  We investigate the evolution of supermassive black hole (SMBH) binaries and
the possibility that their merger is facilitated by ultralight dark matter
(ULDM). When ULDM is the main dark matter (DM) constituent of a galaxy, its
wave nature enables the formation of massive quasiparticles throughout the
galactic halo. Here we show that individual encounters between quasiparticles
and a SMBH binary can lead to the efficient extraction of energy and angular
momentum from the binary. The relatively short coherence time of ULDM provides
a steady-state population of massive quasiparticles, and consequently a
potential solution to the final parsec problem. Furthermore, we demonstrate
that, in the presence of stars, ULDM quasiparticles can also act as massive
perturbers to enhance the stellar relaxation rate locally, replenish the
stellar loss cone efficiently, and consequently resolve the final parsec
problem.
