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Research Interests:

 

Electrons confined to one dimension

The behavior of electrons in a solid-state environment is often qualitatively modified from their vacuum properties due to Coulomb interaction. The low energy properties of such interacting systems are described in terms of dressed elementary excitations known as quasi-particles which interact only weakly among themselves. In two and three-dimensional disordered metals quasi-particles bear a strong resemblance to free electrons. They each carry a charge e and spin half and most importantly, their excitation spectrum, which for non-interacting electrons is simply determined by the underlying band mass m, is only slightly modified by the Coulomb interaction. However, the underlying quasi-particles in a one-dimensional metal, know as a Luttinger-liquid, are utterly different from free electrons. Here, for example, the spin and charge degrees of freedom completely decouple and can be separately excited. Using momentum and energy resolved tunneling between two closely situated parallel wires we have measured the collective excitation spectrum of electrons confined to one-dimension. At high electron densities, spin-charge separation is clearly observed. At low electron densities the system abruptly looses translation invariance and becomes localized. Our measurements indicate that the localization length corresponds to the inter-electron spacing.

Local probes - Imaging localization and fractional charge

In this work we address several outstanding questions pertaining to the microscopic properties of the fractional quantum Hall effect: What is the nature of the particles that participate in the localization but do not contribute to transport and can fractionally charged quasi particles localize in space? Using a scanning single electron transistor we image the individual localized states in the fractional quantum Hall regime and determine the charge of the localizing particles. Highlighting the symmetry between filling factors 1/3 and 2/3, our measurements show that fractionally charged quasi particles localize in space to sub-micron dimensions with e*=e/3, where e is the electron charge. Recently, at filling factors 2/3, we follow the behavior of the fractionally charged localized states through the spin phase transition.

Coherent control and Manipulation of single electron spins

We demonstrate coherent control of a quantum two-level system based on two-electron spin states in a double quantum dot allowing state preparation, coherent manipulation, and projective read-out. These techniques are based on rapid electrical control of the exchange interaction. Separating and later recombining a singlet spin state provides a measurement of the spin dephasing time, T*2 ~ 10 ns, limited by hyperfine interactions with the GaAs host nuclei. Rabi oscillations of two-electron spin states are demonstrated, and spin-echo pulse sequences are used to suppress hyperfine-induced dephasing. Using these quantum control techniques, a coherence time for two-electron spin states exceeding 1 µs is observed.

 

The 5/2 FQHE Excitations

The fractional quantum hall state at filling factor 5/2 is theorized to be qualitatively very different from the more conventional states with filling factors having an odd denominator. Especially of interest is the possibility that excitations of the 5/2 liquid will exhibit non-Abelian braiding statistics, so weaving excitations around each other such that they end up where they started can evolve the sytem into a different ground state. As these "braiding" operations knot up the underlying system, they are robust to the type of decoherence that plagues conventional approaches to quantum computation. While building a topological computer using this sytems is a long-term goal, we are currently attempting to better understand the nature of the excitations and the extent to which they can be manipulated. We are specifically interested in using single electron transistors to look at charging physics and the nature of localized states (due to disorder) at filling factor 5/2. Also of interest are the properties of the nonlocal edge states, which constitute a chiral Luttinger liquid and may be amenable to study using the techniques we have developed for probing one dimensional systems.