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Physical Review A

Collision between magnetically trapped NH molecules in the (N=0,J=1) state

Masatoshi Kajita

Published Sep 27, 2006• 20 citations
Publisher

Abstract

Elastic and inelastic collisions between $\mathrm{NH}$ molecules in the $(N=0,J=1)$ state were analyzed. These analyses showed that the elastic collision is caused mainly by electric dipole-induced dipole interaction, and the inelastic collision is caused mainly by the magnetic dipole-dipole interaction. The collision cross sections obtained by the quantum and classical methods are roughly in good agreement in the kinetic-energy region of $5--500\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. Moreover, the ratio of the inelastic-collision rate to the elastic-collision rate is lower than 1/200. These results show that the $\mathrm{NH}$ molecule is advantageous to perform evaporative cooling.

DOI
10.1103/physreva.74.032710

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Elastic and inelastic collisions between NH\mathrm{NH}NH molecules in the (N=0,J=1)(N=0,J=1)(N=0,J=1) state were analyzed. These analyses showed that the elastic collision is caused mainly by electric dipole-induced dipole interaction, and the inelastic collision is caused mainly by the magnetic dipole-dipole interaction. The collision cross sections obtained by the quantum and classical methods are roughly in good agreement in the kinetic-energy region of 5−−500mK5--500\phantom{\rule{0.3em}{0ex}}\mathrm{mK}5−−500mK. Moreover, the ratio of the inelastic-collision rate to the elastic-collision rate is lower than 1/200. These results show that the NH\mathrm{NH}NH molecule is advantageous to perform evaporative cooling.
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 present an experimental and theoretical study of atom-molecule collisions in a mixture of cold, trapped N atoms and NH molecules at a temperature of $\ensuremath{\sim}600\text{ }\text{ }\mathrm{mK}$. We measure a small N+NH\mathrm{N}+\mathrm{NH}N+NH trap loss rate coefficient of ${k}_{\mathrm{loss}}^{(\mathrm{N}+\mathrm{NH})}=9(5)(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\text{ }\text{ }{\mathrm{cm}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. Accurate quantum scattering calculations based on ab initio interaction potentials are in agreement with experiment and indicate the magnetic dipole interaction to be the dominant loss mechanism. Our theory further indicates the ratio of N+NH\mathrm{N}+\mathrm{NH}N+NH elastic-to-inelastic collisions remains large (>100>100>100) into the mK regime.
Inelastic collisions between dipolar molecules, assumed to be trapped in a static electric field at cold (> 10−3K) temperatures, are investigated and compared with elastic collisions. For molecules with a Λ-doublet energy-level structure, a dipole moment arises because of the existence of two nearly degenerate states of opposite parity, and the collision of two such dipoles can be solved entirely analytically in the energy range of interest. Cross sections and rate constants are found to satisfy simple, universal formulas. In contrast, for molecules in a Σ electronic ground state, the static electric field induces a dipole moment in one of three rotational sublevels. Collisions between two rotor dipoles are calculated numerically; the results scale simply with molecule mass, rotational constant, dipole moment, and field strength. It might be expected that any particles interacting only under the influence of the dipole-dipole interaction would show similar behavior; however, the most important and general result of this research is that at cold temperatures inelastic rate constants and cross sections for dipoles depend strongly upon the internal structure of the molecules. The most prominent difference between the Λ-doublet and rotor molecules is variation of the inelastic cross section with applied field strength. For Λ-doublet dipoles, cross sections decrease with increasing field strength. For rotor dipoles, cross sections increase proportionally with the square of field strength. Furthermore, the rate constants of the two types of molecules depend very differently on the angular orientations of the dipoles in the electric field.
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${}^{\ensuremath{-}1}$.
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 calculate the interaction potential between N atoms and NH molecules and use it to investigate cold and ultracold collisions important for sympathetic cooling. The ratio of elastic to inelastic cross sections is large over a wide range of collision energy and magnetic field for most isotopic combinations, so that sympathetic cooling of NH molecules by N atoms is a good prospect. However, there are important effects due to a p-wave shape resonance that may inhibit cooling in some cases. We show that scaling the reduced mass used in the collision is approximately equivalent to scaling the interaction potential. We then explore the dependence of the scattering properties on the reduced mass and explain the resonant effects observed using angular-momentum-insensitive quantum defect theory.