Towards Analog Quantum Simulation of Three-Body Hamiltonians with Ytterbium Trapped Ions

Trapped ion qubits provide a reliable platform for the analog simulation of quantum spin systems because of their high controllability, scalability, and long coherence times. The mapping of quantum field theories to spin models further enables us to study condensed matter, nuclear, and high energy physics with trapped ions. We will report our experimental progress towards an analog quantum simulator with a trapped Ytterbium ion chain, including the characterization of our trap performance and its stability. Here, we also propose the generalized Molmer-Sorensen scheme using higher order spin-phonon couplings to generate an effective three-body Hamiltonian with trapped ions, which would allow us to simulate the U(1) quantum link model. Furthermore, we will present our individual addressing setup using an arbitrary wave generator and a free-spaced acoustic optical-modulator for local optical pumping. This configuration will be used for spin state initialization, which is necessary to characterize the dynamics of the three-body Hamiltonian.