Structure and interactions of ultracold Yb ions and Rb atoms

In order to study ultracold charge-transfer processes in hybrid atom-ion traps, we have mapped out the potential-energy curves and molecular parameters for several low-lying states of the Rb, Yb${}^{+}$ system. We employ both a multireference configuration interaction and a full configuration interaction (FCI) approach. Turning points, crossing points, potential minima, and spectroscopic molecular constants are obtained for the lowest five molecular states. Long-range parameters, including the dispersion coefficients, are estimated from our ab initio data. The separated-atom ionization potentials and atomic polarizability of the ytterbium atom (${\alpha }_d=128.4$ atomic units) are in good agreement with experiment and previous calculations. We present some dynamical calculations for (adiabatic) scattering lengths for the two lowest (Yb, Rb${}^{+}$) channels that were carried out in our work. However, we find that the pseudopotential approximation is rather limited in validity and only applies to nK temperatures. The adiabatic scattering lengths for both the triplet and singlet channels indicate that both are large and negative in the FCI approximation.

Figure 1

Relative electronic energies for the molecular ion ${\mathrm{YbRb}}^{+}$ as a function of internuclear distance $R$ (MRCI approximation). The $X{}^1{\Sigma }^{+}$ ground state is the Rb${}^{+}$ channel, while the lowest-energy ionic ytterbium states, the triplet $a{}^3{\Sigma }^{+}$ and singlet $A{}^1{\Sigma }^{+}$ pair, are nearly degenerate with the excited charge-transfer channels: ${\mathrm{Rb}}^{+}+{\mathrm{Yb}}^{*}$.

Figure 2

The effective-range function, $k\cot \delta \left(k\right)$, in the limit of low energy as a function of the relative wave number $k$ and equivalent temperature, for the $X{}^1{\Sigma }^{+}$ state in the MRCI approximation. The solid line is the value obtain by numerical integration. The dashed curve displays the low-temperate expansion (5). For this system, it is clear that replacing the scattering by a temperature-independent pseudo-potential (7) is only valid in the nK regime.

Figure 3

The energy-dependent scattering length $a\left(k\right)$, defined by Eq. (12), for the ground-state potential curve ($X{}^1{\Sigma }^{+}$) in the MRCI approximations. The solid curve is the result of numerical integration, the dotted line is the linear approximation (13), and the dashed curve is the nonlinear expansion (5). Even over this ultracold (nK) temperature range the variation of the effective scattering length is significant.