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 (40 Ca , and deduce characteristic coordinates , and , associated to the amplitudes of the displacement operator , and , 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 232 Th Ca crystal, cooled to the ground state, are foreseen in the short-term future. Finally, we underline possible experiments with this unique platform.