Using multiple quantum coherences to diagnose equilibrium quantum phase transitions via out-of-time-ordered correlators without time reversal*

Quantum information science has recently motivated a theoretical push to characterize the critical region of a quantum phase transition (QPT) via information-theoretic quantities such as entanglement or coherence measures. At the same time, there has been a growing focus on the dynamics of quantum information and non-equilibrium systems due to improvements in atomic, molecular, and optical experiments. Here, we propose a new dynamical method to connect equilibrium QPTs and quantum coherence via out-of-time-ordered correlators (OTOCs) [1]. Using paradigmatic examples of QPTs, we show that an abrupt change in coherence and entanglement of the ground state across a QPT is observable in the spectrum of multiple quantum coherences, which are a special type of OTOC. We also develop a robust protocol to obtain the relevant OTOCs using quasi-adiabatic ramps through the ground state phase diagram, allowing for the detection of OTOCs without the need for time reversal of coherent dynamics, and making our protocol applicable for a broad range of current experiments in trapped ions and optical tweezer arrays.

[1] R. J. Lewis-Swan, S. R. Muleady, A. M. Rey, arXiv:2006.01313 (to appear in PRL).