Proposed test of the time independence of the fundamental constantsαandme/mpusing monolithic resonators

A novel method is proposed for a laboratory test of the time independence of the fine-structure constant and of the electron to proton mass ratio, employing only electromagnetic resonators. For a resonator made out of a dielectric ionic or molecular crystal, the resonance frequencies depend on the product ${\alpha }^2\sqrt{m_e{/m}_p}$ through the index of refraction. A test of the time independence of $\alpha$ and $m_e{/m}_p$ can be performed by a search for a long-term change in the difference of two resonance frequencies exhibiting different dispersion. The method can be advantageously implemented with a single resonator. The prospects of implementation using optical resonators, systematic effects, and experimental requirements for a test at the level of $4\times {10}^{-15}/\mathrm{yr}$ relative variation in $\alpha$ or $m_e{/m}_p$ are discussed. On the experimental side, birefringent monolithic sapphire optical resonators with high-reflectivity mirrors are fabricated and characterized. The measurements of optical materials with ultralow absorption loss (ppm/cm level), required for the proposed method, are also reported.