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arXiv:0908.2065 · Physical Review Letters

Dramatic Reductions in Inelastic Cross Sections for Ultracold Collisions near Feshbach Resonances

Jeremy M. Hutson, Musie Beyene, Maykel Leonardo González-Martínez

Published Oct 12, 2009• 35 citations
arXivHTMLPDF

Abstract

We show that low-energy inelastic cross sections can decrease as well as increase in the vicinity of a zero-energy Feshbach resonance. When an external field is used to tune across such a resonance, the real and imaginary parts of the scattering length show asymmetric oscillations with both peaks and troughs. In favorable circumstances, the inelastic collision rate can be reduced to almost zero. This may be important for efforts to achieve evaporative and sympathetic cooling for molecules.

DOI
10.1103/physrevlett.103.163201

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We show that low-energy inelastic cross sections can decrease as well as increase in the vicinity of a zero-energy Feshbach resonance. When an external field is used to tune across such a resonance, the real and imaginary parts of the scattering length show asymmetric oscillations with both peaks and troughs. In favorable circumstances, the inelastic collision rate can be reduced to almost zero. This may be important for efforts to achieve evaporative and sympathetic cooling for molecules.
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.
In the absence of inelastic scattering, Feshbach resonances produce poles in scattering lengths and very large peaks in elastic cross-sections. However, inelastic scattering removes the poles. Whenever the resonant state is coupled comparably to the elastic and inelastic channels, the scattering length exhibits only a small oscillation and peaks in cross-sections are significantly suppressed. A resonant scattering length is defined to characterize the amplitude of the oscillation, and is shown to be small for many collisions of ultracold molecules. The results suggest that cross-sections for some ultracold collision processes will be much less sensitive to details of the potential than has been expected.
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 describe procedures for converging on and characterizing zero-energy Feshbach resonances that appear in scattering lengths for ultracold atomic and molecular collisions as a function of an external field. The elastic procedure is appropriate for purely elastic scattering, where the scattering length is real and displays a true pole. The regularized scattering length procedure is appropriate when there is weak background inelasticity, so that the scattering length is complex and displays an oscillation rather than a pole, but the resonant scattering length ares{a}_{\mathrm{res}}ares​ is close to real. The fully complex procedure is appropriate when there is substantial background inelasticity and the real and imaginary parts of ares{a}_{\mathrm{res}}ares​ are required. We demonstrate these procedures for scattering of ultracold 85Rb^{85}\mathrm{Rb}85Rb in various initial states. All of them can converge on and provide full characterization of resonances, from initial guesses many thousands of widths away, using scattering calculations at only about ten values of the external field.
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.
With the advent of evaporative cooling methods, atomic collisions can be studied at microkelvin and even sub-microkelvin temperatures. At these energies, resonance and threshold phenomena become very pronounced. Near zero-energy resonances lead to large variations in collision cross sections with energy. Magnetically tunable Feshbach resonances have been observed, which allow elastic collision cross sections and scattering lengths to be tuned over large ranges with small changes in an applied magnetic field. These resonance effects are extremely sensitive to small variations in atomic interaction parameters, including scattering lengths. The combined results of ultracold atomic collision and photoassociation spectroscopy experiments is leading to a complete and consistent picture of collisions of ultracold alkali atoms.