Ultracold Collision Properties of Metastable Alkaline-Earth Atoms

Ultracold collisions of spin-polarized ${}^{24}\mathrm{M}\mathrm{g}$, ${}^{40}\mathrm{C}\mathrm{a}$, and ${}^{88}\mathrm{S}\mathrm{r}$ in the metastable ${}^{3}P_2$ excited state are investigated based on molecular potentials obtained from ab initio calculations. We calculate the long-range interaction potentials and estimate the scattering length and the collisional loss rate as a function of magnetic field. The scattering lengths show resonance behavior due to the appearance of a molecular bound state in a purely long-range interaction potential and are positive for magnetic fields below 50 mT. A loss-rate model shows that losses should be smallest near zero magnetic field and for fields slightly larger than the resonance field, where the scattering length is also positive.

Figure 1

Long-range gerade adiabatic potentials correlating to two ${}^{3}P_2$ Sr atoms for $B=10\mathrm{m}\mathrm{T}$ and ${\theta }_B=45°$.

Figure 2

Polar plot of the adiabatic potential for two spin polarized ${\mathrm{S}\mathrm{r}}^{*}$ atoms at $B=10\mathrm{m}\mathrm{T}$. Equipotential curves are shown as dashed, thick dashed, and solid contours for energies that are lower than, equal to, and higher than the dissociation energy of the two atoms, respectively. The contour values are given in mK. The arrow indicates the direction of $\mathbf{B}$.

Figure 3

The coefficients $U_L(R)$ of Eq. (2) for ${\mathrm{S}\mathrm{r}}_2$ as a function of internuclear separation and $B=10\mathrm{m}\mathrm{T}$. The inset shows $U_0(R)$ for $B=5$ and 10 mT.

Figure 4

Scattering length of the $U_0(R)$ potential of spin polarized ${}^{3}P_2$ atoms as a function of magnetic field. Values for ${}^{24}\mathrm{M}\mathrm{g}$, ${}^{40}\mathrm{C}\mathrm{a}$, and ${}^{88}\mathrm{S}\mathrm{r}$ are shown. The arrows show the magnetic fields for which zero-energy resonances occur.