Finite Coherence in Gravitational Waves from Tidally Excited Axion Clouds

Axion clouds around rotating black holes form gravitational atoms whose tidal transitions can radiate gravitational waves in binaries. For strongly coupled Bohr crossings, transition radiation is governed by the outgoing two-level coherence, not by the transition probability alone. This coherence is suppressed both on the adiabatic branch and in the weak passage limit, but survives for intermediate sweep rates, producing a finite transition waveform and a localized orbital response. In more massive systems, fine and hyperfine transitions produce narrowband gravitational radiation and cumulative departures from vacuum binary waveforms. Coherent tidal crossings offer a gravitational-wave probe of axion-cloud dynamics.