Enhancement of variation of fundamental constants in ultracold atom and molecule systems near Feshbach resonances

Abstract

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 model, 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}~10^{-14} can be detected near a narrow magnetic or an optical Feshbach resonance by monitoring the scattering length on the 1% level. Derived formulae may also be used to estimate the isotopic shift of the scattering length.