Non-Ergodic Quantum Manipulation

在相当长的一段时间里，电子输运是物理学中的一个重要课题。2006年，人们首次意识到，一个既有无序又有多体相互作用的封闭量子系统显示了一种全新的行为机制，称为多体局域化（MBL）。这种机制的特征在于平衡统计力学的崩溃，它预测在有限温度下的零电导状态，纠缠可以传播，尽管由于遍历性的崩溃而缺乏热化，表示为违反本征态热化假说，ETH。在凝聚态科学的许多领域都假设遍历性，即整体的子系统是整体的典型，并且在时间上平均的行为与在空间上平均的行为相同。因此，它在这种情况下不成立的事实允许新的现象，因为ETH不再持有而缺乏平衡。可能的新的状态可以通过应用高频MBL形成，这些将在项目中进行研究。迄今为止，在凝聚态系统中还没有持续的实验研究这些预测，尽管使用自然形成封闭量子系统的冷原子有相当大的活动。大量的理论兴趣已在数百篇论文发表的主题。如果实现的话，这种新的物质状态将在凝聚态领域产生重大影响--这就是该项目的目的。我们将利用半导体技术和用于研究介观器件和半导体纳米结构的制造技术来全面研究这种行为。通过制造独立的纳米结构，我们将确保一个封闭的系统，大大减少耦合到声子作为一个热浴。测量的温度将低于毫开尔文区域，无序的长度尺度将随着其他参数（如维数）的变化而变化。电气和热技术将被用作MBL状态的探针。除了对基础物理学的重要性之外，这项工作在量子信息和拓扑物理学中也将具有极其重要的意义，因为这种新的状态提供了一种目前无法获得的量子保护手段。

The subject of electron transport when states are localized by disorder has been an important topic in physics for a considerable time. It was first realized in 2006 that a closed quantum system in which there is both disorder and many body interactions shows a completely new regime of behaviour termed Many Body Localization, MBL. This regime is characterised by a breakdown of equilibrium statistical mechanics, it predicts a zero conductance state at a finite temperature, entanglement can spread although there is a lack of thermalisation due to the breakdown of ergodicity expressed as a violation of the Eigenstate Thermalisation Hypothesis, ETH. Ergodicity is assumed in many areas of condensed matter science, namely that a sub-system of the whole is typical of the whole and that the behaviour averaged over time is identical to that averaged over space. Consequently the fact that it does not hold in this situation allows new phenomena as does the lack of equilibration due to the ETH no longer holding. Possible new states can be formed by the application of high frequencies to MBL and these will be investigated in the project.To date there has been no sustained experimental investigation of these predictions in condensed matter systems although there is considerable activity using cold atoms which naturally form a closed quantum system. Enormous theoretical interest has been expressed in the hundreds of papers published on the topic. It is in the area of condensed matter that this new state of matter would have a major impact if realised - which is the purpose of the project. We will comprehensively investigate this regime of behaviour using semiconductor technology and the fabrication techniques used in investigating mesoscopic devices and semiconductor nanostructures. By fabricating free standing nanostructures we will ensure a closed system by drastically reducing the coupling to the phonons which act as a heat bath. The temperature of measurements will be down the milliKelvin region and the length scale of the disorder will be varied as will other parameters such as dimensionality. Electrical and thermal techniques will be utilised as probes of the MBL state. In addition to the importance for basic physics this work will be extremely significant in quantum information and topological physics as this new state provides a means of quantum protection not presently available.