Theory of ultracold matter

这个提议涉及囚禁玻色气体中的玻色-爱因斯坦凝聚(BEC)的问题。在超低温下，玻色原子的气体表现出一种凝聚，其中大多数原子处于最低可用量子态。在这种新的物质状态下，原子相互作用，在接近宏观尺度的尺度上表现出量子行为。其影响是深远和深远的。潜在的应用包括原子激光、原子光刻和量子计算。他说，拟议的研究可以广泛地描述为对这些被困气体在有限温度下的动力学进行的理论研究。在绝对零度以上，气体由凝聚态、凝聚态和热激发原子组成，这些原子构成了热云。这个原子系统可以经历各种振荡模式，这些模式可以通过实验进行研究。理论上的挑战是提供对这种行为的描述，解释观察到的模式频率和模式随时间衰减的速度。他们发现，人们对这一主题的大部分兴趣源于这样一个事实，即捕获的气体可以通过各种方式进行操纵。例如，通过旋转禁闭势能可以使气体快速旋转。通过这种方式，可以产生涡流阵列。该项目的一部分将解决这些漩涡最初是如何形成的，以及这些漩涡最终如何排列成有序的阵列。他们说，操纵原子的另一种方式是简单地向它们照射光线。如果光形成驻波，就会产生一个周期势，原子就会有效地驻留在晶格上。我们掌握的理论工具将使我们能够探索原子在这种情况下的有趣的动力学行为，特别是在同时存在凝聚云和热云的高温下。从这些研究中获得的知识将进一步扩展我们控制这类系统中原子的能力。

This proposal concerns the subject of Bose-Einstein condensation (BEC) in trapped Bose gases. At ultra-low temperatures, a gas of bosonic atoms exhibits a kind of condensation in which most of the atoms fall into the lowest available quantum state. In this novel state of matter, the atoms act coherently, and exhibit quantum behaviour on scales approaching macroscopic dimensions. The implications are far-reaching and profound. Potential applications include atomic lasers, atomic lithography and quantum computing.     The proposed research can be broadly characterized as the theoretical study of the dynamics of these trapped gases at finite temperatures. Above absolute zero, the gas consists of a combination of the condensed phase, the condensate, and thermally excited atoms that constitute a thermal cloud. This system of atoms can undergo a variety of modes of oscillation that can be studied experimentally. The theoretical challenge is to provide a description of this behaviour that explains the observed mode frequencies and the rate at which the modes decay as a function of time.     Much of the interest in the subject stems from the fact that trapped gases can be manipulated in various ways. For example, the gas can be made to spin rapidly by rotating the confining potential. In this way, arrays of vortices can be generated. Part of the project will address the question of how these vortices are initially formed, and how the vortices finally arrange themselves in an ordered array.     Another way to manipulate the atoms is to simply shine light on them. If the light forms a standing wave, a periodic potential arises and the atoms effectively reside on a lattice. The theoretical tools we have at our disposal will allow us to explore the interesting dynamical behaviour of the atoms in this situation, especially at elevated temperatures when both a condensate and thermal cloud are present. The knowledge gained from such studies will extend even further our ability control atoms in these kinds of systems.