Advances in Quantum Simulation with Planar Ion Crystals
Dr. Ana Maria Rey (JILA, NIST and University of Colorado, Boulder, USA)

I will discuss recent progress on the use of planar crystals with hundreds of ions as a platform for quantum simulation of spin and spin-boson models. The key idea is the use of a pair of lasers to couple two internal levels of the ions, that act as a spin½ degree of freedom, to the vibrational modes, phonons, of the crystal. In the regime when phonons do not play an active role in the dynamics and instead mediate spin-spin interactions we have been able to simulate Ising models with tunable-range spin couplings, and 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 regime when phonons actively participate 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. Our system is the first to demonstrate an enhanced sensitivity resulting from quantum entanglement in a mesoscopic ion crystal with an improvement by a factor of 300 over prior classical protocols in trapped ions and more than an order of magnitude compared to state-of-the-art electrometers based on Rydberg atoms. Overall my talk plans to illustrate the great potential offered by trapped ion crystals not only as quantum simulators but also as feasible near-term detectors of dark matter.