Theory of ultracold atoms: from fundamentals of quantum mechanics to applications

像激光冷却这样的技术现在可以将原子气体冷却到比绝对零度（nK）低几亿分之一度的温度。这些“超冷”原子以非常量子力学的方式表现，因为它们的德布罗意波长非常大（~µm，即比室温下大5个数量级）。超冷原子已经被用来制造新的物质状态，比如玻色-爱因斯坦凝聚体（BECs），其中气体中的每个原子都具有相同的量子波函数。然而，超冷原子的科学潜力不仅仅局限于基本的量子力学；它们的运动状态可以被控制到前所未有的程度，它们也开始在自然力量和常数的精确测量中发挥重要作用。我的研究涉及这两个方面背后的理论。首先，我建议继续我的BECs研究，其中原子通过偶极子-偶极子相互作用相互作用。这与极性分子特别相关。其目的是研究这些远距离和各向异性相互作用如何影响超流动性等性质。其次，我想发起加拿大对光学微腔内超冷原子的研究。这种腔量子电动力学与原子量子运动的结合结合了我们最好的两个控制物理系统，因此有望成为量子信息处理和短距离力精确测量的天然舞台。第三，我计划研究超冷原子的宏观叠加如何遭受退相干，例如在约瑟夫森结中。这与上述第二个主题密切相关，并与加拿大目前正在进行的一些超冷原子实验有关。

Techniques such as laser cooling can now cool gases of atoms to temperatures as low as a few billionths of one degree above absolute zero (nK). These "ultracold" atoms behave in a very quantum mechanical way because their de Broglie wavelengths are so large (~µm, i.e., 5 orders of magnitude larger than at room temperature). Ultracold atoms have already been used to make new states of matter such as Bose-Einstein condensates (BECs) in which every atom in the gas has the same quantum wave function. However, the scientific potential of ultracold atoms is not just confined to fundamental quantum mechanics; their motional state can be controlled to such an unprecedented degree that they are also beginning to play an important role in precision measurements of nature's forces and constants. My research concerns the theory behind both of these aspects.Firstly, I propose to continue my studies of BECs in which the atoms interact via dipole-dipole interactions. This is of particular relevance to polar molecules. The idea is to investigate how these long-range and anisotropic interactions affect properties such as superfluidity. Secondly, I want to initiate Canadian studies of ultracold atoms trapped inside optical microcavities. This marriage of cavity quantum electrodynamics with the quantum motion of atoms combines two of our best controlled physical systems and so promises to be a natural arena for quantum information processing as well as precision measurement of forces at short distances. Thirdly, I plan to investigate how macroscopic superpositions of ultracold atoms suffer from decoherence, e.g. in Josephson junctions. This is closely tied in to the second topic above and is relevant to a number of ultracold atom experiments currently being carried out in Canada.