Quantifying coherence and entanglement in trapped ions using the multiple quantum spectrum

The multiple quantum coherence (MQC) spectrum of a quantum state, originally introduced for highly mixed states in the context of NMR, quantifies coherence between different magnetization sectors. The MQC spectrum of a spin system is measurable by a sequence of rotations and evolution under an interaction Hamiltonian, provided that the evolution can be time reversed. Such a many-body echo can be realized in systems of trapped ions. We study the relation of the multiple quantum intensities with entanglement measures and witnesses such as Fisher information and concurrence and discuss the impact of decoherence mechanisms present in current trapped ion experiments on the proposed scheme for measuring the MQC spectrum. Supported by: JILA-NSF-PFC-1125844, NSF-PHY-1521080, ARO, AFOSR, AFOSR-MURI