Fatty,
The only connection I know of between Atomic Clocks and Relativity, is that these clocks are accurate enough that they can be used to observe time dilation predicted by relativity.
The change in energy states which make Cesium Atomic clocks accurate actually is a consequence of quantum effects. Quantum physics is not really related to relativity in any obvious way. It must be related in some non-obvious ways, but Quantum physics was developed without much regard to Relativity. They will all come together someday in a TOE (Theory of Everything).
http://science.howstuffworks.com/atomic-clock4.htm
