Extreme-mass-ratio inspirals (EMRIs) and intermediate-mass-ratio inspirals
(IMRIs) are important gravitational-wave (GW) sources for the Laser
Interferometer Space Antenna (LISA). So far, their formation and evolution are
considered to be independent, but recent theories suggest that stellar-mass
black holes (sBHs) and intermediate-mass black hole (IMBHs) can coexist in the
accretion disk of an active galactic nucleus (AGN), which indicates that EMRIs
and IMRIs may form in the same place. Motivated by the fact that a gas giant
migrating in a protoplanetary disk could trap planetesimals close to its orbit,
we study in this paper a similar interaction between a gap-opening IMBH in an
AGN disk and the sBHs surrounding it. We analyse the torques imposed on the
sBHs by the disk as well as by the IMBH, and show that the sBHs can be trapped
by the IMBH if they are inside the orbit of the IMBH. Then we implement the
torques in our numerical simulations to study the migration of an outer IMBH
and an inner sBH, both embedded in an AGN disk. We find that their migration is
synchronized until they reach a distance of about ten Schwarzschild radii from
the central supermassive black hole, where the pair breaks up due to strong GW
radiation. This result indicates that LISA may detect an EMRI and an IMRI
within several years from the same AGN. Such a GW source will bring rich
information about the formation and evolution of sBHs and IMBHs in AGNs.
