Signatures of relativistic effects in quantum dynamics of atomic clocks

Relativistic time dilation is well tested with atomic clocks. Their remarkable precision allows for the verification of this effect at mm-scales. However, all experiments to date consider the high-temperature regime whereby the clock's centre-of-mass can be modelled semi-classically. Here I will discuss the novel dynamics that arise for trapped atomic clocks in the low-temperature regime. I will analyse the fundamental limitations on precision measurements imposed by the clock's relativistic motion, which may play a significant role in next generation clocks. This work paves the way for probing genuinely quantum and relativistic effects at low energies.