  We demonstrate an optical tweezer based single atom trapping on an optical
nanofiber cavity. We show that the fluorescence of single atoms trapped on the
nanofiber cavity can be readily observed in real-time through the fiber guided
modes. The photon correlation measurements further clarify the atom number and
the dynamics of the trap. The trap lifetime is measured to be 52$\pm$5 ms. From
the photon statistics measured for different cavity decay rates, the effective
coupling rate of the atom-cavity interface is estimated to be 34$\pm$2 MHz.
This yields a cooperativity of 5.4$\pm$0.6 and a cavity enhanced channeling
efficiency of 85$\pm$2% for a cavity mode having a linewidth of 164 MHz. These
results may open new possibilities for building trapped single atom based
quantum interfaces on an all-fiber platform.
