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Physical Review A

Collisions of trapped molecules with slow beams

Timur V. Tscherbul, Zoran Miroslav Pavlovic, H. R. Sadeghpour, Robin Côté, A. Dalgarno

Published Aug 10, 2010• 16 citations
Publisher

Abstract

We present a theoretical study of molecular-trap loss induced by collisions with slow atomic beams based on an explicit analysis of collision kinematics in the laboratory frame and a rigorous quantum description of atom-molecule scattering in external fields. The theory is applied to elucidate the effects of nonuniform magnetic and optical trapping fields on low-temperature collisions of OH ($J=3/2,{M}_{J}=3/2,f$) molecules with $^{4}\mathrm{He}$ atoms. Our calculations quantify the extent to which both elastic and inelastic cross sections are suppressed by external trapping fields, clarify the role of small-angle scattering in trap loss, and may benefit future experiments on collisional cooling of molecules in electromagnetic traps. The calculated cross sections for trap loss in $^{4}\mathrm{He}$ $+$ OH collisions are consistent with recent experimental observations at low beam energies [B. C. Sawyer et al., Phys. Rev. Lett. 101, 203203 (2008)], demonstrating the importance of including the effects of nonuniform trapping fields in theoretical simulations of cold collision experiments with trapped molecules and slow atomic beams.

DOI
10.1103/physreva.82.022704

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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.

•Jan 1, 2011•0 citations
We present a theoretical study of molecular-trap loss induced by collisions with slow atomic beams based on an explicit analysis of collision kinematics in the laboratory frame and a rigorous quantum description of atom-molecule scattering in external fields. The theory is applied to elucidate the effects of nonuniform magnetic and optical trapping fields on low-temperature collisions of OH (J=3/2,MJ=3/2,fJ=3/2,{M}_{J}=3/2,fJ=3/2,MJ​=3/2,f) molecules with 4He^{4}\mathrm{He}4He atoms. Our calculations quantify the extent to which both elastic and inelastic cross sections are suppressed by external trapping fields, clarify the role of small-angle scattering in trap loss, and may benefit future experiments on collisional cooling of molecules in electromagnetic traps. The calculated cross sections for trap loss in 4He^{4}\mathrm{He}4He +++ OH collisions are consistent with recent experimental observations at low beam energies [B. C. Sawyer et al., Phys. Rev. Lett. 101, 203203 (2008)], demonstrating the importance of including the effects of nonuniform trapping fields in theoretical simulations of cold collision experiments with trapped molecules and slow atomic beams.
Research in the field of cold polar molecules is progressing rapidly. An array of interesting\ntopics is being developed including precision measurement and fundamental tests, quantum phase transitions, and ultracold chemistry. In particular, dipolar molecules in well-defined quantum states enable exquisite control of their interactions via applied electric fields. The long-range, anisotropic interaction between dipolar molecules leads to new collision dynamics that could be used for novel collective effects, quantum state engineering, and information processing. The focus of this Thesis is the production of cold samples of neutral OH molecules via Stark deceleration and magnetic trapping for novel collision experiments. This novelty results from our combination of cold external beams and trapped target molecules which facilitates observation of dipolar effects as well as low temperature collision resonances. The large permanent electric dipole moment of OH allows us to precisely tune the lab-frame velocity of the molecular packets from ∼ 500 m/s to rest. We have magnetically trapped OH packets at the terminus of our Stark decelerator at a temperature of 70 mK and density of 106 cm−3. With improved understanding of Stark deceleration, we optimize the decelerator efficiency and its coupling to the magnetic trap. Our latest trap design uses permanent ring magnets to create a three-dimensional magnetic quadrupole field. Use of magnetically trapped OH molecules for collision experiments with external beams allow us the unique opportunity of observing both elastic and inelastic collisions. In addition, the trap confinement yields sensitivity to differential elastic cross sections at low collision energies. This open magnetic trap has allowed measurement of collision cross sections between trapped OH and external supersonic beams of He and D2, the latter of which is of astrophysical interest due to the role of H2-OH collisions in pumping interstellar OH megamasers. The combination of trapped OH molecules and temperature tuned beams of He and D2 has facilitated measurement of the lowest-energy D2-OH collision cross sections yet reported. More recently, we report the first observation of electric-field dependent cross sections between two different species of cold polar molecules - OH and ND3 - thereby demonstrating control over molecular scattering in the cold regime. By combining for the first time the production techniques of Stark deceleration and buffer gas cooling, we increase the molecular interaction time by∼ 105 over traditional crossed-beam experiments to gain enhanced sensitivity at the characteristic densities of cold molecule production.
This tutorial chapter provides an introduction to the vibrant field of cold molecular collisions in the presence of external electromagnetic fields. The kinetic energy of molecules confined in electromagnetic traps is small compared to their interactions with external fields, so the influence of molecule -field interactions on molecular collisions at ultralow temperatures can no longer be neglected or treated perturbatively. The intricate topology of spin-dependent, multidimensional intermolecular interactions makes it necessary to use accurate, non-perturbative quantum scattering techniques for solving the Schrodinger equation for molecules colliding in the presence of external fields. The primary goal of this chapter is to provide an overview of multichannel quantum scattering theory of molecular collisions in external fields, with a focus on rigorous coupled-channel methodology applied to molecules of current experimental interest. We also present an overview of the mechanisms for controlling elastic and inelastic molecular collisions with external magnetic fields.
This thesis describes an experiment to produce the first laser cooled mixtures of atoms and polar molecules in magneto-optical and magnetic quadrupole traps. Inelastic collision processes between CaF molecules and Rb atoms are studied in both trapping arrangements. When molecules occupy the first rotationally excited state it is found that loss from either trap occurs at near the universal rate due to collisions with co-trapped atoms. When the molecular sample is transferred to the ground rotational state the loss rate is suppressed by at least an order of magnitude. The experimental results are compared to a quantum scattering model based on quantum defect theory and the results seem to be encouraging for observing a high ratio of elastic to inelastic collision rates in this system. In addition, improvements to the experimental apparatus are presented which led to the first measurements of the elastic cross-section for collisions between CaF and Rb. Although at the currently attainable number densities no thermalization is observed, an upper bound on the value of the cross section is placed.
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.
We describe calculations of elastic and inelastic scattering of neutral molecules and cold ions in a magnetic field. The molecule is assumed to have a magnetic and electric dipole moment. The external magnetic field splits the ground rovibrational energy levels of the molecule. The highest energy state within the ground rovibrational manifold increases in energy as the distance to the ion decreases leading to a repelling potential. At low energy, inelastic collisions are strongly suppressed due to the large distance of closest approach. Thus, a collision between a neutral molecule and a cold ion will lead to a decrease in the molecule's kinetic energy with no change in internal energy. We present results for the specific case of OH molecules cooled by Be+{\mathrm{Be}}^{+}Be+, Mg+{\mathrm{Mg}}^{+}Mg+, or Ca+{\mathrm{Ca}}^{+}Ca+ ions. Also, we perform molecular dynamics simulations of ions and molecules in a combined Paul trap and time-averaged orbiting potential trap. Our results suggest that sympathetic cooling of neutral molecules by ions would be possible if cold ions and molecules could be simultaneously trapped.
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.