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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 and scalable radio-frequency composite-pulse spectroscopy at second long coherence times in the magnetic sublevels of the long-lived $^{2}F_{7/2}$ state of a trapped $^{172}$Yb$^{+}$ ion. 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$$\ $$^{2}S_{1/2}$ electronic ground state of $^{172}$Yb$^{+}$ 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 $^2F_{7/2}$ 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 $^2F_{7/2}$ manifold and a coherent signal of up to $2.5\,$s is reached. We have implemented the sequence and used it to perform the most stringent test of LLI in the electron-photon sector to date. Due to the 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 $^{2}F_{7/2}$ state, obtaining a value of $\Theta\,=\,-0.0298(38)\,ea^{2}_{0}$ which is in agreement with the value deduced from clock measurements., Comment: 19 pages, 7 figures

We report on a comparative analysis of quenched sideband cooling in trapped ions. We introduce a theoretical approach for time-efficient simulation of the temporal cooling characteristics and derive the optimal conditions providing fast laser cooling into the ion's motional ground state. The simulations were experimentally benchmarked with a single $^{172}$Yb$^+$ ion confined in a linear Paul trap. Sideband cooling was carried out on a narrow quadrupole transition, enhanced with an additional clear-out laser for controlling the effective linewidth of the cooling transition. Quench cooling was thus for the first time studied in the resolved sideband, intermediate and semi-classical regime. We discuss the non-thermal distribution of Fock states during laser cooling and reveal its impact on time dilation shifts in optical atomic clocks., Comment: 20 pages, 10 figures