Generating coherent states of entangled spins

A coherent state of many spins contains quantum entanglement, which increases with the decrease of the collective spin value. We present a scheme to engineer this class of pure state based on incoherent spin pumping with several collective raising and lowering operators. In a pumping scenario aimed for maximum entanglement, the $N$-qubit steady state realizes the ideal resource for the $1\to N/2$ quantum telecloning. We show how the scheme can be implemented in the cold atomic system in an optical lattice. Error analysis shows that high-fidelity state engineering is possible for $N\sim O(100)$ spins in the presence of decoherence. The scheme can also prepare the large-scale Affleck-Kennedy-Lieb-Tasaki state.