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arXiv:physics/0408125 · Journal of Physics B Atomic Molecular and Optical Physics

Ultracold atomic collisions in tight harmonic traps: perturbation theory, ionization losses and application to metastable helium atoms

T J Beams, G. Peach, I B Whittingham

Published Nov 9, 2004• 6 citations
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Abstract

Collisions between tightly confined atoms can lead to ionization and hence to loss of atoms from the trap. We develop second-order perturbation theory for a tensorial perturbation of a spherically symmetric system and the theory is then applied to processes mediated by the spin-dipole interaction. Redistribution and loss mechanisms are studied for the case of spin-polarized metastable helium atoms and results obtained for the five lowest s states in the trap and trapping frequencies ranging from 1 kHz to 10 MHz.

DOI
10.1088/0953-4075/37/22/014

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Collisions between tightly confined atoms can lead to ionization and hence to loss of atoms from the trap. We develop second-order perturbation theory for a tensorial perturbation of a spherically symmetric system and the theory is then applied to processes mediated by the spin-dipole interaction. Redistribution and loss mechanisms are studied for the case of spin-polarized metastable helium atoms and results obtained for the five lowest s states in the trap and trapping frequencies ranging from 1 kHz to 10 MHz.
Collisions between tightly confined atoms can lead to ionization and hence to loss of atoms from the trap. We develop second-order perturbation theory for a tensorial perturbation of a spherically symmetric system and the theory is then applied to processes mediated by the spin-dipole interaction. Redistribution and loss mechanisms are studied for the case of spin-polarized metastable helium atoms and results obtained for the five lowest s states in the trap and trapping frequencies ranging from 1 kHz to 10 MHz.
Spin-dipole mediated interactions between tightly confined metastable helium atoms couple the spin-polarized quintet ${^{5}\ensuremath{\sum}}_{g}^{+}$ state to the singlet ${^{1}\ensuremath{\sum}}_{g}^{+}$ state from which autoionization is highly probable, resulting in finite lifetimes for the trap eigenstates. We extend our earlier study on spherically symmetric harmonic traps to the interesting cases of axially symmetric anisotropic harmonic traps and report results for the lowest 10 states in ``cigarlike'' and ``pancakelike'' traps with average frequencies of 100 kHz and 1 MHz. We find that there is a significant suppression of ionization, and subsequent increase in lifetimes, at trap aspect ratios A=p/qA=p/qA=p/q, where ppp and qqq are integers, for those states that are degenerate in the absence of collisions or spin-dipole interactions.
We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two highly efficient computational methods for determining the bound state energies and eigenfunctions of such systems. The perturbed harmonic oscillator problem is characterized by a long asymptotic region beyond the effective range of the interatomic potential. The first method, which is based on quantum defect theory and is an adaptation of a technique developed by one of the authors (G.P.) for highly excited states in a modified Coulomb potential, is very efficient for integrating through this outer region. The second method is a direct numerical solution of the radial Schr\"odinger equation using a discrete variable representation of the kinetic energy operator and a scaled radial coordinate grid. The methods are applied to the case of trapped spin-polarized metastable helium atoms. The calculated eigenvalues agree very closely for the two methods, and with the eigenvalues computed using the generalized self-consistent method.
Scattering and ionizing cross sections and rates are calculated for ultracold collisions between metastable helium atoms using a fully quantum-mechanical close-coupled formalism. Homonuclear collisions of the bosonic 4He∗+4He∗^{4}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}4He∗+4He∗ and fermionic 3He∗+3He∗^{3}\mathrm{He}^{*}+^{3}\mathrm{He}^{*}3He∗+3He∗ systems, and heteronuclear collisions of the mixed 3He∗+4He∗^{3}\mathrm{He}^{*}+^{4}\mathrm{He}^{*}3He∗+4He∗ system, are investigated over the temperature range 1 $\ensuremath{\mu}\mathrm{K}$ to 1 K. Carefully constructed Born-Oppenheimer molecular potentials are used to describe the electrostatic interaction between the colliding atoms, and complex optical potentials to represent loss through ionization from the ${}^{1,3}\mathrm{\ensuremath{\Sigma}}$ states. Magnetic spin-dipole-mediated transitions from the ${}^{5}\mathrm{\ensuremath{\Sigma}}$ state are included and results reported for spin-polarized and unpolarized systems. Comparisons are made with experimental results, previous semiclassical models, and a perturbed single-channel model.
A quantum-mechanical close-coupled calculation for collisions of spin-polarized triplet helium atoms in a magnetostatic trap is presented in which the Penning and associative ionization processes are represented by a complex optical potential. The rate coefficients for the spin relaxation and relaxation-induced Penning ionization processes for a range of magnetic fields and temperatures, spanning the cold and ultracold temperature regimes, have been calculated and the sensitivity of these results to uncertainties in the molecular potentials and autoionization width investigated. The rate constants for both elastic and inelastic processes were found to be particularly sensitive to the short-range ${}^{5}{\ensuremath{\Sigma}}_{g}^{+}$ molecular potential and, to a lesser extent, the rate constants for relaxation-induced Penning ionization displayed sensitivity to the short-range form of the ${}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ molecular potential and the autoionization width.
Spin-polarized metastable atoms of ultracold ytterbium are trapped at high density and their inelastic collisional properties are measured. We reveal that in collisions of Yb(3P2{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2}3P2​) with Yb(1S0{}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}1S0​) there is relatively weak inelastic loss, but with a significant spin dependence consistent with Zeeman sublevel changes as being the dominant decay process. This is in strong contrast to our observations of Yb(3P2{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2}3P2​)--Yb(3P2{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2}3P2​) collisional losses, which are, at low field, much more rapid and have essentially no spin dependence. Our results give a guideline to using the 3P2{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{2}3P2​ states in many possible applications.