Coherent Imaging Spectroscopy of a Quantum Many-Body Spin System*

Trapped-ion quantum simulators are a promising candidate for exploring quantum-many-body physics, such as quantum magnetism, that are difficult to examine in condensed-matter experiments or using classical simulation. We demonstrate a coherent imaging spectroscopic technique to validate a quantum simulation [1]. In this work, we study fully-connected transverse Ising models with a chain of up to 18 $^{171}$Yb$^+$ ions. Here, We resolve the state of each spin by collecting the spin-dependent fluorescence on a camera in order to map the complete energy spectrum and fully characterize the spin-spin couplings, while also engineering entangled states and measuring the critical gap near a quantum phase transition. We expect this general technique to become an important verification tool for quantum simulators.\\[4pt] [1] C. Senko, et al, arXiv:1401.5751 (2014).