Probing the coherence of quantum spin liquids with time-reversal protocols

Quantum simulators have reached levels of coherence and control over large system sizes enabling them to target quantum spin liquids - phases of matter characterized by their structure of entanglement rather than a local order parameter. Universal, robust and accessible observables are a major obstacle to fully characterize the phases, such as the coherences between loop configurations in the toric code.

Here, we propose an experimentally feasible protocol to measure multiple quantum coherences (MQCs), first developed in nuclear magnetic resonances and recently implemented in trapped ions via time reversal. MQCs can be seen as a type of out-of-time-order correlator. We benchmark our method from snapshots of the extended toric code obtained by quantum Monte Carlo simulations. Our protocol detects the topological phase transition requiring only few samples, and hence serves as a novel, experimentally accessible order parameter.

The scheme has several applications to current quantum simulation frontiers: From resonating valence bond states in dipolar Rydberg arrays, to utilizing local control in order to extract the coherence length of quantum spin lakes.