Many-body protected entanglement generation in interacting spin systems

We discuss a method to achieve decoherence resistant entanglement generation in strongly interacting ensembles of two-level spin systems. Our method uses designed gapped Hamiltonians to create a protected manifold of multidegenerate levels which is robust against local decoherence processes. We apply the protected evolution to achieve decoherence resistant generation of many-particle Greenberger-Horne-Zeilinger (GHZ) states in two specific physical systems, trapped ions and neutral atoms in optical lattices, and discuss how to engineer the desired many-body protected manifold with them. We analyze the fidelity of GHZ generation and show our method can significantly increase the sensitivity in frequency spectroscopy.