Localization Transition in a Ballistic Quantum Wire
  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 quantum 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. 
H. Steinberg, O. M. Auslaender, A. Yacoby, J. Qian, G. A. Fiete, Y.   Tserkovnyak, B. I. Halperin, K. W. Baldwin, L. N. Pfei...