Tunneling and Bulk Resistance Measurements in the Fractional Quantum Hall States

分数量子霍尔态中的准粒子的性质不同于非相互作用粒子（费米子或玻色子）的性质。据预测，在大多数分数量子霍尔态中，准粒子的交换会导致波函数的变化，相位因子是一个复数，幅度为1，但不同于+/-1，就像费米子和玻色子一样。更令人惊讶的是，对于填充分数i= 5/2的特殊状态，粒子的交换并不简单地改变波函数的相位，而是导致完全不同的波函数。 在这种情况下，统计量被称为非阿贝尔。 为了确定准粒子的统计特性，需要建造一个干涉仪，在干涉仪中，准粒子可以沿着两条不同的路径到达探测器。实验被提议研究粒子访问两条路径的隧穿过程，并且一旦理解，就创建干涉仪来测试关于非阿贝尔统计的想法。 这项研究可能有助于量子计算策略的发展。 研究生和博士后科学家在这里提出的那种研究的教育是非常有价值的。 通过学习纳米制造技术，超低温物理技术，以及深入思考基本物理问题，年轻人对小型和大型企业以及学术界都非常有价值。Non-Technical AbstractResearch被提议研究一种新的系统，这可能是量子计算机的基础。 事实证明，这种计算机可以解决传统计算机无法解决的问题。 例如，经典计算机无法将非常大的数字分解为素因子。 这一事实被用来保护我们的银行账户和许多国家的国防机密。 量子计算机可以做到这一点。 目前还没有人建造这样的量子计算机，但如果可以做到，我们首先在美国这样做是很重要的，这样就可以找到新的安全方法。这里提出的工作是研究一个系统，这可能对量子计算有用。 当电子被迫在半导体内部仅二维移动并置于强磁场中时，它们形成一种具有特殊性质的液体。 液体的行为就好像它是由新粒子而不是电子组成的，这些新粒子可能用于量子计算。 从事该项目的研究生和博士后研究人员将学习半导体技术以及量子力学的深层物理学。 这将使他们准备在小型和大型公司的前沿技术，这将使国家更具竞争力的工作。

Technical AbstractThe properties of the quasiparticles in the fractional quantum Hall states are different from those of non-interacting particles, which are either Fermions or Bosons. It is predicted that in most fractional quantum Hall states the interchange of quasiparticles results in a change of the wave function by a phase factor that is a complex number, with magnitude one, but different from +/-1, as for Fermions and Bosons. Even more surprising is the possibility, for a special state at filling fraction i= 5/2, that interchange of the particles does not simply change the wave function's phase, but results in a completely different wave function. For this case, the statistics are called non-Abelian. To determine the statistics of quasiparticles requires building an interferometer, in which the quasiparticles can travel on two distinct paths to the detector. Experiments are proposed to study the tunneling process by which the particles access the two paths, and, once it is understood, to create an interferometer to test the ideas about non-Abelian statistics. This research could contribute to the development of strategies for quantum computing. The education of graduate students and postdoctoral scientists in the kind of research proposed here is very valuable. By learning nano-fabrication techniques, ultra-low temperature physics techniques, as well as thinking deeply about fundamental physics issues, young people become extremely valuable to small and large businesses, as well as to academia.Non-Technical AbstractResearch is proposed to study a novel system, which might be the basis of a quantum computer. It has been shown that such a computer could solve problems that conventional computers cannot. For example, a classical computer cannot factor very large numbers into its prime factors. This fact is used to protect our bank accounts and many of the Nation's defense secrets. However, a quantum computer could do this. No one has built such a quantum computer yet, but if it can be done, it is important for us to do it in the US first, so that new approaches to security can be found. The work proposed here is to study a system, which might be useful for quantum computing. When electrons are forced to move in only two dimensions inside semiconductors and are placed in a strong magnetic field, they form a kind of liquid, with special properties. The liquid acts as though it is made of new particles, instead of electrons, and these new particles may be used for quantum computing. Graduate students and postdoctoral researchers working on this project will learn semiconductor technology as well as learning the deep physics of quantum mechanics. This will prepare them to work in small and large corporations on forefront technologies that will make the Nation more competitive.