Bose-Einstein condensation of ${}^{88}\mathrm{Sr}$ through sympathetic cooling with ${}^{87}\mathrm{Sr}$

We report Bose-Einstein condensation of ${}^{88}\mathrm{Sr}$, which has a small, negative $s$-wave scattering length ($a_{88}=-2a_0$). We overcome the poor evaporative cooling characteristics of this isotope by sympathetic cooling with ${}^{87}\mathrm{Sr}$ atoms. ${}^{87}\mathrm{Sr}$ is effective in this role despite the fact that it is a fermion because of the large ground-state degeneracy arising from a nuclear spin of $I=9/2$, which reduces the impact of Pauli blocking of collisions. We observe a limited number of atoms in the condensate ($N_{\max }\approx {10}^4$) that is consistent with the value of $a_{88}$ and the optical dipole trap parameters.

Figure 1

Partial level diagram for ${}^{88}\mathrm{Sr}$ (- -) and ${}^{87}\mathrm{Sr}$ (—) showing hyperfine structure and isotope shifts [22, 23, 24]. Total quantum number $F$ is indicated for ${}^{87}\mathrm{Sr}$ levels.

Figure 2

(A) Temperature evolution in an ODT with a trap depth of $U/k_B=23\hspace{0.5em}\mu$K for samples of ${}^{88}\mathrm{Sr}$ and ${}^{87}\mathrm{Sr}$ alone and for each in a mixture. The number of each isotope present initially is approximately ${10}^6$. (B) Number and (C) temperature for a mixture along a typical forced evaporation trajectory.

Figure 3

Appearance of Bose-Einstein condensation in absorption images (left) and areal density profiles (right). Data correspond to 16 ms (bottom) or 22 ms (top three) of free expansion after indicated evaporation times ($t$). Images on the left have the same time stamp as on the right. The areal density profiles are from a vertical cut through the center of the atom cloud, and temperatures are extracted from two-dimensional Bose-Einstein distribution fits to the thermal pedestal. At 7.5 s, a bimodal distribution is evident, indicative of Bose-Einstein condensation. A pure condensate is shown at 9 s of evaporation. The Maxwell-Boltzmann distribution does not accurately describe low-velocity atoms near degeneracy, and the Bose-Einstein distribution does not describe the condensate contribution. So in these respective regimes, a central region slightly larger than the condensate radius is excluded from fitting. For bimodal data, fugacity is constrained to 1.

Figure 4

Comparison of observed condensate number and maximum condensate number predicted by a model of the trapping potential along the evaporation trajectory.