In this thesis I describe how we achieve control over the quantum state of a single H2+ hydrogen molecular ion. Scientific progress is based on the comparison of theories with experimental measurements. For the simplest molecular quantum systems, such as the hydrogen molecular ions H2+ or HD+, the theoretical predictions of quantum electrodynamics are very accurate. In order to test the theory or to extract fundamental constants from the combination of theory and experiments, the experiments must also achieve high precision. In the recent past, hydrogen molecular ions were mainly measured in ensembles. For example, measurements exist both on molecular beams and with dissociative detection in ion traps. However, the spectroscopy of single ions is one of the most precise measurement methods in physics, which was demonstrated by the spectroscopy of a single ytterbium ion in an ion trap. To perform spectroscopy of a single ion in this way, it must have a suitable energy structure for laser cooling, state preparation and fluorescence detection. This is not the case for many ions, including H2+. Quantum logic spectroscopy (QLS) is a technique that makes it possible to perform measurements on an ion without such an energy structure. The ion to be measured (spectroscopy ion) is trapped in an ion trap with a second ion (helper ion), which has the properties described in the previous paragraph. The shared modes of motion between the two ions allow cooling, preparation and detection of the spectroscopy ion via the helper ion. This was demonstrated with an aluminum spectroscopy ion co-trapped with a magnesium helper ion. QLS can also be used for molecules. This has been shown with MgH+, CaH+ and N2+. We implement QLS to enable spectroscopy of a single H2+ ion. For this we trap H2+ together with a 9Be+ ion. We cool the joint motion of the ions to their ground state. We combine buffer gas cooling with a laser and microwave pulse based state preparation sequence to prepare the H2+ molecule in a pure quantum state. This allows us to perform high contrast QLS on a single H2+ ion. Furthermore, we can change and control the quantum state in the hyperfine structure using microwave pulses. We demonstrate the power of our technique by performing microwave spectroscopy on a magnetic field insensitive hyperfine transition. We use QLS to read out the result of the measurement. Within half an hour, we can achieve a statistical uncertainty of 2 Hz. This paves the way for future high-precision measurements on H2+. The techniques described here could potentially be applied to other light molecular ions.
We present a general technique for precision spectroscopy of atoms that lack suitable transitions for efficient laser cooling, internal state preparation, and detection. In our implementation with trapped atomic ions, an auxiliary "logic" ion provides sympathetic laser cooling, state initialization, and detection for a simultaneously trapped "spectroscopy" ion. Detection is achieved by applying a mapping operation to each ion, which results in a coherent transfer of the spectroscopy ion's internal state onto the logic ion, where it is then measured with high efficiency. Experimental realization, by using 9Be+ as the logic ion and 27Al+ as the spectroscopy ion, indicates the feasibility of applying this technique to make accurate optical clocks based on single ions.
High precision comparisons of the proton and antiproton g-factor enable stringent tests of CPT symmetry in the baryonic sector. However, current measurement routines suffer from long preparation times and high particle temperatures, which complicate the increase of the precision beyond the parts per billion regime. As a solution, new sympathetic cooling schemes based on co-trapped laser-cooled ions may be used to cool (anti-)protons to the ground state of motion and to significantly decrease particle preparation times. In addition, motional coupling to an auxiliary ion in a double-well potential can be used for the implementation of new readout schemes based on quantum logic spectroscopy for the spin-state of the (anti-)protons. This thesis describes a cryogenic Penning trap system for ground state cooling of single 9Be+ ions, which represents the latest development of the BASE experiment in Hannover towards the implementation of sympathetic cooling schemes and quantum logic spectroscopy of single (anti-)protons. Furthermore, the setup and implementation of lasers systems at 313nm for Doppler cooling, repumping and Raman interactions are described. To this end, an optical platform for laser beam delivery to the vacuum system and an optical phase-locked loop for the stabilization of the relative phase of two lasers at 313 nm are presented. In this work, the laser systems are used for measurements of the optical resonance frequencies for cooling, probing and repumping of 9Be+ ions. In addition, stimulated Raman transitions are demonstrated using two phase-locked lasers at 313nm. In the following, this technique is used for high-precision measurements of the qubit frequency and the magnetic field, as well as themometry measurements with 9Be+ ions. The temperature of the ions after Doppler cooling is measured as a function of the cooling laser parameters and a minimal axial mode temperature of 1.77(10) mK is obtained. The results of this thesis pave the way for sideband spectroscopy and ground state cooling of single 9Be+ ions in Penning traps, which is an essential prerequisite for sympathetic ground state cooling of single (anti-)protons and the application of quantum logic spectroscopy to (anti-)proton g-factor measurements in the future.