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Sub-parsec binary massive black holes (BBHs) are long anticipated to exist inmany QSOs but remain observationally elusive. In this paper, we propose a novelmethod to probe sub-parsec BBHs through microlensing of lensed QSOs. If a QSOhosts a sub-parsec BBH in its center, it is expected that the BBH is surroundedby a circum-binary disk, each component of the BBH is surrounded by a smallaccretion disk, and a gap is opened by the secondary component in between thecircum-binary disk and the two small disks. Assuming such a BBH structure, wegenerate mock microlensing light curves for some QSO systems that host BBHswith typical physical parameters. We show that microlensing light curves of aBBH QSO system at the infrared-optical-UV bands can be significantly differentfrom those of corresponding QSO system with a single massive black hole (MBH),mainly because of the existence of the gap and the rotation of the BBH (and itsassociated small disks) around the center of mass. We estimate the half-lightradii of the emission region at different wavelengths from mock light curvesand find that the obtained half-light radius vs. wavelength relations of BBHQSO systems can be much flatter than those of single MBH QSO systems at awavelength range determined by the BBH parameters, such as the total mass, massratio, separation, accretion rates, etc. The difference is primarily due to theexistence of the gap. Such unique features on the light curves and half-lightradius-wavelength relations of BBH QSO systems can be used to select and probesub-parsec BBHs in a large number of lensed QSOs to be discovered by currentand future surveys, including the Panoramic Survey Telescope and Rapid ResponseSystem (Pan-STARRS), the Large Synoptic Survey telescope (LSST) and Euclid.

Microlensing of Sub-parsec Massive Binary Black Holes in Lensed QSOs: Light Curves and Size-Wavelength Relation