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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. Here, we describe a family of quasi-1D nanostructures, based on LaAlO 3 /SrTiO 3 electron waveguides, in which a sinusoidal transverse spatial modulation is imposed. These devices display unique dispersive features in the subband spectra, namely, a sizeable shift (∼7 T) in the spin-dependent subband minima, and fractional conductance plateaus. 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. The ability to engineer these interactions in quantum wires contributes to the tool set of a 1D solid-state quantum simulation platform. 

One-dimensional electronic systems can support exotic collective phases because of the enhanced role of electron correlations. We describe the experimental observation of a series of quantized conductance steps within strongly interacting electron waveguides formed at the lanthanum aluminate–strontium titanate (LaAlO 3 /SrTiO 3 ) interface. The waveguide conductance follows a characteristic sequence within Pascal’s triangle: (1, 3, 6, 10, 15, …) ⋅ e 2 /h , where e is the electron charge and h is the Planck constant. This behavior is consistent with the existence of a family of degenerate quantum liquids formed from bound states of n = 2, 3, 4, … electrons. Our experimental setup could provide a setting for solid-state analogs of a wide range of composite fermionic phases.