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，这些问题涉及到物质的新形式。最近的实验在宇宙中前所未有的低温下创造了一种新材料。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人员的直接控制之下，甚至在材料被创造出来后可以改变成完全不同的东西。在日常材料和实验室中创造的材料中，原子、电子和离子之间相互作用：这导致原子之间有一个优选的距离，这决定了材料的结构和性能。然而，在这种新材料中，原子在极低的温度下被捕获成一种规则的模式：这种模式是由一组实验学家可以控制的激光产生的。例如，只要改变激光的强度，就很容易使原子保持静止，而不是在这个规则的模式上跳跃。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，与真正的固体不同，这种人造材料没有污垢和缺陷。所有这些都必须在极低的温度下发生，这样原子就不能移动太多。然后，原子遵守量子力学定律：小距离和低温下的基本物理定律，它说像原子这样的粒子也表现得像波（如光波）。因此，在这种新的人造材料中可以出现更丰富、更奇怪的现象。有了这种轻松和控制水平，研究一系列在普通材料中难以或不可能研究的基本量子现象成为可能。我计划与实验学家并行工作，研究当原子之间存在强烈的相互作用时，被困的冷原子会发生什么。例如，当原子被迫保持在一条直线上时，它们不能互相避开（就像在交通堵塞中一样！）。当一个原子移动一点时，就会影响到它的邻居，而邻居又会影响到它们的邻居，以此类推。最终的结果是，所有的原子一起参与形成一个整体的运动模式：原子的个性完全丧失了。物理学家已经开发出复杂的数学方法来处理实际固体中的这种行为。我计划使用这些技术（也许还会发明一些新的技术），看看当我们改变这种新材料的各个方面时，新的奇特形式的物质会如何发展。例如，如果我们放入不止一种类型的原子，不同类型的原子之间有吸引力，而同一类型的原子之间有排斥力，那么每种类型的原子可能聚集在一起形成一个新粒子，这些新粒子可能反过来形成一个新的整体模式。此外，实验学家可以及时地跟踪变化是如何发生的，这在普通材料中很难做到。因此，我打算研究当我们缓慢或突然地改变物质的某些方面时，物质的新形式是如何从一种形式转变为另一种形式的。在我提议的工作中，我将计算这些新形式物质的性质，并与实验进行比较。这反过来可能会提出新的实验来帮助我们理解这些新物质形式背后的基本原理。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，有人提出这种人造材料可以用于量子计算。这利用了原子类似量子波的特性来并行处理信息，从而极大地提高了计算能力。我的工作将为这种潜在的革命性应用提供必要的基本理解。

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.