  Sources of photons with controllable quantum properties such as entanglement
and squeezing are desired for applications in quantum information, metrology,
and sensing. However, fine-grained control over these properties is hard to
achieve, especially for two-photon sources. Here, we propose a new mechanism
for generating entangled and squeezed photon pairs using superluminal and/or
accelerating modulations of the refractive index in a medium. By leveraging
time-changing dielectric media, where quantum vacuum fluctuations of the
electromagnetic field can be converted into photon pairs, we show that energy-
and momentum-conservation in multi-mode systems give rise to frequency and
angle correlations of photon pairs which are controlled by the trajectory of
the index modulation. These radiation effects are two-photon analogues of
Cherenkov and synchrotron radiation by moving charged particles such as free
electrons. We find the particularly intriguing result that synchrotron-like
radiation into photon pairs exhibits frequency correlations which can enable
the realization of a heralded single photon frequency comb. We conclude with a
general discussion of experimental viability, showing how solitons, ultrashort
pulses, and nonlinear waveguides may enable pathways to realize this two-photon
emission mechanism. For completeness, we discuss in the Supplementary
Information how these effects, sensitive to the local density of photonic
states, can be strongly enhanced using photonic nanostructures. As an example,
we show that index modulations propagating near the surface of graphene produce
entangled pairs of graphene plasmons with high efficiency, leading to
additional experimental opportunities.
