  High-mobility complex-oxide heterostructures and nanostructures offer new
opportunities for extending the paradigm of quantum transport beyond the realm
of traditional III-V or carbon-based materials. Recent quantum transport
investigations with LaAlO$_3$/SrTiO$_3$-based quantum dots have revealed the
existence of a strongly correlated phase in which electrons form spin-singlet
pairs without becoming superconducting. Here we report evidence for
micrometer-scale ballistic transport of electron pairs in quasi-one-dimensional
(quasi-1D) LaAlO$_3$/SrTiO$_3$ nanowire cavities. In the paired phase,
Fabry-Perot-like quantum interference is observed, in sync with conductance
oscillations observed in the superconducting regime (at zero magnetic field).
Above a critical magnetic field $B_p$, electron pairs unbind and conductance
oscillations shift with magnetic field. These experimental observations extend
the regime of ballistic electronic transport to strongly correlated phases.
