  The observation that free electrons can interact coherently with quantized
electromagnetic fields and matter systems has led to a plethora of proposals
leveraging the unique quantum properties of free electrons. At the heart of
these proposals lies the assumption of a strong quantum interaction between a
flying free electron and a photonic mode. However, existing schemes are
intrinsically limited by electron diffraction, which puts an upper bound on the
interaction length and therefore the quantum coupling strength. Here, we
propose the use of "free-electron fibers'': effectively one-dimensional
photonic systems where free electrons co-propagate with two guided modes. The
first mode applies a ponderomotive trap to the free electron, effectively
lifting the limitations due to electron diffraction. The second mode strongly
couples to the guided free electron, with an enhanced coupling that is orders
of magnitude larger than previous designs. Moreover, the extended interaction
lengths enabled by our scheme allows for strong single-photon nonlinearities
mediated by free electrons. We predict a few interesting observable quantum
effects in our system, such as deterministic single-photon emission and
complex, nonlinear multimode dynamics. Our proposal paves the way towards the
realization of many anticipated effects in free-electron quantum optics, such
as non-Gaussian light generation, deterministic single photon emission, and
quantum gates controlled by free-electron--photon interactions.
