Towards the analog quantum simulation of field theories with trapped ions

The high controllability, scalability, and long coherence times of trapped ions make them a promising platform for the analog simulation of quantum spin ensembles. We can study quantum field theories of condensed matter, nuclear, and high energy systems by mapping them to spin models. We will present our experimental progress on the construction of an analog quantum simulator for field theories with a trapped Ytterbium ion chain. Our trap assembly consists of a segmented four-blade Paul trap that allows for a quasi-uniformly spaced ion chain with a homogenous radiofrequency confinement field along the trap axis and large numerical apertures for high-resolution imaging (NA~0.6) and individual addressing (NA~0.3). This setup serves as a prototype design for the future monolithic three-dimensional trap with high precision electrode alignment using laser writing and controlled glass etching techniques for universal accessibility to ion trapping. We will report the characteristics of our trap performance and the stability of our system. Furthermore, we will propose an experimental scheme to simulate the U(1) lattice gauge field theory in 1+1 dimensions via three-body interactions with trapped ions.