  Supermassive black hole binaries (SMBHBs) are expected by the hierarchical
galaxy formation model in $\Lambda$CDM cosmology. There is some evidence in the
literature for SMBHBs in AGNs, but there are few observational constraints on
the evolution of SMBHBs in inactive galaxies and gas-poor mergers. On the
theoretical front, it is unclear how long is needed for a SMBHB in a typical
galaxy to coalesce. In this paper we investigate the tidal interaction between
stars and binary BHs and calculate the tidal disruption rates of stellar
objects by the BH components of binary. We derive the interaction cross
sections between SMBHBs and stars from intensive numerical scattering
experiments with particle number $\sim10^7$ and calculate the tidal disruption
rates by both single and binary BHs for a sample of realistic galaxy models,
taking into account the general relativistic effect and the loss cone refilling
because of two-body interaction. We estimate the frequency of tidal flares for
different types of galaxies using the BH mass function in the literature. We
find that because of the three-body slingshot effect, the tidal disruption rate
in SMBHB system is more than one order of magnitude smaller than that in single
SMBH system. The difference is more significant in less massive galaxies and
does not depend on detailed stellar dynamical processes. Our calculations
suggest that comparisons of the calculated tidal disruption rates for both
single and binary BHs and the surveys of X-ray or UV flares at galactic centers
could tell us whether most SMBHs in nearby galaxies are single and whether the
SMBHBs formed in gas-poor galaxy mergers coalesce rapidly.
