Martinez, Victor — Mass defect, time dilation and second order Doppler effect in trapped-ion optical clocks

In this work we present a low-order relativistic correction to the multipolar atom-light Hamiltonian for two bound particles corresponding to a simple model for hydrogen-like atoms and ions. From this result, we can systematically predict frequency shifts in atomic clocks based on trapped ions due to the mass defect. We derive the fractional frequency shift with by the use of T-periodic ladder operators, treating the full dynamics of a Paul trap including micro-motion and non-perfect traps, finding accordance with previous results and new corrections with the cross talk of gravity and the so called excess micro-motion.