Motional quantum metrology in a Penning trap

We propose to measure the six motional frequencies of an unbalanced two-ion crystal in a Penning trap using a scheme that has been demonstrated in a quantum-metrology experiment with a single ion in a linear Paul trap. To study the feasibility, we derive the quantum Hamiltonian for the unbalanced crystal formed by a target and a sensor ion (Ca-40(+)), and deduce characteristic coordinates xi(+/-)(c'), xi(+/-)(z), and xi(+/-)(m), associated to the amplitudes of the displacement operator alpha(+/-)(c'), alpha(+/-)(z), and alpha(+/-)(m), respectively, when a dipolar time-varying field is applied. The final state after excitation is read out using rapid adiabatic passage. We also present the status of the 7 tesla open-ring Penning trap where first experiments on the Th-232(+)-Ca-40(+) crystal, cooled to the ground state, are foreseen in the short-term future. Finally, we underline possible experiments with this unique platform. Copyright (C) 2021 EPLA