Decoherence of the quantum superradiant cloud from graviton emission

Black hole superradiance amplifies vacuum fluctuations into a macroscopic cloud of a massive bosonic field around a rotating black hole. Under free evolution, the quantum cloud is a two-mode squeezed state that remains entangled even at large occupation numbers, while its growing component admits a classical statistical description. In this work, we study how graviton emission changes the quantum state of the cloud. We find that graviton emission suppresses interference between cloud configurations with different amplitudes, but leaves interference between configurations that differ only by an overall sign unchanged. For typical configurations realized under vacuum fluctuations, the suppression becomes significant when the expected number of emitted gravitons is of order unity.We also show that, at larger occupation numbers, all first and second moments can be reproduced by a statistical mixture of coherent states. For the astrophysical black holes, both changes occur much before the spin-down of the black hole becomes significant.