Mass-energy equivalence in harmonically trapped particles

Abstract

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. Analogous effects will arise in other trapping potentials, especially in periodic lattices, and may play a role in correlation dynamics and thermalisation process in many-body systems and cold gases.

arXiv comment4+3.2 pages, 2 figures

References in corpus (5)

• Proposal for a Quantum Test of the Weak Equivalence Principle with Entangled Atomic Species
• Equivalence Principle for Quantum Systems: Dephasing and Phase Shift of Free-Falling Particles
• Mass-energy and anomalous friction in quantum optics
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Cited by in corpus (2)

• Post-Newtonian Hamiltonian description of an atom in a weak gravitational field
• On the feasibility of detecting quantum delocalization effects on relativistic time dilation in optical clocks