Magnetic Quantum-Phase Control between Two Entangled Macroscopic Nuclear Ensembles

Heralded generation and manipulation of quantum entanglement between two macroscopic and spatially separated crystals at room temperature is theoretically studied. We show that by combining an x-ray parametric down-conversion source and x-ray interferometry with nuclear resonant scattering techniques, two macroscopic crystals hosting M\"ossbauer nuclei located each on an interferometer arm can be entangled for few tens of nanoseconds. The coherence time of the entanglement state can be prolonged up to values comparable to the lifetime of a single nuclear excited state, on the order of hundred nanoseconds. A non-mechanical magnetic control of the quantum phase between the two spatially separated entangled nuclear crystals is put forward.