Enhanced Sensitivity to Fundamental Constants In Ultracold Atoms and Molecules near Feshbach Resonances

Scattering length, which can be measured in Bose-Einstein condensate and Feshbach molecule experiments, is extremely sensitive to the variation of fundamental constants, in particular, the electron-to-proton mass ratio ($m_{e}$/$m_{p}$ or $m_{e}$/$\Lambda _{QCD}$, where $\Lambda_{QCD}$ is the QCD scale). Based on single- and two-channel scattering models, we show how the variation of the mass ratio propagates to the scattering length. Our results suggest that variation of $m_{e}$/$m_{p}$ on the level of 10$^{-11}\sim $10$^{-14}$ can be detected near a narrow Feshbach resonance by monitoring the scattering length on the 1{\%} level. In this talk, we will present evidences that demonstrate the ultrahigh high sensitivity on atomic mass and suggest possible experiment approaches to precisely determine the scattering lengths.