Advances in Quantum Simulation with Planar Ion Crystals

One of the most important goals of modern quantum sciences is to learn how to control and entangle many-body systems and use them to make powerful and improved quantum devices, materials and technologies. In this tutorial I will summarize recent progress on the use of a planar crystal arrays in the NIST Penning trap, made with tens to a few hundred ions, as a platform for quantum simulation of spin and spin-boson models. In this system a pair of lasers can be used to couple the spins, encoded in two internal levels of the ions, to the vibrational modes (phonons) of the crystal and generate entanglement starting from easily prepared uncorrelated states. The quantum simulator can operate in two regimes. In one regime, phonons do not play an active role in the dynamics and instead are used to mediate spin-spin interactions. I will discuss how operating in this regime we have been able to simulate Ising models with tunable-range spin couplings, the well know One-Axis-Twisting model, which we used to generate spin squeezing, and more recently, a many-body echo sequence which we used to measure out-of-time-order correlations (OTOCs), a type of correlations that quantify the scrambling of quantum information across the system's many-body degrees of freedom. In the other regime, phonons actively participate. I will describe how by operating in this regime we have been able to simulate the Dicke model, an iconic model in quantum optics which describes the coupling of a (large) spin to an oscillator and more recently realize a many-body quantum-enhanced sensor that can detect weak displacements and electric fields with at the least one order of magnitude better sensitivity than state-of-the-art Rydberg atom electric field sensors operated with classical particles. This capability opens a path for the use of trapped ion crystals for dark matter searches.