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

authored by: V. J. Martinez-Lahuerta, S. Eilers, T. E. Mehlstaeubler, P. O. Schmidt, K. Hammerer
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 semi-classical arguments. We complement and clarify recent discussions in the literature on the role of time dilation and mass defect in ion clocks.
Organisation(s): CRC 1227 Designed Quantum States of Matter (DQ-mat)
Institute of Theoretical Physics
QuantumFrontiers
Institute of Quantum Optics
External Organisation(s): National Metrology Institute of Germany (PTB)
Type: Article
Journal: Physical Review A
Volume: 106
ISSN: 2469-9926
Publication date: 03.09.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Atomic and Molecular Physics, and Optics
Electronic version(s): https://doi.org/10.1103/PhysRevA.106.032803 (Access: Closed)

BibTeX

@article{72a398ac0df044eda23af3cb6b70c690,
title = "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 semi-classical arguments. We complement and clarify recent discussions in the literature on the role of time dilation and mass defect in ion clocks. ",
keywords = "physics.atom-ph, quant-ph",
author = "Martinez-Lahuerta, {V. J.} and S. Eilers and Mehlstaeubler, {T. E.} and Schmidt, {P. O.} and K. Hammerer",
note = "Funding Information: We acknowledge support from Deutsche Forschungsgemeinschaft (German Research Foundation) under Germany's Excellence Strategy, EXC-2123 QuantumFrontiers, Grant No. 390837967, and Project No. 274200144, SFB 1227 (DQ-mat, Projects No. A05, No. A06, and No. B03). This project received funding from the EMPIR Program cofinanced by the Participating States and from the European Unions Horizon 2020 research and innovation program. This work was supported by the EMPIR Project No. 18SIB05 Robust Optical Clocks for International Timescales. This work was also supported by the Max Planck-RIKEN-PTB-Center for Time, Constants and Fundamental Symmetries. We thank Jan Kiethe and Marius Schulte for comments on early versions of the paper and Philip Schwartz and Domenico Giulini for discussions.",
year = "2022",
month = sep,
day = "3",
doi = "10.1103/PhysRevA.106.032803",
language = "English",
volume = "106",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "3",
}