Quantum Simulation with Low-Dimensional Ultracold Atomic Gases

当原子气体被冷却到极低的温度，低于1微开尔文时，量子效应出现，其行为发生了巨大的变化。一种由全同玻色子（具有整数自旋的粒子）组成的气体经历玻色-爱因斯坦凝聚，这是一种相变，在1925年被预测为一种新的物质状态，但直到1995年才被实验观察到。这种完全相干的物质波（由单个宏观量子力学波函数描述）和经典气体（如空气）之间的差异类似于激光和灯泡发出的光之间的差异。玻色-爱因斯坦凝聚（BEC）也表现出超流性，即没有任何摩擦的流动能力。相反，相同的费米子（具有半整数自旋的粒子）必须占据不同的量子力学状态，但也可以配对成复合玻色子并经历更复杂的凝聚形式。这种配对和凝聚是超导现象的核心。由于我们可以相对容易地操纵它们，超冷原子气体对于研究这些和许多其他基本的集体量子现象非常有用。例如，原子物理学的精确工具使我们能够调整原子之间相互作用的强度，并将它们捕获在不同几何形状的人造晶体中，这些晶体由干涉激光束形成。因此，我们可以量子模拟复杂的多体汉密尔顿，比传统凝聚态系统具有更大的灵活性。这种量子模拟的想法首先由费曼提出，他指出，一个复杂量子系统的行为只能由另一个量子系统有效地模拟，而不是使用经典计算机。最终，我们希望这些用于测量量子系统的方法将使我们能够回答凝聚态物理学中的许多悬而未决的问题，一个突出的例子是高温超导性（HTSC）的未解之谜。这也将允许为实际应用更系统地设计新材料。在这项工作中，我们将通过实验解决几个重要的悬而未决的问题，设计和探测越来越复杂的玻色和费米多体系统。我们将集中在低维气体，这是迷人的，因为在减少维数的量子和热涨落的重要性增加。我们将研究的层状二维系统也特别有趣，因为它们与HTSC材料的结构相似。我们还将致力于发展干涉测量方法，这种方法可以直接获得多体波函数的相位，从而为粒子之间的复杂相关性提供强有力的探测。最后，我们将探索在原子气体中引入长程相互作用的新方法，这是原子系统和通过长程库仑势相互作用的电子气体之间完全类比的一个重要缺失成分，并研究具有快速变化的哈密顿量的系统中的平衡多体物理。超越多体凝聚态物理学和材料科学的可能应用的主题，我们还将探索使用低维原子气体量子模拟其他领域的突出问题的可能性，从统计到高能物理。这将使超冷气体成为费曼所设想的真正通用的量子模拟器。我们关于动态变化的哈密顿量的工作也可能与量子计算的新方法有关。这项工作将在剑桥大学物理系原子、介观和光学物理（AMOP）小组的量子气体和集体现象小组中进行。

When a gas of atoms is cooled to extremely low temperatures, below one microkelvin, quantum effects emerge and its behaviour changes dramatically. A gas of identical bosons (particles with integer spin) undergoes Bose-Einstein condensation, a phase transition to a new state of matter which was predicted in 1925 but experimentally observed only in 1995. The difference between this fully coherent matter-wave, described by a single macroscopic quantum mechanical wave function, and a classical gas (such as air) is analogous to the difference between the light from a laser and that from a light bulb. Bose-Einstein condensate (BEC) also exhibits superfluidity, the ability to flow without any friction. In contrast, identical fermions (particles with half-integer spin) have to occupy different quantum mechanical states, but can also pair up into composite bosons and undergo a more complicated form of condensation. Such pairing and condensation are at the heart of the phenomenon of superconductivity. Thanks to the relative ease with which we can manipulate them, ultra-cold atomic gases have become extremely useful for studies of these and many other fundamental collective quantum phenomena. For example, precise tools of atomic physics allow us to tune the strength of the interactions between the atoms, and to trap them in artificial crystals of different geometries, which are formed by interfering laser beams. We can thus quantum simulate complex many-body Hamiltonians with more flexibility than is available in conventional condensed matter systems. This idea of quantum simulation was first put forward by Feynman, who pointed out that a behaviour of a complex quantum system can be efficiently simulated only by another quantum system, rather than for example using a classical computer. Ultimately we hope that these made to measure quantum systems will allow us to answer many open questions in condensed matter physics, a prominent example being the unsolved puzzle of high-temperature superconductivity (HTSC). This would also allow for a more systematic design of novel materials for practical applications. In this work we will experimentally address several important outstanding questions related to designing and probing of increasingly more intricate Bose and Fermi many-body systems. We will concentrate on low-dimensional gases, which are fascinating because of the increased importance of quantum and thermal fluctuation in reduced dimensionality. Layered two-dimensional systems which we will study are also particularly interesting because of their structural similarity to HTSC materials. We will also work on the development of interferometric methods which allow direct access to the phase of the many-body wave function, thus offering a powerful probe of the complex correlations among the particles. Finally, we will explore new ways to introduce long-range interactions in atomic gases, an essential missing ingredient for a complete analogy between atomic systems and the electron gases which interact via the long-range Coulomb potential, and investigate the out-of equilibrium many-body physics in systems with rapidly changing Hamiltonians. Going beyond the topics of many-body condensed matter physics and possible applications to material science, we will also explore the possibility to use low-dimensional atomic gases for quantum simulation of outstanding problems in other fields, ranging from statistical to high energy physics. This would establish ultra-cold gases as truly general quantum simulators, in the sense envisioned by Feynman. Our work on dynamically changing Hamiltonians may also be relevant for new approaches to quantum computation. This work will be carried out in the Quantum Gases & Collective Phenomena subgroup within the Atomic, Mesoscopic and Optical Physics (AMOP) group in the University of Cambridge Department Of Physics.