Spin-Energy Entanglement of a Time-Focused Neutron

Intra-particle entanglement of individual particles such as neutrons couldenable a new class of scattering probes that are sensitive to entanglement inquantum systems and materials. In this work, we present experimental resultsdemonstrating quantum contextuality as a result of entanglement between thespin and energy modes (i.e., degrees of freedom) of single neutrons in a beamusing a pair of resonant radio-frequency neutron spin flippers in the MIEZEconfiguration (Modulated IntEnsity with Zero Effort). We verified themode-entanglement by measuring a Clauser-Horne-Shimony-Holt (CHSH)contextuality witness S defined in the spin and energy subsystems, observinga clear breach of the classical bound of |S| ≤ 2, obtaining S = 2.40 ±0.02. These entangled beams could enable novel approaches for directly probingdynamics and entanglement in quantum materials whose low-energy excitationscales match those of the incident entangled neutron.