Ultracold molecules: new probes on the variation of fundamental constants

Ultracold molecules offer brand new opportunities to probe the variation of fundamental constants with unprecedented sensitivity. This paper summarizes theoretical background and current constraints on the variation of the fine structure constant and electron-to-proton mass ratio, as well as proposals and experimental efforts to measure the variations based on ultracold molecules. In particular, we describe two novel spectroscopic schemes on ultracold molecules that have greatly enhanced sensitivity to fundamental constants: resonant scattering near Feshbach resonances and spectroscopy on close-lying energy levels of ultracold molecules.