  We develop a theory of the dynamical response of a minimal model of quantum
spin ice (QSI) by means of inelastic light scattering. In particular, we are
interested in the Raman response of the fractionalized U(1) spin liquid
realized in the XXZ QSI. We show that the low-energy Raman intensity is
dominated by spinon and gauge fluctuations. We find that the Raman response in
the QSI state of that model appears only in the $T_{2g}$ polarization channel.
We show that the Raman intensity profile displays a broad continuum from the
spinons and coupled spinon and gauge fluctuations, and a low-energy peak
arising entirely from gauge fluctuations. Both features originate from the
exotic interaction between photon and the fractionalized excitations of QSI.
Our theoretical results suggest that inelastic Raman scattering can in
principle serve as a promising experimental probe of the nature of a U(1) spin
liquid in QSI.
