Quantum many body interactions in a two dimensional solid state system

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Quantum-Many-Body interactions still remain one of the main challenges in modern physics. They are related to various phenomena, like quantum phase transitions, spin frustration and become important for the emerging quantum technology. In this work we plan to study quantum many-body interactions in a two dimensional network of several hundred coupled nuclear spins. The latter will be coherently controlled using radio frequency pulses and their spin states will be polarised and read out using a nearby single optically active colour centre in diamond. We will perform nuclear magnetic resonance spectroscopy of the nuclear ensemble and study its relaxation and coherence properties. Afterwards multiple quantum coherence and entanglement states will be created and their time evolution observed. Furthermore, quantum magnetic phase transitions will be simulated with this physical system, by implementing various interaction Hamiltonians. Finally spin polarisation will be injected in one part of the network of nuclear spins and its propagation monitored using a second colour centre located few tens of nanometres away.