Mass-energy equivalence in harmonically trapped particles

Understand

Precise understanding of the dynamics of trapped particles is crucial for nascent quantum technologies, including atomic clocks and quantum simulators.

• Here we present a framework to systematically include quantum effects arising from the mass-energy equivalence in harmonically trapped systems.
• We find that the mass-energy equivalence leads to squeezing, displacement and frequency changes of harmonic modes associated with different internal energies.
• The framework predicts new phenomena, notably, the existence of a lower bound to the fractional frequency shift in atomic clocks arising from the interplay between gravitational effects and so-called time dilation shifts.