  Entangled photon pairs are a key resource in future quantum-optical
communication and information technologies. While high-power laser light
propagating in bulk nonlinear optical crystals is conventionally used to
generate entangled photons that are routed into optical configurations, such
schemes suffer from low efficiency due to the weak intrinsic nonlinear optical
response of known materials and losses associated with photon in- and
out-coupling. Here, we propose a scheme to generate entangled polariton pairs
directly within optical waveguides using free electrons, whereby the measured
energy loss of undeflected electrons heralds the production of
counter-propagating polaritons pairs that are entangled in energy and direction
of emission. As a paradigmatic example, we study the excitation of plasmon
polaritons in metal strip waveguides that, within specific frequency regimes,
strongly enhance light-matter interactions that lead to two-plasmon generation
in comparison to the probability of single-plasmon excitation. We demonstrate
that, under appropriate conditions, an electron energy loss detected in an
optimal frequency range can reliably signal the generation of a plasmon pair
entangled in energy and momentum. Our proposed scheme can be directly applied
to other types of optical waveguides for in situ generation of entangled photon
pairs in quantum-optics applications.
