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Bulletin of the American Physical Society

Reduced dimensional model of ultracold molecule-molecule scattering

Christopher Ticknor, Brian K. Kendrick, Jeffery A. Leiding

Published Jun 8, 2017• 0 citations
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Abstract Motivated by the recent experimental developments in ultracold molecules and atoms, we propose a simple theoretical model to address the disassociation, reflection, and transmission probability of a one-dimensional cold molecule via quantum scattering. First, we show the Born approximation results in the weak interaction regime. Then, by employing the Lippmann–Schwinger equation, we give the numerical solution and investigate the disassociation’s dependence on the injection momentum and the interaction strengths. We find that the maximum disassociation rate has a limit when increasing the interaction strengths and injection momentum. We expect that our model can be realized in experiments in the near future.
We present an accurate quantum mechanical study of molecule–molecule collisions in the presence of a magnetic field. The work focuses on the analysis of elastic scattering and spin relaxation in collisions of O 2 ( 3 Σ 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 × 10 –11 cm –3 s –1 . The magnetic field dependence of elastic and inelastic scattering cross sections at ultracold temperatures is dominated by a manifold of Feshbach resonances with the density of ∼100 resonances per Tesla for collisions of molecules in the absolute ground state. This suggests that the scattering length of ultracold molecules in the absolute ground state can be effectively tuned in a very wide range of magnetic fields. Our calculations demonstrate that the number and properties of the magnetic Feshbach resonances are dramatically different for molecules in the absolute ground and excited spin states. The density of Feshbach resonances for molecule–molecule scattering in the low-field-seeking Zeeman state is reduced by a factor of 10.
We consider the coherent control of ultracold molecule-molecule scattering, impacted by a dense set of rovibrational resonances. To characterize the resonance spectrum, a rudimentary model based on multichannel quantum defect theory has been used to study the control of the scattering cross section and the reaction rate. Complete control around resonance energies is shown to be possible, but thermal averaging over a large number of resonances significantly reduces the extent of control of reaction rates related to the random distribution of optimal control parameters between resonances. We show that measuring the extent of coherent control could be used to extract meaningful information about the relative contribution of direct scattering versus collision complex formation, as well as about the statistical regime.