Atomic clocks demonstrate time dilation effects under both special relativity and general relativity.
In special relativity, time dilation arises due to relative motion between observers. When two observers are in relative motion, each will perceive the other's clock as running slower. This effect is reciprocal, meaning that both observers experience time dilation relative to each other. Atomic clocks, which are extremely precise and accurate, have been used in experiments to confirm the predictions of time dilation in special relativity.
In general relativity, time dilation is caused by gravitational fields. According to general relativity, the presence of a gravitational field affects the flow of time. Clocks in stronger gravitational fields will appear to run slower when observed from a region with weaker gravity. This effect is known as gravitational time dilation.
Again, atomic clocks have been employed to verify the predictions of time dilation in general relativity. For example, experiments conducted at different altitudes, where the strength of the gravitational field is slightly different, have shown that clocks closer to the Earth's surface run slightly slower than those at higher altitudes, as predicted by general relativity.
So, atomic clocks serve as essential tools to investigate and confirm both the time dilation effects predicted by special relativity (due to relative motion) and general relativity (due to gravitational fields).