Strong correlation physics in ultra cold atomic gases

我计划从理论上研究物理学中的一些基本问题，这些问题涉及到新的物质形式。最近的实验创造了一种在创纪录低温下的新材料，这在宇宙中以前从未见过。与世界各地实验室制造的材料不同，这种材料的大部分方面都在实验者的直接控制下，甚至可以在材料创造后改变成完全不同的东西。在日常材料和实验室创造的材料中，原子、电子和离子相互作用：这导致原子之间有一个合适的距离，这决定了材料的结构和性质。然而，在这种新材料中，原子在极低的温度下被捕获成规则的图案：这种图案是由一组实验者可以控制的激光创造的。例如，只要改变激光的强度，就可以很容易地让原子保持静止，而不是在这种规则的图案上跳来跳去。或者我们可以改变被困在这种模式中的原子的类型和数量；甚至原子之间的相互作用也可以改变。此外，与真实固体不同，这种人造材料中没有污垢和缺陷。所有这一切都必须在极低的温度下发生，这样原子才不会移动太多。然后，原子遵守量子力学定律：在短距离和低温下的基本物理学定律，即粒子像原子一样也像波一样(就像光波一样)。因此，在这种新的人造材料中可能会出现更丰富和更奇怪的现象。有了这种轻松和高度的控制，就有可能研究在正常材料中难以研究或不可能研究的一系列基本量子现象。在与实验者并行工作的同时，我计划研究当原子之间存在强烈相互作用时，被困的冷原子会发生什么。例如，当原子被迫排成一队时，它们无法相互避开(就像在交通堵塞中一样！)当一个原子稍微移动时，就会影响它的邻居，进而影响它们的邻居，以此类推。最终的结果是，所有的原子共同参与，形成一种全球运动模式：原子的个性完全丧失。物理学家已经开发出复杂的数学方法来处理真实固体中的这种行为。我计划使用这些技术(也许还会发明一些新技术)，看看当我们改变这种新材料的各个方面时，新的奇异物质形式是如何发展出来的。例如，如果我们放入不止一种类型的原子，不同类型之间有吸引，但相同类型之间有排斥，那么每种类型的一个原子可能聚集在一起形成一个新的粒子，这些新的粒子又可能形成一个新的全局模式。此外，实验者可以及时跟踪变化是如何发生的，这在正常材料中是相当难做到的。因此，我计划研究当我们缓慢地或突然地改变材料的某些方面时，新的物质形式如何从一种形式变化到另一种形式。在我提议的工作中，我将计算这些新形式物质的性质，以便与实验进行比较。这反过来可能会提出新的实验，以帮助我们理解这些新形式物质背后的基本原理。此外，这些新原理可能有助于研究更普通材料中的强相互作用。最后，提出了这种人工材料可以用于量子计算。这利用了原子的量子波性质来并行处理信息，从而极大地提高了计算能力。我的工作将为这一潜在的革命性应用提供所需的基本理解。

I plan to study theoretically some fundamental questions in physics, which involves new forms of matter. Very recent experiments have created a new material at record low temperatures, never seen before in the Universe. Unlike materials made by labs all over the world, most aspects of this material is under the direct control of the experimentalists, and can even be changed into something completely different after the material was created. In everyday materials and materials created in labs, the atoms, electrons and ions interact amongst themselves: this leads to the atoms having a preferred distance between each other, and this dictates what the structure and properties the material has. In this new material however, the atoms are trapped at extremely low temperatures into a regular pattern: this pattern is created by a set of lasers that experimentalists can control. For example, it is easy to make the atom stay at rest, rather than hop around on this regular pattern, just by changing the intensity of the laser. Or we can change the types and number of atoms trapped in this pattern; even the interactions between the atoms can be changed. Furthermore, there are no dirt nor defects in this artificial material, unlike in real solids. All this has to happen at extremely low temperatures, so that the atoms cannot move around too much. Then, atoms obey the laws of quantum mechanics: the basic laws of physics at small distances and low temperatures, which say that particles like atoms also behave like waves (as in light waves). Thus, much richer and stranger phenomena can occur in this new artificial material.With this ease and level of control, it becomes possible to study a whole range of fundamental quantum phenomena that are difficult--or impossible--to study in normal materials. Working in parallel with experimentalists, I plan to study what happens to the trapped cold atoms, when there are strong interactions between the atoms. For example, when atoms are forced to stay in a line, they cannot avoid each other (just as in a traffic jam!). When one atom moves a bit, this affects its neighbours, which in turn affects their neighbours, and so on. The end result is that all of the atoms participate together to form a global pattern of motion: the individuality of the atoms are lost altogether. Physicists have developed sophisticated mathematical methods to treat such behaviour in real solids. I plan to use such techniques (and perhaps invent some new ones) to see how new exotic forms of matter can develop, when we change various aspects of this new material . For example, if we put in more than one type of atoms, and there is attraction between the different types, but repulsion between the same type, then one atom of each type may clump together to form a new particle, and these new particles may in turn form a new global pattern. Furthermore, experimentalists can follow in time how changes occur, which is rather hard to do in normal materials. Thus, I plan to study how the new forms of matter may change from one form to another, when we slowly or suddenly change some aspects of the material . In my proposed work, I will calculate properties of these new forms of matter, to compare with experiments. This in turn may suggest new experiments to help us understand the basic principles underlying these new forms of matter. Furthermore, these new principles may benefit the study of strong interactions in more normal materials. Finally, it has been proposed that this sort of artificial material can be used for quantum computing. This takes advantage of the quantum wave-like nature of atoms to process information in parallel, to hugely increase computing power. My work will provide the basic understanding needed for this potentially revolutionary application.