  We experimentally study the ground state coherence properties of cesium atoms
in a nanofiber-based two-color dipole trap, localized 200 nm away from the
fiber surface. Using microwave radiation to coherently drive the clock
transition, we record Ramsey fringes as well as spin echo signals and infer a
reversible dephasing time $T_2^\ast=0.6$ ms and an irreversible dephasing time
$T_2^\prime=3.7$ ms. By theoretically modelling the signals, we find that, for
our experimental parameters, $T_2^\ast$ and $T_2^\prime$ are limited by the
finite initial temperature of the atomic ensemble and the heating rate,
respectively. Our results represent a fundamental step towards establishing
nanofiber-based traps for cold atoms as a building block in an optical fiber
quantum network.
