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We propose and experimentally investigate a scheme for narrow-line cooling ofKRb molecules in the rovibrational ground state. We show that thespin-forbidden $\mathrm{X^1\Sigma^+} \rightarrow \mathrm{b^3\Pi_{0^+}}$transition of KRb is ideal for realizing narrow-line laser cooling of moleculesbecause it has highly diagonal Franck-Condon factors and narrow linewidth. Inorder to confirm the prediction, we performed the optical and microwavespectroscopy of ultracold $^{41}$K$^{87}$Rb molecules, and determined thelinewidth ($2\pi\times$ 4.9(4) kHz) and Franck-Condon factors for the$\mathrm{X^1\Sigma^+} (v''=0) \rightarrow \mathrm{b^3\Pi_{0^+}} (v'=0)$transition (0.9474(1)). This result opens the door towards all-opticalproduction of polar molecules at sub-microkelvin temperatures.

Prospects for Narrow-line Cooling of KRb Molecules in Rovibrational Ground State