Ab initio quantum theory of mass defect and time dilation in trapped-ion optical clocks

Abstract

We derive a Hamiltonian for the external and internal dynamics of an electromagnetically bound, charged two-particle system in external electromagnetic and gravitational fields, including leading-order relativistic corrections. We apply this Hamiltonian to describe the relativistic coupling of the external and internal dynamics of cold ions in Paul traps, including the effects of micromotion, excess micromotion, and trap imperfections. This provides a systematic and fully quantum-mechanical treatment of relativistic frequency shifts in atomic clocks based on single trapped ions. Our approach reproduces well-known formulas for the second-order Doppler shift for thermal states, which were previously derived on the basis of semiclassical arguments. We complement and clarify recent discussions in the literature on the role of time dilation and mass defect in ion clocks.

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• Atom interferometers in weakly curved spacetimes using Bragg diffraction and Bloch oscillations
• Quantum field theory for multipolar composite bosons with mass defect and relativistic corrections
• Finite Pulse-Time Effects in Long-Baseline Quantum Clock Interferometry
• Quantum signatures of proper time in optical ion clocks
• Witnessing mass-energy equivalence with trapped atom interferometers
• A unified theory of tunneling times promoted by Ramsey clocks
• Universality of quantum time dilation
• Unified laboratory-frame analysis of atomic gravitational-wave sensors
• On the feasibility of detecting quantum delocalization effects on relativistic time dilation in optical clocks
• General Relativistic Center-of-Mass Coordinates for Composite Quantum Particles