Measuring facets of quantum criticality in an analog quantum simulation of the Lipkin-Meshkov-Glick model

The Lipkin-Meshkov-Glick (LMG) model is a prototypical model of quantum critical behavior in complex many-body systems. It originated as a model for numeric calculations of interacting two level spins and has been experimentally realized as interacting qubits, bosons, and more. In an experimental set up with a large (but far from infinite) spin in the LMG model, how could signs of a phase transition be measured? In this talk, we first broadly discuss our recent experimental results that realize the LMG model in a single analog qudit. Then, we will discuss our experimentally motivated theoretical progress in identifying and measuring signatures of the critical properties of the LMG in this finite size system, especially as it pertains to detecting the excited state quantum phase transition (ESQPT) and investigating the Kibble Zurek Mechanism (KZM) that are are known to take place in the LMG model. By developing a framework utilizing adiabatic ramps and observing Rabi oscillations, we can extract arbitrary energy gaps and thus reconstruct the system’s full spectrum. We discuss how this framework allows us to observe precursors of an ESQPT and investigate the KZM through measurements of excitations (heat) produced near quasi-critical points.