Deterministic preparation of Dicke states of donor nuclear spins in silicon by cooperative pumping

For donor nuclear spins in silicon, we show how to deterministically prepare various symmetric and asymmetric Dicke states which span a complete basis of the many-body Hilbert space. The state preparation is realized by cooperative pumping of nuclear spins by coupled donor electrons, and the required controls are in situ to the prototype Kane proposal for quantum computation. This scheme only requires a sub-gigahertz donor exchange coupling which can be readily achieved without atomically precise donor placement, hence it offers a practical way to prepare multipartite entanglement of spins in silicon with current technology. All desired Dicke states appear as the steady state under various pumping scenarios and therefore the preparation is robust and does not require accurate temporal controls. Numerical simulations with realistic parameters show that Dicke states of 10-20 qubits can be prepared with high fidelity in presence of decoherence and unwanted dynamics.