We report on measurements of quantum many-body modes in ballistic wires and their dependence on Coulomb interactions, obtained from tunneling between two parallel wires in a GaAs/AlGaAs heterostructure while varying electron density. We observe two s
pin modes and one charge mode of the coupled wires, and map the dispersion velocities of the modes down to a critical density, at which spontaneous localization is observed. Theoretical calculations of the charge velocity agree well with the data, although they also predict an additional charge mode that is not observed. The measured spin velocity is found to be smaller than theoretically predicted.
The many-body wave-function of an interacting one-dimensional electron system is probed, focusing on the low-density, strong interaction regime. The properties of the wave-function are determined using tunneling between two long, clean, parallel quan
tum wires in a GaAs/AlGaAs heterostructure, allowing for gate-controlled electron density. As electron density is lowered to a critical value the many-body state abruptly changes from an extended state with a well-defined momentum to a localized state with a wide range of momentum components. The signature of the localized states appears as discrete tunneling features at resonant gate-voltages, corresponding to the depletion of single electrons and showing Coulomb-blockade behavior. Typically 5-10 such features appear, where the one-electron state has a single-lobed momentum distribution, and the few-electron states have double-lobed distributions with peaks at $pm k_F$. A theoretical model suggests that for a small number of particles (N<6), the observed state is a mixture of ground and thermally excited spin states.
We have measured the low temperature conductance of a one-dimensional island embedded in a single mode quantum wire. The quantum wire is fabricated using the cleaved edge overgrowth technique and the tunneling is through a single state of the island.
Our results show that while the resonance line shape fits the derivative of the Fermi function the intrinsic line width decreases in a power law fashion as the temperature is reduced. This behavior agrees quantitatively with Furusakis model for resonant tunneling in a Luttinger-liquid.
