  We study the gravitational-wave (GW) signatures of clouds of ultralight
bosons around black holes (BHs) in binary inspirals. These clouds, which are
formed via superradiance instabilities for rapidly rotating BHs, produce
distinct effects in the population of BH masses and spins, and a continuous
monochromatic GW signal. We show that the presence of a binary companion
greatly enriches the dynamical evolution of the system, most remarkably through
the existence of resonant transitions between the growing and decaying modes of
the cloud (analogous to Rabi oscillations in atomic physics). These resonances
have rich phenomenological implications for current and future GW detectors.
Notably, the amplitude of the GW signal from the clouds may be reduced, and in
many cases terminated, much before the binary merger. The presence of a boson
cloud can also be revealed in the GW signal from the binary through the imprint
of finite-size effects, such as spin-induced multipole moments and tidal Love
numbers. The time dependence of the cloud's energy density during the resonance
leads to a sharp feature, or at least attenuation, in the contribution from the
finite-size terms to the waveforms. The observation of these effects would
constrain the properties of putative ultralight bosons through precision GW
data, offering new probes of physics beyond the Standard Model.
