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

TL;DR

This paper explores how variations in fundamental constants, especially the electron-to-proton mass ratio, influence scattering lengths in ultracold atom systems near Feshbach resonances, proposing methods for detection and estimation.

Contribution

It introduces a model linking fundamental constant variations to scattering length changes, enabling potential detection of tiny variations in the mass ratio.

Findings

Variation of m_e/m_p can be detected near Feshbach resonances.

Derived formulae estimate isotopic shifts in scattering length.

Sensitivity to fundamental constants is enhanced near narrow 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.