Enhanced effects of variation of the fundamental constants in laser interferometers and application to dark matter detection

We outline new laser interferometer measurements to search for variation of the electromagnetic fine-structure constant $\alpha$ and particle masses (including a non-zero photon mass). We propose a strontium optical lattice clock -- silicon single-crystal cavity interferometer as a novel small-scale platform for these new measurements. Multiple passages of a light beam inside an interferometer enhance the effects due to variation of the fundamental constants by the mean number of passages ($N_{\textrm{eff}} \sim 10^2$ for a large-scale gravitational-wave detector, such as LIGO, Virgo, GEO600 or TAMA300, while $N_{\textrm{eff}} \sim 10^5$ for a strontium clock -- silicon cavity interferometer). Our proposed laser interferometer measurements may be implemented as an extremely precise tool in the direct detection of scalar dark matter that forms an oscillating classical field or topological defects.