Trapped ions are widely used in quantum simulation, precision spectroscopy, quantum information and computation experiments. The excellent level of control, long coherence times and accessibility to commercially available instruments make them very attractive for these kind of experiments. Furthermore, the combination of external motional and internal electronic degrees of freedom can lead to rich and interesting dynamics. Here we present a novel technique to measure the motional state of the ion based on the Autler-Townes effect that is more efficient than the standard approach and can be employed in a non demolition manner. Furthermore, we use the combination of motional and electronic dynamics to simulate the dynamics of an atom in a cross cavity setup and investigate the emergence of interference both for quantum and coherent states. Both experiments are main results in other PhD theses and already published with major contributions from me. Moreover, the experimental setup was upgraded to allow for better motional control of the ion, better automatization with an up todate control system and an improved Rydberg addressing setup. Especially the last point will be crucial for future experiments since it allows controlled Rydberg excitation of individual ions in an ion string which will be needed for future research in quantum simulation and computation experiments with Rydberg ions.

Trapped-ion experiments are a leading platform for many fields of quantum technology. Most state-of-the-art experiments rely on precise control and characterisation of the ions’ motional state, so improving this area is essential. This thesis presents two novel phonon number measurements: one using the Autler-Townes effect and another using a composite pulse sequence. Additionally, it also presents a spectroscopic investigation of a conformational change of an ion crystal induced by Rydberg excitation. The resulting change in the trapping potential creates a strong coupling between the electronic and vibrational states. This opens new pathways for quantum simulations of molecules. A major challenge in Rydberg ion experiments is double ionisation caused by blackbody radiation. The final part of this thesis offers a solution to this issue by presenting the design of two new cryogenic experiments, one macroscopic and one surface trap.

Trapped ion systems are at the forefront of the development of various forms of quantum technology. Continuing to improve and establish new devices and techniques for the control of trapped ions is a vital element of ongoing research. In this thesis, a range of experiments which aim to expand the quantum toolkit of trapped ion systems are presented. These results primarily focus on the control and detection of bound motional states of a single trapped ⁸⁸Sr+ ion for the purposes of quantum simulation and computation. We demonstrate how the interference between motional modes can reveal an interesting new interpretation of the mechanism behind light-matter interaction and introduce two separate techniques for the detection of motional states, based on the Autler-Townes effect and the use of composite pulses respectively. Additionally, we introduce a novel method to perform micromotion compensation and build upon previous works studying the effects of trapping electric fields on a single trapped Rydberg ion, observing the second-order quadrupolar response of the ion with a highly precise sensitivity.

Trapped ions are one of the leading platforms for quantum technologies due to their excellent control over their internal electronic and external motional degrees of freedom. Many techniques and interesting effects rely on the coupling of the ions to their motion, which makes precise control of them paramount.

In this work, two novel techniques for motional state detection are presented. They allow the probing of certain motional states with a single measurement, without affecting the motion of the measured ion. These techniques are employed to generate and detect a highly entangled state between two motional modes in a novel manner. Furthermore, we harness the rich and intricate dynamics arising from the coupling of the ion's motion to its electronic degrees of freedom to study the emergence of interference. Theoretical predictions, describing interference both in the quantum and the classical regimes, are verified, offering a new and more intuitive description of interference, not just for trapped ions, but for a variety of systems that can be described in a similar way.

On the other hand, Rydberg excitation with trapped ions enables new interaction mechanisms and makes them extremely sensitive to their surroundings. This thesis presents advances towards Rydberg experiments with longer ion strings and concludes with a first demonstration of coherent population transfer between Rydberg states in trapped ions. The methods developed significantly increase the toolbox for trapped Rydberg ions, enabling more sophisticated experiments, especially when multiple different Rydberg states are involved, and allow more flexibility when using longer ion strings.

Fångade joner är en av de främsta plattformarna för kvantteknik tack vare den utmärkta kontrollen över deras interna elektroniska och externa rörelsefrihetsgrader. Många tekniker och intressanta effekter bygger på kopplingen mellan jonerna och deras rörelse, vilket gör att en exakt styrning av dessa är av avgörande betydelse.

I detta arbete presenteras två nya tekniker för detektering av rörelsetillstånd. De möjliggör undersökning av vissa rörelsetillstånd med en enda mätning, utan att påverka det uppmätta jonets rörelse. Dessa tekniker används för att generera och detektera ett starkt sammanflätat tillstånd mellan två rörelsemoder på ett nytt sätt. Vidare utnyttjar vi den rika och komplexa dynamiken som uppstår genom kopplingen mellan jonens rörelse och dess elektroniska frihetsgrader för att studera uppkomsten av interferens. Teoretiska förutsägelser, som beskriver interferens både i kvant- och klassiska regimer, verifieras, vilket ger en ny och mer intuitiv beskrivning av interferens, inte bara för infångade joner, utan för en mängd olika system som kan beskrivas på liknande sätt.

Å andra sidan möjliggör Rydberg-excitation med infångade joner nya interaktionsmekanismer och gör dem extremt känsliga för sin omgivning. Denna avhandling presenterar framsteg mot Rydberg-experiment med längre jonsträngar och avslutas med en första demonstration av koherent populationöverföring mellan Rydberg-tillstånd i infångade joner. De utvecklade metoderna utökar verktygslådan för infångade Rydberg-joner avsevärt, vilket möjliggör mer sofistikerade experiment, särskilt när flera olika Rydberg-tillstånd är inblandade, och ger större flexibilitet vid användning av längre jonsträngar.