Random to Chaotic Statistic Transformation in Low-Field Fano-Feshbach Resonances of Cold Thulium Atoms

Here, we report on the observation of a random to chaotic temperature transformation in the statistics of nearest-neighbor spacings of Fano-Feshbach resonances in the ultracold polarized gas of thulium-169 atoms. We associate this transformation to the appearance of so-called $d$ resonances as well as the shift of other resonances with the temperature. In addition to this statistical change, it has been observed that the characters of $s$- and $d$-resonance temperature shifts are quite different: $s$ resonances experience almost no shift or even negative shift with the temperature, while $d$ resonances experience an obvious positive shift. The sign change was attributed to the difference in polarizability of Feshbach molecules and free thulium atoms. In addition, careful analysis of the broad Fano-Feshbach resonances enabled the determination of the sign of thulium's background scattering length. A rethermalization experiment made it possible to estimate a length value of ${a}_{\mathrm{bg}}=+144\ifmmode\pm\else\textpm\fi{}38\text{ }\text{ }\mathrm{a}.\mathrm{u}.$ This indicates that thulium atoms are suitable for achieving Bose-Einstein condensation.