  Superradiant clouds of ultralight bosons can leave an imprint on the
gravitational waveform of black hole binaries through "ionization" and
"resonances". We study the sequence of resonances as the binary evolves, and
show that there are only two possible outcomes, each with a distinct imprint on
the waveform. If the cloud and the binary are nearly counter-rotating, then the
cloud survives in its original state until it enters the sensitivity band of
future gravitational wave detectors, such as LISA. In all other cases,
resonances destroy the cloud, while driving the binary to co-rotate with it and
its eccentricity close to a fixed point. This opens up the possibility of
inferring the existence of a new boson from the statistical analysis of a
population of black holes binaries.
