Partitioning dysprosiums electronic spin to reveal entanglement in non-classical states

Quantum spins of mesoscopic size are a well-studied playground for engineering non-classical states. If the spin represents the collective state of an ensemble of qubits, its non-classical behavior is linked to entanglement between the qubits. In this work, we report on an experimental study of entanglement in dysprosiums electronic spin. Its ground state, of angular momentum $J=8$, can formally be viewed as a set of $2J$ qubits symmetric upon exchange. To access entanglement properties, we partition the spin by optically coupling it to an excited state $J=J-1$, which removes a pair of qubits in a state defined by the light polarization. Starting with the well-known W and squeezed states, we extract the concurrence of qubit pairs, which quantifies their non-classical character. We also directly demonstrate entanglement between the 14- and 2-qubit subsystems via an increase in entropy upon partition. In a complementary set of experiments, we probe decoherence of a state prepared in the excited level $J=J+1$ and interpret spontaneous emission as a loss of a qubit pair in a random state. This allows us to contrast the robustness of pairwise entanglement of the W state with the fragility of the coherence involved in a Schrodinger cat state. Our findings open up the possibility to engineer novel types of entangled atomic ensembles, in which entanglement occurs within each atoms electronic spin as well as between different atoms.