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Physical Review A

Complex scattering lengths for ultracold He collisions with rotationally excited linear and nonlinear molecules

Benhui Yang, Robert C. Forrey, Phillip C. Stancil, N. Balakrishnan

Published Nov 30, 2010• 6 citations
Publisher

Abstract

The translational and internal level cooling of atoms and molecules in ultracold gases results from a combination of elastic and inelastic collisional processes. While elastic collisions lead to rapid thermalization, exoergic inelastic collisions may lead to heating and trap loss. To date, most collisional studies have targeted low-lying levels of diatomic molecules. Here we investigate inelastic quenching and elastic scattering of rotationally excited linear (H${}_{2}$, HD, CO, ${\mathrm{O}}_{2}$, and CO${}_{2}$) and nonlinear (H${}_{2}$O and NH${}_{3}$) molecules in ultracold collisions with He and report the corresponding complex scattering lengths. It has been found that the ratio of the imaginary component $\ensuremath{\beta}$ to the real component $\ensuremath{\alpha}$ of the scattering length generally increases with decreasing rotational constant for linear molecules. With the exception of CO, $\ensuremath{\beta}$ becomes significantly smaller than $\ensuremath{\alpha}$ as the energy gap for rotational transitions increases. In all cases, $\ensuremath{\beta}$ decreases with rotational energy gap for relatively large rotational excitation, allowing for convenient fits to an exponential energy gap formula. Excited rotational levels of ${\mathrm{H}}_{2}$ and HD appear to be collisionally stable due to the very low values of $\ensuremath{\beta}/\ensuremath{\alpha}$. Rotationally excited ${\mathrm{H}}_{2}$O also appears to be a viable candidate for He buffer gas cooling due to relatively small values of $\ensuremath{\beta}$.

DOI
10.1103/physreva.82.052711

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The translational and internal level cooling of atoms and molecules in ultracold gases results from a combination of elastic and inelastic collisional processes. While elastic collisions lead to rapid thermalization, exoergic inelastic collisions may lead to heating and trap loss. To date, most collisional studies have targeted low-lying levels of diatomic molecules. Here we investigate inelastic quenching and elastic scattering of rotationally excited linear (H2{}_{2}2​, HD, CO, O2{\mathrm{O}}_{2}O2​, and CO2{}_{2}2​) and nonlinear (H2{}_{2}2​O and NH3{}_{3}3​) molecules in ultracold collisions with He and report the corresponding complex scattering lengths. It has been found that the ratio of the imaginary component \ensuremathβ\ensuremath{\beta}\ensuremathβ to the real component \ensuremathα\ensuremath{\alpha}\ensuremathα of the scattering length generally increases with decreasing rotational constant for linear molecules. With the exception of CO, \ensuremathβ\ensuremath{\beta}\ensuremathβ becomes significantly smaller than \ensuremathα\ensuremath{\alpha}\ensuremathα as the energy gap for rotational transitions increases. In all cases, \ensuremathβ\ensuremath{\beta}\ensuremathβ decreases with rotational energy gap for relatively large rotational excitation, allowing for convenient fits to an exponential energy gap formula. Excited rotational levels of H2{\mathrm{H}}_{2}H2​ and HD appear to be collisionally stable due to the very low values of \ensuremathβ/\ensuremathα\ensuremath{\beta}/\ensuremath{\alpha}\ensuremathβ/\ensuremathα. Rotationally excited H2{\mathrm{H}}_{2}H2​O also appears to be a viable candidate for He buffer gas cooling due to relatively small values of \ensuremathβ\ensuremath{\beta}\ensuremathβ.
The study of molecular inelastic collision processes at cold and ultracold temperatures is of considerable interest as schemes are currently being developed to efficiently cool and trap neutral polar molecules. In this work, quantum-mechanical scattering calculations are presented for the quenching of rotationally excited CO due to collisions with H, He and H 2 for collision energies between 10 −5 and 10 cm −1 . The calculations were performed using the close-coupling approach and the coupled-states approximation. Cross sections for the quenching of the j = 1–10, 20, 30 and 40 levels of CO are presented and mechanism and trends of energy transfer in these systems are discussed.
Building on recent advances in ultrafast lasers and methods to slow molecules, an experiment is proposed to produce translationally cold CO2{}_{2}2​ super-rotors ($j\ensuremath{\sim}200$) by combining an optical centrifuge with helium-buffer-gas cooling. Quantum mechanical calculations of the complex scattering length for He-CO2{}_{2}2​ collisions demonstrate that the efficiency of rotational quenching decreases rapidly with increasing rotational excitation jjj in the ultracold regime. Extrapolating to helium cryogenic temperatures, rotational quenching is predicted to remain inefficient up to $\ensuremath{\sim}$1 K, allowing for the possible creation of a beam of translationally cold, rotationally hot molecules.
Cold collisions involving highly rotationally excited diatomic molecules are investigated. As the translational energy is lowered, the total inelastic cross section decreases sharply for specific channels where quasiresonant transitions are no longer energetically allowed. Rate coefficients are given for collisional quenching of rotationally excited H2,D2,T2,{\mathrm{H}}_{2},{\mathrm{D}}_{2},{\mathrm{T}}_{2},H2​,D2​,T2​, and O2{\mathrm{O}}_{2}O2​ at zero temperature. The specific rotational states that are stable against collisional relaxation would be interesting prospects for cooling and trapping. The application of collisional cooling methods together with recently developed schemes for producing rotationally hot molecules may allow high densities of ultracold ``super rotors'' to be achieved.
Cold and ultracold collisions involving rotationally hot CO\mathrm{CO}CO molecules are investigated using quantum mechanical coupled channel, coupled states, and effective potential scattering formulations. Quenching rate coefficients are given for initial rotational levels near the dissociation threshold. The stability of the CO\mathrm{CO}CO ``super rotors'' against collisional decay is compared to previous investigations involving homonuclear molecules. It is found that quasiresonant transitions provide a significantly stronger contribution to the total relaxation rate than in the comparable case of O2{\mathrm{O}}_{2}O2​. As in the case of H2{\mathrm{H}}_{2}H2​, sharp structures in the distribution of total quenching rate coefficients are found at rotational levels where quasiresonant scattering is not allowed.
We have carried out bound-state and low-energy quantum scattering calculations on He + NH (triplet Sigma) in magnetic fields, with the NH molecule in its n=1 rotationally excited states. We have explored the pattern of levels as a function of magnetic field and identified the nearly good quantum numbers in different regimes. We have used the bound-state calculations to locate low-energy Feshbach resonances. When the magnetic field is used to tune across such a resonance, the real and imaginary part of the scattering length show asymmetric oscillations and peaks with amplitude between 1 and 3 Angstroms. The scattering length does not pass through a pole at resonance. The resonant behavior is characterized by a complex resonant scattering length a_res. The corresponding inelastic cross sections show troughs as well as peaks near resonance. This may be important for efforts to achieve evaporative and sympathetic cooling for molecules, because it offers the hope that inelastic trap losses can be reduced by tuning close to a Feshbach resonance.
The dynamics of the elastic and inelastic scattering of helium atoms in collisions with oxygen atoms in different fine-structure levels O(3Pj)\mathrm{O}{(}^{3}{P}_{j})O(3Pj​) at cold and ultracold temperatures is investigated using two sets of interaction potentials of the molecule HeO in the ground \ensuremath{\Sigma} and \ensuremath{\Pi} states. Scattering resonances occur in the collisions at low energies. The positions and shapes of the resonance peaks in the inelastic channels do not always mirror those in the elastic channels. The real parts of the scattering lengths are all positive with values in the range 2.5--4.2 \AA{}. The rate coefficients for the quenching of the 3P0{}^{3}{P}_{0}3P0​ and 3P1{}^{3}{P}_{1}3P1​ fine-structure levels decrease almost by one order of magnitude as the temperature decreases from 1 to 0 K and their zero temperature values are, respectively, $3.09\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ and $3.27\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ ${\mathrm{cm}}^{3}{\mathrm{sec}}^{\ensuremath{-}1}.$