  We study the U(1) quantum spin liquid on the pyrochlore spin ice systems. For
the non-Kramers doublets such as Pr$^{3+}$ and Tb$^{3+}$, 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 "$\pi$" 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 Pr$_2$TM$_2$O$_7$ and
Tb$_2$TM$_2$O$_7$ (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".
