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The global coupling of few-level quantum systems (``spins") to a discrete set of bosonic modes is a key ingredient for many applications in quantum science, including large-scale entanglement generation, quantum simulation of the dynamics of long-range interacting spin models, and hybrid platforms for force and spin sensing. In this talk, I will first discuss our recent collaboration with the experimental group of John Bollinger at NIST verifying entanglement, in the form of spin squeezing, in arrays of hundreds of trapped ions. Here, Ising interactions between the effective spins of the ions are generated by coupling to the normal modes of the trapped ion crystal via a spin-dependent optical force. In the latter part of my talk, I will discuss ways to numerically tackle more general problems of spins coupled to bosons numerically using matrix product states, a class of lowly-entangled quantum states. Host: Sebastian Deffner |