Partitioning dysprosium's electronic spin to reveal entanglement in non-classical states*

Entanglement is one of the defining characteristics of quantum systems, while being challenging to detect and quantify. In this talk, I will present a study of the entanglement properties associated with non-classical states of dysprosium atoms' electronic spin J=8, which can be viewed as the collective spin describing a set of 2J=16 qubits symmetric upon exchange. Entanglement is often considered irrelevant here, since the qubit ensemble cannot be partitioned. In our experiments, we use optical coupling to an excited electronic state J'=J-1 to split it in two parts. The absorption of a photon corresponds to the annihilation of a qubit pair in a state defined by the light polarization. Firstly, we investigate the non-classicality of W and squeezed states, by measuring this light-spin coupling as a function of light polarization, to give direct access to the concurrence - the most common measure of pairwise entanglement. Then, we investigate the separability of the 2/14 partition by studying the mixed nature of the reduced two-qubit density matrix. For a W state and a Schrödinger cat-like state, the min-entropy of the 2-qubit subsystem exceeds the value in the initial state, thereby proving entanglement. Finally, we study the loss of qubit pairs via spontaneous emission, for states prepared in an excited level J'=J+1. We contrast W states, whose entanglement is robust to particle loss, with cat states, known to be very fragile in this regard.