  We study experimentally various physical limitations and technical
imperfections that lead to damping and finite contrast of optically-driven Rabi
oscillations between ground and Rydberg states of a single atom. Finite
contrast is due to preparation and detection errors and we show how to model
and measure them accurately. Part of these errors originates from the finite
lifetime of Rydberg states and we observe its $n^3$-scaling with the principal
quantum number $n$. To explain the damping of Rabi oscillations, we use simple
numerical models, taking into account independently measured experimental
imperfections, and show that the observed damping actually results from the
accumulation of several small effects, each at the level of a few percents. We
discuss prospects for improving the coherence of ground-Rydberg Rabi
oscillations in view of applications in quantum simulation and quantum
information processing with arrays of single Rydberg atoms.
