• DOI:10.1038/nphys4119
• Corpus ID: 52085472

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet

@article{Grttner2016MeasuringOC,
  title={Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet},
  author={Martin G{\"a}rttner and Justin Gary Bohnet and Arghavan Safavi-Naini and Michael L. Wall and John J. Bollinger and Ana Maria Rey},
  journal={Nature Physics},
  year={2016},
  volume={13},
  pages={781 - 786}
}

• M. Gärttner, J. Bohnet, +3 authors A. Rey
• Published 31 August 2016
• Physics
• Nature Physics

Controllable arrays of ions and ultracold atoms can simulate complex many-body phenomena and may provide insights into unsolved problems in modern science. To this end, experimentally feasible protocols for quantifying the buildup of quantum correlations and coherence are needed, as performing full state tomography does not scale favourably with the number of particles. Here we develop and experimentally demonstrate such a protocol, which uses time reversal of the many-body dynamics to measure out-of-time-order correlation functions (OTOCs) in a long-range Ising spin quantum simulator with more than 100 ions in a Penning trap. By measuring a family of OTOCs as a function of a tunable parameter we obtain fine-grained information about the state of the system encoded in the multiple quantum coherence spectrum, extract the quantum state purity, and demonstrate the buildup of up to 8-body correlations. Future applications of this protocol could enable studies of many-body localization, quantum phase transitions, and tests of the holographic duality between quantum and gravitational systems. Characterizing the correlations of quantum many-body systems is known to be hard, but there are ways around: for example, a new method for measuring out-of-time correlations demonstrated in a Penning trap quantum simulator with over 100 ions.