Advanced LIGO, LISA, and Cosmic Explorer as dark matter transducers

We present a method to search for scalar field ultralight dark matter directly interacting with gravitational-wave interferometers via a modulation of the fine structure constant and the electron mass. This modulation induces an effective strain in solid materials at a frequency determined by the mass of the dark matter particle. We study the prospects for looking for such an effect in the LIGO detectors by using the solid cavity which is nominally used for pre-stabilizing the laser frequency and we project upper limits. We contextualize them with previous limits from GEO600, possible limits from a similar strain in the LIGO beamsplitter, and with potential limits from upcoming experiments like LISA, Cosmic Explorer and from an upgraded solid cavity. We find that with the sensitivity of Advanced LIGO, competitive upper limits on DM coupling can be placed at the level of $\left\vert d_{m_e}+d_e\right\vert \sim 0.2$ for $m_\text{DM} \sim 10^{-13}\,\mathrm{eV}/\mathrm{c}^2$ with a combination of two searches using the solid cavity and the beamsplitter in LIGO; future experiments could reduce this upper limit to $\sim10^{-3}$.