu}$ changes and show the overall deexcitation cross sections to markedly depend on the initial vibrational state of the molecule, in line with earlier results on H2+He{\mathrm{H}}_{2}+\mathrm{He}H2​+He [Balakrishan et al. Phys. Rev. Lett. 80, 3224 (1998)] vibrational quenching. A connection is made with very recent measurements on the vibrational quenching of ultracold Cs2{\mathrm{Cs}}_{2}Cs2​ molecules in optical traps that were instead found to behave in a very different manner. Numerical experiments on the present system as well as on the H3{\mathrm{H}}_{3}H3​ reaction strongly suggest a possible explanation for such differences.
A potential energy surface for the lowest quartet electronic state ((4)A(')) 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 have developed a potential-energy surface for spin-polarized $\mathrm{K}(^{2}S)+{\mathrm{K}}_{2}(^{3}\ensuremath{\Sigma}_{u}^{+})$ collisions and carried out quantum dynamical calculations of vibrational quenching at low and ultralow collision energies for both bosons 39K^{39}\mathrm{K}39K and 41K^{41}\mathrm{K}41K and fermions 40K^{40}\mathrm{K}40K. At collision energies above about 0.1mK0.1\phantom{\rule{0.3em}{0ex}}\mathrm{mK}0.1mK the quenching rates are well described by a classical Langevin model, but at lower energies a fully quantal treatment is essential. We find that for the low initial vibrational state considered here (v=1)(v=1)(v=1), the ultracold quenching rates are not substantially suppressed for fermionic atoms. For both bosons and fermions, vibrational quenching is much faster than elastic scattering in the ultralow-temperature regime. This contrasts with the situation found experimentally for molecules formed via Feshbach resonances in very high vibrational states.
Collisions of 6Li2 molecules with free 6Li atoms reveal a striking deviation from universal predictions based on long-range van der Waals interactions. Li2 closed-channel molecules are formed in the highest vibrational state near a narrow Feshbach resonance and decay via two-body collisions with Li2, Li, and Na. For Li2 + Li2 and Li2 + Na, the decay rates agree with the universal predictions of the quantum Langevin model. In contrast, the rate for Li2 + Li is exceptionally small, with an upper bound 10 times smaller than the universal prediction. This can be explained by the low density of available decay states in systems of light atoms [G. Quéméner, J.-M. Launay, and P. Honvault, Phys. Rev. A 75, 050701 (2007)], for which such collisions have not been studied before.
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.