Trapped ions in optical tweezers and their applications to quantum computing

This thesis explores the integration of optical tweezers into the field of trapped ion quantum simulations and quantum computing. Two theoretical approaches for engineering two-qubit gates using optical tweezers are presented.
The first proposal combines state-dependent tweezers with a classical oscillating field. Optical tweezers manipulate the trapping frequency of two target ions based on their internal state. When using an electric field that exclusively interacts with the centre of mass mode of a linear chain of N trapped ions, the speed of the gate operation remains constant, regardless of the separation between the ions.
The second proposal is based on the optical Magnus effect. This effect emerges in tightly focused laser beams, where polarization components separate due to the intense field curvature. Making use of this effect, we can modulate the motion of two ions based on their internal states, achieving high-fidelity two-qubit gates.
Additionally, we provide an overview of the experimental setup developed during this PhD work. We detail the modified linear Paul trap capable of confining two-dimensional ion crystals, along with the laser apparatus essential for ion trapping and cooling.
Finally, we describe the setup's characterization, the construction of the ion trap, and the alignment process for the optical tweezers setup. Initial results are presented, demonstrating the alignment of a single ion with an infrared optical tweezer and outlining the associated experimental challenges and future steps in this research endeavour.