  In the $\Lambda$CDM scenario, small galaxies merge to produce larger
entities. Since supermassive black holes (SMBHs) are found in galaxies of all
sizes, SMBH binaries (SMBHBs) are generally expected to form during the
amalgamation of galaxies. It is unclear what fraction of these binaries could
eventually merge, but a general consensus is that initially the orbital decay
is mediated by the surrounding gas and stars. In this Letter, we show that in
active galactic nulcei (AGNs) the radiation field also causes the orbits of the
accreting SMBHs to shrink. The corresponding mechanism, known as the
"Poynting-Robertson drag" (PR drag), takes effect on a well-defined timescale
$CT_{\rm Sal}$, where $T_{\rm Sal}$ is the Salpeter timescale of the AGN,
presumably coincide with the primary SMBH, and
$C=4\xi^{-1}\epsilon^{-1}q^{1/3}(1+q)^{2/3}(1-\epsilon)$ is a constant
determined by the radiative efficiency $\epsilon$, the mass ratio $q$ of the
two black holes, and a parameter $\xi$ characterizing the size of the
circum-secondary accretion disk. We find that when $q\lesssim$a
few$\times10^{-5}$, the PR drag is more efficient in shrinking the binary than
many other mechanisms, such as dynamical friction and type-I migration. Our
finding points to a possible new channel for the coalescence of unequal SMBHBs
and the clearing of intermediate-massive black holes in AGNs.
