  Cavity-mediated adiabatic transfer (CMAT) is a robust way to perform a
two-qubit gate between trapped atoms inside an optical cavity. In the previous
study by Goto and Ichimura [H. Goto and K. Ichimura, Phys. Rev. A 77, 013816
(2008).], the upper bound of success probability of CMAT was shown where the
operation is adiabatically slow. For practical applications, however, it is
crucial to operate CMAT as fast as possible without sacrificing the success
probability. In this paper, we investigate the operational speed limit of CMAT
conditioned on the success probability being close to the upper bound. In CMAT
both the adiabatic condition and the decay of atoms and cavity modes limit the
operational speed. We show which of these two conditions more severely limits
the operational speed in each cavity-QED parameter region, and find that the
maximal operational speed is achieved when the influence of cavity decay is
dominant compared to spontaneous emission.
