LIGO, LISA and Ultralight Axion-like Dark Matter

A coherent cosmic background of axion-like particles (ALPs) coupled to photons can produce a small periodic differential phase or polarization modulation for photons traversing separate arms in gravitational wave interferometers, peaked at a frequency associated with the particle mass, and suppressed whenever the dark-matter coherence length ${\lambda }_{\mathrm{c}\mathrm{o}\mathrm{h}}$ exceeds the arm length~$L$. For the LIGO audio frequency band the sensitivity to cosmic ALPs is below current bounds. For LISA, however, the natural mass range $m_a\sim 4\times {10}^{-19}$–$4\times {10}^{-16}$~eV – corresponding to a sideband frequency in LISA’s science band of $0.1$~mHz–$0.1$~Hz – may be observable. A 1-year shot-noise-limited search projects a sensitivity $g_{a\gamma \gamma }\lesssim 5\times {10}^{-14}$~GeV${}^{-1}$ across most of the band, reaching $\sim 7\times {10}^{-15}$~GeV${}^{-1}$ near $0.1$~Hz, which is ${10}^3$–${10}^4$ below the CAST helioscope bound. An RF heterodyne photodetection upgrade – to either detector – might extend the search sensitivity to $g_{a\gamma \gamma }\sim 6.5\times {10}^{-14}$~GeV${}^{-1}$ at $m_a\sim 3\times {10}^{-7}$~eV for LIGO and $g_{a\gamma \gamma }\sim 3.3\times {10}^{-17}$~GeV${}^{-1}$ at $m_a\sim 5\times {10}^{-13}$~eV for LISA. Dark-matter substructure can affect the signal in a several interesting ways.