Quantum simulation of spin ordering with nuclear spins in a solid-state lattice

An experiment demonstrating the quantum simulation of a spin-lattice Hamiltonian is proposed. Dipolar interactions between nuclear spins in a solid state lattice can be modulated by rapid radio-frequency pulses. In this way, the effective Hamiltonian of the system can be brought to the form of an antiferromagnetic Heisenberg model with long range interactions. Using a semiconducting material with strong optical properties such as InP, cooling of nuclear spins could be achieved by means of optical pumping. An additional cooling stage is provided by adiabatic demagnetization in the rotating frame down to a nuclear spin temperature at which we expect a phase transition from a paramagnetic to antiferromagnetic phase. This phase transition could be observed by probing the magnetic susceptibility of the spin lattice. Our calculations suggest that employing current optical pumping technology, observation of this phase transition is within experimental reach.