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arXiv:1012.2814 · Physical Review A

Cold and ultracold NH-NH collisions in magnetic fields

Liesbeth M. C. Janssen, Piotr Szymon Żuchowski, Ad van der Avoird, Gerrit C. Groenenboom, Jeremy M. Hutson

Published Feb 28, 2011• 42 citations
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Abstract

Elastic and spin-changing inelastic collision cross sections are presented for cold and ultracold magnetically trapped NH. The cross sections are obtained from coupled-channel scattering calculations as a function of energy and magnetic field. We specifically investigate the influence of the intramolecular spin-spin, spin-rotation, and intermolecular magnetic dipole coupling on the collision dynamics. It is shown that $^{15}\mathrm{N}$H is a very suitable candidate for evaporative cooling experiments. The dominant trap-loss mechanism in the ultracold regime originates from the intermolecular dipolar coupling term. At higher energies and fields, intramolecular spin-spin coupling becomes increasingly important. Our qualitative results and conclusions are fairly independent of the exact form of the potential and of the size of the channel basis set.

DOI
10.1103/physreva.83.022713

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Dipolar collisions in cooling and trapping of paramagnetic atoms

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In this dissertation, I present ab initio theoretical results on cold and ultra-cold collision of atomic and molecular systems with magnetic and electric dipole moments. The collisions of different isotopes of maximally spin-polarized chromium atoms (52Cr and 53Cr), alkali-metal atom (Rb) - chromium atom, and magnetically trapped hydroxide (OH) with cold supersonic helium beam are considered in this thesis. Spin-changing cross sections and rate constants in Cr-Cr isotopic collision in the presence of a magnetic field are calculated by propagating a set of multichannel equations in the field. The coupling between dipole-dipole allowed and hyperfine channels are included. The short range electrostatic interactions between atoms and atom-molecule are represented with highly-accurate Born-Oppenheimer (BO) potential energy curves. Due to the large spin multiplicity in Cr-Cr and Rb-Cr interactions, more than the usual singlet and triplet channels are obtained. The long-range van der Waals (vdW) interactions between atoms are calculated, for Cr, by including accurate transition frequencies, discrete dipole matrix elements, and photoionization continuum oscillator strengths, and for Rb, using published dynamic polarizabilities. The vdW coefficients for Cr-Cr and Rb-Cr are obtained. In the cold collision regime, I investigate the influence of angular momentum shape resonances on the elastic and inelastic (loss channel) rate coefficients, and when the Zeeman relaxation, resulting in the loss of atoms from the trap, dominates elastic collision. Dipolar collisions are crucial to achieving quantum degeneracy. Magnetically tuned Fano-Feshbach closed-channel resonances are used to obtain zero-energy scattering lengths in comparison with observation of trap loss. In bosonic chromium collisions, resonances appear due only to dipolar interaction. The interplay between hyperfine and dipolar resonances in mixed-species Cr-Cr and Rb-Cr collisions is studied. In Rb-Cr, it is found that the molecule has broken symmetry and therefore contains a large permanent electric dipole moment in the ground state. A recent collisional experiment at JILA of a supersonic helium beam with a magnetically trapped OH radical found the onset of a quantum threshold in the total OH loss rate. Using ab initio BO energy surfaces, I calculated the spin-changing collisions which removed OH from the trap. Only after including the effect of the trapping potential on the collision dynamics, some agreement with observation was found. ^

•Jan 1, 2011•1 citation
Elastic and spin-changing inelastic collision cross sections are presented for cold and ultracold magnetically trapped NH. The cross sections are obtained from coupled-channel scattering calculations as a function of energy and magnetic field. We specifically investigate the influence of the intramolecular spin-spin, spin-rotation, and intermolecular magnetic dipole coupling on the collision dynamics. It is shown that 15N^{15}\mathrm{N}15NH is a very suitable candidate for evaporative cooling experiments. The dominant trap-loss mechanism in the ultracold regime originates from the intermolecular dipolar coupling term. At higher energies and fields, intramolecular spin-spin coupling becomes increasingly important. Our qualitative results and conclusions are fairly independent of the exact form of the potential and of the size of the channel basis set.
We present elastic and inelastic spin-changing cross sections for cold and ultracold NH(X (3)Σ(-)) + NH(X (3)Σ(-)) collisions, obtained from full quantum scattering calculations on an accurate ab initio quintet potential-energy surface. Although we consider only collisions in zero field, we focus on the cross sections relevant for magnetic trapping experiments. It is shown that evaporative cooling of both fermionic (14)NH and bosonic (15)NH is likely to be successful for hyperfine states that allow s-wave collisions. The calculated cross sections are very sensitive to the details of the interaction potential, due to the presence of (quasi)bound state resonances. The remaining inaccuracy of the ab initio potential-energy surface therefore gives rise to an uncertainty in the numerical cross-section values. However, based on a sampling of the uncertainty range of the ab initio calculations, we conclude that the exact potential is likely to be such that the elastic-to-inelastic cross-section ratio is sufficiently large to achieve efficient evaporative cooling. This likelihood is only weakly dependent on the size of the channel basis set used in the scattering calculations.
We investigate the ultracold reaction dynamics of magnetically trapped NH(X (3)Σ(-)) radicals using rigorous quantum scattering calculations involving three coupled potential energy surfaces. We find that the reactive NH+NH cross section is driven by a short-ranged collisional mechanism, and its magnitude is only weakly dependent on magnetic field strength. Unlike most ultracold reactions observed so far, the NH+NH scattering dynamics is nonuniversal. Our results indicate that chemical reactions can cause more trap loss than spin-inelastic NH+NH collisions, making molecular evaporative cooling more difficult than previously anticipated.
Abstract We explore the combined effect of the uncertainties due to the interaction potential and basis set convergence on low-temperature collisional properties of spin-polarized NH molecules in a magnetic field. We show that quantum scattering calculations with different rotational basis sets and λ -scaled interaction potentials produce qualitatively different ratios of elastic to inelastic cross sections for collision energies above 10 −3 cm −1 , leading to favorable (unfavorable) prospects for sympathetic cooling of NH molecules depending on the basis set cutoff parameter N max . The physical reason behind this effect is that the resonance widths, which determine the maximum variation of the scattering cross sections with λ , tend to depend strongly on N max . At ultralow collision energies, all basis sets produce highly uncertain (and statistically indistinguishable) elastic and inelastic cross sections; however, their ratio γ is much less sensitive to small variations of the interaction potential. Our results highlight the importance of basis set convergence in quantum scattering calculations and establish the existence of parameter regimes where unconverged calculations can still be used to make qualitatively accurate predictions of scattering observables.
We investigate the effect of hyperfine interactions on ultracold molecular collisions in magnetic fields, using 24{}^{24}24Mg(1S)+14{}^{1}S){+}^{14}1S)+14NH(${}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}}$) as a prototype system. We explore the energy and magnetic-field dependence of the cross sections, comparing the results with previous calculations that neglected hyperfine interactions [A.O.G. Wallis and J. M. Hutson, Phys. Rev. Lett. 103, 183201 (2009)]. The main effect of hyperfine interactions for spin relaxation cross sections is that the kinetic energy release of the dominant outgoing channels does not reduce to zero at low fields. This results in reduced centrifugal suppression of the cross sections and increased inelastic cross sections at low energy and low field. We also analyze state-to-state cross sections, for various initial states, and show that hyperfine interactions introduce additional mechanisms for spin relaxation. In particular, there are hyperfine-mediated collisions to outgoing channels that are not centrifugally suppressed. However, for Mg+NH\mathrm{Mg}+\mathit{NH}Mg+NH these unsuppressed channels make only small contributions to the total cross sections. We consider the implications of our results for sympathetic cooling of NH by Mg and conclude that the ratio of elastic to inelastic cross sections remains high enough for sympathetic cooling to proceed.
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 this dissertation, I present ab initio theoretical results on cold and ultra-cold collision of atomic and molecular systems with magnetic and electric dipole moments. The collisions of different isotopes of maximally spin-polarized chromium atoms (52Cr and 53Cr), alkali-metal atom (Rb) - chromium atom, and magnetically trapped hydroxide (OH) with cold supersonic helium beam are considered in this thesis. Spin-changing cross sections and rate constants in Cr-Cr isotopic collision in the presence of a magnetic field are calculated by propagating a set of multichannel equations in the field. The coupling between dipole-dipole allowed and hyperfine channels are included. The short range electrostatic interactions between atoms and atom-molecule are represented with highly-accurate Born-Oppenheimer (BO) potential energy curves. Due to the large spin multiplicity in Cr-Cr and Rb-Cr interactions, more than the usual singlet and triplet channels are obtained. The long-range van der Waals (vdW) interactions between atoms are calculated, for Cr, by including accurate transition frequencies, discrete dipole matrix elements, and photoionization continuum oscillator strengths, and for Rb, using published dynamic polarizabilities. The vdW coefficients for Cr-Cr and Rb-Cr are obtained. In the cold collision regime, I investigate the influence of angular momentum shape resonances on the elastic and inelastic (loss channel) rate coefficients, and when the Zeeman relaxation, resulting in the loss of atoms from the trap, dominates elastic collision. Dipolar collisions are crucial to achieving quantum degeneracy. Magnetically tuned Fano-Feshbach closed-channel resonances are used to obtain zero-energy scattering lengths in comparison with observation of trap loss. In bosonic chromium collisions, resonances appear due only to dipolar interaction. The interplay between hyperfine and dipolar resonances in mixed-species Cr-Cr and Rb-Cr collisions is studied. In Rb-Cr, it is found that the molecule has broken symmetry and therefore contains a large permanent electric dipole moment in the ground state. A recent collisional experiment at JILA of a supersonic helium beam with a magnetically trapped OH radical found the onset of a quantum threshold in the total OH loss rate. Using ab initio BO energy surfaces, I calculated the spin-changing collisions which removed OH from the trap. Only after including the effect of the trapping potential on the collision dynamics, some agreement with observation was found. ^