Coherent imaging spectroscopy of a quantum many-body spin system

Characterization of a quantum simulator Ultracold gases can be used to simulate the behavior of more complicated systems, such as solid materials. Senko et al. developed a method similar to nuclear magnetic resonance that can be used to validate the properties of such simulators. They demonstrated the method on an array of interacting trapped ions that simulate magnetism. A modulated magnetic field resonantly enhanced the transfer of the population between the different configurations of the system. The authors varied the modulation frequency to measure the energy of each configuration and mapped the effective interactions. Science, this issue p. 430 A method for validating quantum simulations is based on interrogating the system with a modulated magnetic field. Quantum simulators, in which well-controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics inaccessible to modeling with classical computers. However, checking the results of such simulations also becomes classically intractable as system sizes increase. Here, we introduce and implement a coherent imaging spectroscopic technique, akin to magnetic resonance imaging, to validate a quantum simulation. We use this method to determine the energy levels and interaction strengths of a fully connected quantum many-body system. Additionally, we directly measure the critical energy gap near a quantum phase transition. We expect this general technique to become a verification tool for quantum simulators once experiments advance beyond proof-of-principle demonstrations and exceed the resources of conventional computers.