Trapped-ion quantum sensors have become highly sensitive tools for the search of physics beyond the Standard Model. Recently, stringent tests of local Lorentz-invariance (LLI) have been conducted with precision spectroscopy in trapped ions. We here elaborate on robust radio-frequency composite-pulse spectroscopy at second long coherence times in the magnetic sublevels of the long-lived 2F7/2 state of a trapped 172Yb+ ion which is scalable to spatially extended multi-ion systems. We compare two Ramsey-type composite rf pulse sequences, a generalized spin-echo (GSE) sequence and a sequence based on universal rotations with 10 rephasing pulses (UR10) that decouple the energy levels from magnetic field noise, enabling robust and accurate spectroscopy. Both sequences are characterized theoretically and experimentally in the spin-1/2\ 2S1/2 electronic ground state of 172Yb+ and results show that the UR10 sequence is 38 (13) times more robust against pulse duration (frequency detuning) errors than the GSE sequence. We extend our simulations to the eight-level manifold of the 2F7/2 state, which is highly sensitive to a possible violation of LLI, and show that the UR10 sequence can be used for high-fidelity Ramsey spectroscopy in noisy environments. The UR10 sequence is implemented experimentally in the 2F7/2 manifold and a coherent signal of up to 2.5\,s is reached. In reference [Dreissen et al., Nature Communications 13, 7314 (2022)] we have implemented this sequence and used it to perform the most stringent test of LLI in the electron-photon sector to date with a single Yb+ ion. Due to the high robustness of the UR10 sequence, it can be applied on larger ion crystals to improve tests of Lorentz symmetry further. We demonstrate that the sequence can also be used to extract the quadrupole moment of the meta-stable 2F7/2 state, obtaining a value of θ=-0.0298(38)\,ea02 which is in agreement with the value deduced from clock measurements.
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