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

激光冷却等技术现在可以将原子气体冷却到比绝对零度高几十亿分之一度的温度。这些“超冷”原子的行为方式是非常量子力学的，因为它们的德布罗意波长非常大(~微米，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(BEC)，在这种凝聚中，气体中的每个原子都有相同的量子波函数。然而，超冷原子的科学潜力不仅限于基本的量子力学；它们的运动状态可以控制到前所未有的程度，以至于它们也开始在精确测量自然力和常数方面发挥重要作用。我的研究涉及到这两个方面背后的理论。首先，我建议继续我对原子通过偶极-偶极相互作用的BEC的研究。这与极性分子特别相关。这个想法是为了研究这些长程和各向异性的相互作用是如何影响超流等性质的。其次，我想启动加拿大对捕获在光学微腔中的超冷原子的研究。腔量子电动力学与原子的量子运动的结合结合了我们最好控制的两个物理系统，因此有望成为量子信息处理以及近距离精确测力的天然舞台。第三，我计划研究超冷原子的宏观叠加如何受到退相干的影响，例如在约瑟夫森结中。这与上面的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.