Multichannel ultracold collisions between metastable bosonic88Sr and fermionic87Sr atoms

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.