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Bound-state quantum electrodynamics (QED) accurately describes the energy levels of hydrogen-like systems, with high-precision laser spectroscopy serving as a stringent test of the theory. The hydrogen-like He⁺ ion is of particular interest due to its sensitivity to higher-order QED corrections, which scale with large exponents of the nuclear charge.

At the Max Planck Institute for Quantum Optics in Garching, Germany, we are working on high-precision laser spectroscopy of the 1s-2s transition in He⁺ using a Paul trap setup. He⁺ ions are co-trapped with laser-cooled Be⁺ ions for sympathetic cooling, creating ideal conditions for precision measurements in the field-free region of the trap.

Our experimental setup consists of two main components: the extreme ultraviolet frequency comb and the ion trap setup. In this talk, I will focus on the ion trap and highlight several related experiments, such as the photodissociation of BeH⁺ molecules, the measurement of AC Stark shifts in the hyperfine levels of the Be⁺ ground state, and our secular excitation-based detection scheme for He²⁺ ions generated by ionization following excitation of the 1s-2s transition. These experiments are crucial for preparing the system for high-precision He⁺ spectroscopy.