Spin-Energy Entanglement of a Time-Focused Neutron

Intra-particle mode entanglement in individual neutrons enables a potential new probe of entanglement in quantum systems and materials. We have demonstrated a contextual result in the spin and energy phases (modes) of a neutron beam using two resonant spin flippers in the MIEZE (Modulated IntEnsity with Zero Effort) configuration, where amplitude (rather than polarization) modulations are brought into focus at a detector. This is an extension of previous findings of neutron mode entanglement in spin-echo small-angle neutron scattering (SESANS). The spin phase is the phase of the Larmor precession and the energy phase is manipulated by the resonant spin flippers. Analogous to violation of Bell-type inequalities to prove non-classical correlations, we constructed a Clauser-Horne-Shimony-Holt (CHSH) contextuality witness using the spin and energy phases, and observed a clear breach of the classical bound |S| <= 2, obtaining S = 2.4. We expect these quantum entangled beams to enable novel approaches for directly probing dynamics and entanglement in quantum materials whose low-energy excitation scales match those of the neutron energy subsystem. Importantly, the instrument set-up is the same as a standard MIEZE experiment, meaning that these witness measurements can be straightforward and routine.