High resolution photoassociation spectroscopy of the $^{6}$Li$_2$ $A(1^1Sigma_u^+)$ state

We present spectroscopic measurements of seven vibrational levels $v=29-35$ of the $A(1^1Sigma_u^+)$ excited state of Li$_2$ molecules by the photoassociation of a degenerate Fermi gas of $^6$Li atoms. The absolute uncertainty of our measurements is $pm 0.00002$ cm$^{-1}$ ($pm 600$ kHz) and we use these new data to further refine an analytic potential for this state. This work provides high accuracy photo-association resonance locations essential for the eventual high resolution mapping of the $X(1^1Sigma_g^+)$ state enabling further improvements to the s-wave scattering length determination of Li and enabling the eventual creation of ultra-cold ground state $^6$Li$_2$ molecules.