  The quest to understand, design, and synthesize new forms of quantum matter
guides much of contemporary research in condensed matter physics.
One-dimensional (1D) electronic systems form the basis for some of the most
interesting and exotic phases of quantum matter. The variety of
experimentally-accessible ballistic 1D electronic systems is highly restricted,
and furthermore these systems typically have few tuning parameters other than
electric and magnetic fields. However, electron waveguides formed from
two-dimensional (2D) LaAlO$_3$/SrTiO$_3$ heterointerfaces exhibit remarkable 1D
properties, including ballistic multi-mode transport and strong attractive
electron-electron interaction, but these systems conspicuously lack strong or
tunable spin-orbit interactions. Here we describe a new class of quasi-1D
nanostructures, based on LaAlO$_3$/SrTiO$_3$ electron waveguides, in which a
sinusoidal transverse spatial modulation is imposed. Nanowires created with
this "serpentine" modulation display unique dispersive features in the subband
spectra, namely (1) a significant shift ($\sim$ 7 tesla) in the spin-dependent
subband minima, and (2) fractional conductance plateaus, some of which are
continuously tunable with a magnetic field. The first property can be
understood as an engineered spin-orbit interaction associated with the periodic
acceleration of electrons as they undulate through the nanowire
(ballistically), while the second property signifies the presence of enhanced
electron-electron scattering in this system due to the imposed periodic
structure. The ability to engineer these interactions in quantum wires
contributes to the tool set of a 1D solid-state quantum simulation platform.
