Long Range Interactions of Ytterbium in Mixed Quantum Gases

A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited state atoms with strong decay channel to the ground state. Accurate values of long-range interaction parameters are needed for efficient production, cooling, and control of molecules. We used the developed methodology to calculate a number of $C_6$ and $C_8$ coefficients for Yb-Yb, Yb-Rb, and Yb-Li dimers which are of particular interest for development of optical lattice clocks, studies of fundamental symmetries and quantum gas mixtures, and practical realization of quantum simulation proposals. Our calculations include $C_6$ coefficients for the Yb--Yb $^1\!S_0+\,^3\!P^o_{0,1}$ and $^3\!P^o_0+\,^3\!P^o_{0}$ dimers, $C_8$ coefficients for the $^1\!S_0+\,^1\!S_0$ and $^1\!S_0+\,^3\!P^o_1$ dimers, $C_6$ coefficients for the Yb--Rb $^3\!P_1^o+5s\, ^2\!S_{1/2}$ and $^1\!S_0+5p\, ^2\!P^o_{1/2}$ dimers, and the $C_8$ coefficients for the Yb--Li $^1\!S_0+2s\, ^2\!S_{1/2}$ and Yb--Rb $^1\!S_0+5s\, ^2\!S_{1/2}$ dimers. We performed detailed uncertainty analysis and provided stringent bounds on all quantities obtained in this work to allow future benchmark tests of experimental methodologies and theoretical molecular models.