SAMOP 2021 – wissenschaftliches Programm
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A: Fachverband Atomphysik
A 6: Atomic systems in external fields
A 6.4: Poster
Dienstag, 21. September 2021, 16:30–18:30, P
Mass defect, time dilation and second order Doppler effect in trapped-ion optical clocks — •Victor Jose Martinez Lahuerta1, Simon Eilers1, Marius Schulte1, Tanja Mehlstäubler2, Piet Schmidt2,3, and Klemens Hammerer1 — 1Institute for Theoretical Physics and Institute for Gravitational Physics (Albert-Einstein-Institute), Leibniz University Hannover — 2Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig — 3Institute for Quantum optics, Leibniz University Hannover, Welfengarten 1, 30167 Hannover
We derive an approximate relativistic Hamiltonian for the center of mass and internal dynamics of an electromagnetically bound, charged two-particle system in external electromagnetic and gravitational fields. This extends earlier work by Sonnleitner and Barnett and Schwartz and Giulini to hydrogen-like ions. We apply this Hamiltonian to describe the relativistic coupling of the center of mass and internal dynamics of cold ions in Paul traps, including the effects of micromotion. In this way, we are able to provide a systematic fully quantum mechanical treatment of relativistic frequency shifts and their standard deviation in atomic clocks based on trapped ions. Our approach reproduces known formulas for the second order Doppler shift, which were previously derived on the basis of semi-classical arguments. We also complement and clarify recent discussions on the role of time dilation and mass defect in ion clocks.