Multichannel Quantum Defect Theory with Numerical Reference Functions: Applications to Cold Atomic Collisions

Abstract

We develop a method for calculating multichannel wavefunctions in the spirit of quantum defect theory, based on numerically calculated reference functions. We benchmark the method by calculating cold collisional properties of ${}^{85}$Rb and ${}^6$Li in the presence of external magnetic fields tuned across specific $s$-wave Feshbach resonances and thereby reproducing known results. We then apply the method to calculate experimentally observed $d$-wave Feshbach resonance {[\textit{Phys. Rev. Lett.} {\bf 119}, 203402 (2017)]} %MDPI: Is this a reference citation? If so, please note that ref. citations are not allowed in Abstract and should be removed. in ${}^{87}$Rb-${}^{85}$Rb cold collisions. Our numerical results for this $d$-wave resonance show good agreement with the experimental observations. The method is applicable to arbitrary interaction potentials and to any energy range near the scattering threshold. The implementation of our method to any multichannel two-body scattering problem is straightforward.

arXiv comment5 figures, 12 pages

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