Mixing of and observed in the hyperfine and Zeeman structure of ultracold molecules

Abstract

We study the combination of the hyperfine and Zeeman structure in the spin–orbit coupled ${A}^{1}{\Sigma }_{u}^{+}-{b}^{3}{\Pi }_{u}$ complex of ${}^{87}{\mathrm{Rb}}_{2}$ . For this purpose, absorption spectroscopy at a magnetic field around $B=1000$ G is carried out. We drive optical dipole transitions from the lowest rotational state of an ultracold Feshbach molecule to various vibrational levels with ${0}^{+}$ symmetry of the $A-b$ complex. In contrast to previous measurements with rotationally excited alkali-dimers, we do not observe equal spacings of the hyperfine levels. In addition, the spectra vary substantially for different vibrational quantum numbers, and exhibit large splittings of up to $160$ MHz, unexpected for ${0}^{+}$ states. The level structure is explained to be a result of the repulsion between the states ${0}^{+}$ and ${0}^{-}$ of ${b}^{3}{\Pi }_{u}$ , coupled via hyperfine and Zeeman interactions. In general, ${0}^{-}$ and ${0}^{+}$ have a spin–orbit induced energy spacing Δ , that is different for the individual vibrational states. From each measured spectrum we are able to extract Δ , which otherwise is not easily accessible in conventional spectroscopy schemes. We obtain values of Δ in the range of $\pm 100$ GHz which can be described by coupled channel calculations if a spin–orbit coupling is introduced that is different for ${0}^{-}$ and ${0}^{+}$ of ${b}^{3}{\Pi }_{u}$ .

Keywords

• ultracold molecules
• spectroscopy
• dipole transitions
• hyperfine structure
• Zeeman effect
• spin–orbit coupling