  We perform spectroscopy on the hyperfine splitting of $^{85}$Rb atoms trapped
in far-off-resonance optical traps. The existence of a spatially dependent
shift in the energy levels is shown to induce an inherent dephasing effect,
which causes a broadening of the spectroscopic line and hence an inhomogeneous
loss of atomic coherence at a much faster rate than the homogeneous one caused
by spontaneous photon scattering. We present here a number of approaches for
reducing this inhomogeneous broadening, based on trap geometry, additional
laser fields, and novel microwave pulse sequences. We then show how hyperfine
spectroscopy can be used to study quantum dynamics of optically trapped atoms.
