What does inelastic neutron scattering measure in pyrochlore ice spin liquids?

We study the U(1) quantum spin liquid on the pyrochlore spin ice systems. For the non-Kramers doublets such as Pr³⁺ and Tb³⁺, we point out that the inelastic neutron scattering not only detects the low-energy gauge photon, but also contains the continuum of the "magnetic monopole" excitations. Unlike the spinons, these "magnetic monopoles" are purely of quantum origin and have no classical analogue. We further point out that the ``magnetic monopole" experiences a background dual π flux due to the spin-1/2 nature of the local moment when the "monopole" hops on the dual diamond lattice. We then predict that the "monopole" continuum has an enhanced spectral periodicity. This prediction can be examined among the existing data on the non-Kramers doublet spin liquid candidate materials like Pr₂TM₂O₇ and Tb₂TM₂O₇ (with TM = "transition metal"). The application to the Kramers doublet systems and numerical simulation is further discussed. Finally, we present a general classification of distinct symmetry enriched U(1) quantum spin liquids based on the translation symmetry fractionalization patterns of "monopoles" and "spinons".