Hyperentanglement of divalent neutral atoms by Rydberg blockade

Hyperentanglement (HE), the simultaneous entanglement between two particles in more than one degree of freedom, is relevant to both fundamental physics and quantum technology. Previous study on HE has been focusing on photons. Here, we study HE in individual neutral atoms. In most alkaline-earth-like atoms with two valence electrons and a nonzero nuclear spin, there are two stable electronic states, the ground state and the long-lived clock state, which can define an electronic qubit. Meanwhile, their nuclear spin states can define a nuclear qubit. By the Rydberg blockade effect, we show that the controlled-$Z$ (cz) operation can be generated in the electronic qubits of two nearby atoms, and simultaneously in their nuclear qubits as well, leading to a cz$\ensuremath{\bigotimes}$cz operation which is capable to induce HE. The possibility to induce HE in individual neutral atoms offers opportunities to study quantum science and technology based on neutral atoms.