Proposed detection of variation in m_p/m_e using a vibrational transition frequency of a CaH⁺ ion

This paper proposes the detection of the variation in the proton-to-electron mass ratio β by measuring a pure vibrational transition frequency of a cold CaH⁺ ion. The uncertainty of the this frequency can potentially be on the order of 10^-16, because the uncertainties of the Zeeman and Stark shifts are lower than 10^-16 and the electric quadrupole shift is zero. It is practicable to produce a CaH⁺ ion at a certain quantum state and perform sympathetic cooling by using the collisions with a laser-cooled Ca⁺ ion.