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Physical Review A

Multichannel ultracold collisions between metastable bosonic 88 Sr and fermionic 87 Sr atoms

Deshui Yu

Published Sep 6, 2012• 2 citations
Publisher

Abstract

Ultracold collisions between metastable bosonic ${}^{88}$Sr [$(5s5p){\phantom{\rule{0.16em}{0ex}}}^{3\phantom{\rule{-0.16em}{0ex}}}\phantom{\rule{-0.16em}{0ex}}{P}_{2}$] and fermionic ${}^{87}$Sr [$(5s5p){\phantom{\rule{0.16em}{0ex}}}^{3\phantom{\rule{-0.16em}{0ex}}}\phantom{\rule{-0.16em}{0ex}}{P}_{2}$ $(i=9/2)$] atoms are investigated based on an approach of tensorial analysis. The scattering physics of two atoms in fully polarized $s$-wave entrance channels is studied in detail. In the Born-Oppenheimer approximation, the strong anisotropic interatomic interaction is demonstrated to induce formations of long-range molecular potential wells. However, besides significantly modifying the elastic scattering, the anisotropic interatomic interaction leads to the strong multichannel coupling between different partial waves, which triggers a high rate of inelastic losses. By applying an external static magnetic field ${\mathbf{B}}_{0}={\mathcal{B}}_{0}{\mathbf{e}}_{\mathrm{z}}$, the inelastic scattering can be suppressed while the elastic scattering is significantly enhanced. Additionally, the energy-dependent complex $s$-wave scattering lengths at a given relative collision energy strongly depend on the strength of magnetic field. We, moreover, self-consistently investigate ultracold collisions of two atoms at low temperatures in an optical lattice site. In the $\ensuremath{\delta}$-function pseudopotential approximation, we derive the effective $s$-wave scattering lengths, energy eigenvalues, elastic and inelastic scattering rates, and their dependence on the external magnetic field. We find that (i) the effective scattering lengths of ultracold atoms in entrance channels of interest display resonance behavior at certain values of magnetic field and (ii) the extra Zeeman interaction not only leads to the suppression of inelastic scattering but also enlarges the elastic scattering rates.

DOI
10.1103/physreva.86.032703

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Ultracold collisions between metastable bosonic 88{}^{88}88Sr [(5s5p)3P2(5s5p){\phantom{\rule{0.16em}{0ex}}}^{3\phantom{\rule{-0.16em}{0ex}}}\phantom{\rule{-0.16em}{0ex}}{P}_{2}(5s5p)3P2​] and fermionic 87{}^{87}87Sr [(5s5p)3P2(5s5p){\phantom{\rule{0.16em}{0ex}}}^{3\phantom{\rule{-0.16em}{0ex}}}\phantom{\rule{-0.16em}{0ex}}{P}_{2}(5s5p)3P2​ (i=9/2)(i=9/2)(i=9/2)] atoms are investigated based on an approach of tensorial analysis. The scattering physics of two atoms in fully polarized sss-wave entrance channels is studied in detail. In the Born-Oppenheimer approximation, the strong anisotropic interatomic interaction is demonstrated to induce formations of long-range molecular potential wells. However, besides significantly modifying the elastic scattering, the anisotropic interatomic interaction leads to the strong multichannel coupling between different partial waves, which triggers a high rate of inelastic losses. By applying an external static magnetic field B0=B0ez{\mathbf{B}}_{0}={\mathcal{B}}_{0}{\mathbf{e}}_{\mathrm{z}}B0​=B0​ez​, the inelastic scattering can be suppressed while the elastic scattering is significantly enhanced. Additionally, the energy-dependent complex sss-wave scattering lengths at a given relative collision energy strongly depend on the strength of magnetic field. We, moreover, self-consistently investigate ultracold collisions of two atoms at low temperatures in an optical lattice site. In the \ensuremathδ\ensuremath{\delta}\ensuremathδ-function pseudopotential approximation, we derive the effective sss-wave scattering lengths, energy eigenvalues, elastic and inelastic scattering rates, and their dependence on the external magnetic field. We find that (i) the effective scattering lengths of ultracold atoms in entrance channels of interest display resonance behavior at certain values of magnetic field and (ii) the extra Zeeman interaction not only leads to the suppression of inelastic scattering but also enlarges the elastic scattering rates.
We present a multichannel-scattering calculation of elastic and inelastic cold collisions between two low-field seeking, metastable 88Sr [(5s5p)3P2] atoms in the presence of an external magnetic field. The scattering physics is governed by strong anisotropic long-range interactions, which lead to pronounced coupling among the partial waves of relative motion. As a result, nonadiabatic transitions are shown to trigger a high rate of inelastic losses. At relatively high energies, T>100 microK, the total inelastic collision rate is comparable with the elastic rate. However, at lower collisional energy, the elastic rate decreases, and at T approximately 1 microK, it becomes substantially smaller than the inelastic rate. Our study suggests that magnetic trapping and evaporative cooling of 88Sr [(5s5p)3P2] atoms, as well as 40Ca [(4s4p)3P2], in low-field seeking states will prove difficult to achieve experimentally.
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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.
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