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 clouds 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.
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