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arXiv:0808.3592 · New Journal of Physics

Magnetic field modification of ultracold molecule–molecule collisions

Timur V. Tscherbul, Yu. V. Suleimanov, Vincenz̊o Aquilanti, Roman V. Krems

Published May 14, 2009• 72 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/11/5/055021

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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.
In this work we investigate the potential of controlling cold (O(K)−mK) and ultracold (mK-μK) atom-molecule collisions by tuning scattering states across Feshbach resonances using magnetic fields. We are interested in particular in the prospect of suppressing the often undesirable inelastic collisions. The He-O_2 system provides the vehicle for our study. We calculate bound and quasi-bound states of several isotopic combinations, including their Zeeman structure, to reveal the underlaying pattern for easier characterization of quasi-bound states in terms of rigorous and approximately good quantum numbers. These calculations also help us locate the fields at which zero-energy resonances will occur. Scattering calculations are then performed for collisions of 3^He and 4^He with {16}^O_2 at fixed (1 μK) energy but varying magnetic field. The field is varied to sweep the scattering state across resonance. At low and ultralow energies we enter the Wigner threshold regime where the S-partial wave dominates the wavefunction. The cross sections, and the real and imaginary parts of the scattering length, vary dramatically across resonance. Their profiles are used to analyze the resonances. In a highlight of our results we show that dramatic suppression of inelastic cross sections occur for 4^He-{16}^O_2 . The resonances are relatively wide (of order 100 Gauss), with suppression of inelastic scattering over a similarly wide range of fields and for temperatures ranging from 10 mK down to 1 μK. We conclude that under certain conditions it is possible to almost completely eliminate inelastic collisions. This is potentially very important for cooling techniques, such as evaporative and sympathetic cooling, that require efficient elastic cross sections. Suppression of inelastic collisions can not only increase thermalization efficiency but it can also result in longer trap-lifetimes by reducing transitions to untrapable states.
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 collision dynamics of (17)O(2)((3)Σ(g)(-)) + (17)O(2)((3)Σ(g)(-)) in the presence of a magnetic field is studied within the close-coupling formalism in the range between 10 nK and 50 mK. A recent global ab initio potential energy surface (PES) is employed and its effect on the dynamics is analyzed and compared with previous calculations where an experimentally derived PES was used [T. V. Tscherbul et al., New J. Phys 134, 055021 (2009)]. Compared to the results using the older PES, magnetic-field dependence of the low-field-seeking state in the ultracold regime is characterized by a very large background scattering length, a(bg), and cross sections exhibit broader and more pronounced Feshbach resonances. The marked resonance structure is somewhat surprising considering the influence of inelastic scattering but it can be explained by resorting to the analytical van der Waals theory, where the short-range amplitude of the entrance channel wavefunction is enhanced by the large a(bg). This strong sensitivity to the short range of the ab initio PES persists up to relatively high energies (10 mK). After this study and despite quantitative predictions are very difficult, it can be concluded that the ratio between elastic and spin relaxation scattering is generally small, except for magnetic fields which are either low or close to an asymmetric Fano-type resonance. Some general trends found here, such as a large density of quasibound states and a propensity toward large scattering lengths, could be also characteristic of other anisotropic molecule-molecule systems.
We have generalized the BOUND and MOLSCAT packages to allow calculations in basis sets where the monomer Hamiltonians are off diagonal and used this capability to carry out bound-state and scattering calculations on $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ and $^{4}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$ as a function of magnetic field. Following the bound-state energies to the point where they cross thresholds gives very precise predictions of the magnetic fields at which zero-energy Feshbach resonances occur. We have used this to locate and characterize two very narrow Feshbach resonances in $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{NH}$. Such resonances can be used to tune elastic and inelastic collision cross sections, and sweeping the magnetic field across them will allow a form of quantum control in which separated atoms and molecules are associated to form complexes. For the first resonance, where only elastic scattering is possible, the scattering length shows a pole as a function of magnetic field and there is a very large peak in the elastic cross section. For the second resonance, however, inelastic scattering is also possible. In this case the pole in the scattering length is dramatically suppressed and the cross sections show relatively small peaks. The peak suppression is expected to be even larger in systems with stronger inelasticity. The results suggest that calculations on ultracold molecular inelastic collisions may be much less sensitive to details of the potential energy surface than has been believed.
Rigorous calculations of magnetic Feshbach resonances and Zeeman relaxation cross sections in an ultracold and cold chromium gas are reported. This work presents the calculation of such inelastic processes in collisions of atoms with large magnetic moments. Using our recently constructed accurate interaction potentials for the chromium dimer, we compute the positions and widths of magnetically tuned resonances in an optically trapped ultracold Cr gas. We find good agreement with recent experimental data and report that spin-change collision cross sections quickly increase with decreasing collision energy and magnetic-field strength at energies below 1 K and magnetic fields larger than 40 G.
We calculate the cross sections for elastic scattering and Zeeman relaxation in binary collisions of molecules in the rovibrational ground state of a ${}^{2}\ensuremath{\Sigma}$ electronic state and the Zeeman state with the electron spin projection MS=12{M}_{S}=\frac{1}{2}MS​=21​ on the magnetic field axis. This is the lowest-energy state of ${}^{2}\ensuremath{\Sigma}$ molecules confined in a magnetic trap. The results are averaged over calculations with multiple molecule-molecule interaction potentials, which yield the expectation intervals for the cross sections and the elastic-to-inelastic cross-section ratios. We find that the elastic-to-inelastic cross-section ratios under conditions corresponding to trapped molecular ensembles at $T\ensuremath{\sim}{10}^{\ensuremath{-}3}$ K exceed 100 for the majority of ${}^{2}\ensuremath{\Sigma}$ molecules. The range of ${}^{2}\ensuremath{\Sigma}$ molecules expected to be collisionally unstable in magnetic traps at $T<{10}^{\ensuremath{-}3}$ K is limited to molecules with the spin-rotation interaction constant ${\ensuremath{\gamma}}_{\mathrm{SR}}>0.5$ cm${}^{\ensuremath{-}1}$ and the rotational constant Be<4{B}_{e}<4Be​<4 cm${}^{\ensuremath{-}1}$.