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，量子效应就会出现，其行为也会发生巨大变化。一种由相同玻色子（具有整数自旋的粒子）组成的气体经历了玻色-爱因斯坦凝聚，这是一种向物质新状态的相变，这种状态在1925年被预测到，但直到1995年才被实验观察到。这种由单一宏观量子力学波函数描述的完全相干的物质波与经典气体（如空气）之间的区别类似于激光和灯泡发出的光之间的区别。玻色-爱因斯坦凝聚物（BEC）也表现出超流动性，即在没有任何摩擦的情况下流动的能力。相比之下，相同的费米子（自旋为半整数的粒子）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。这种配对和冷凝是超导现象的核心。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变得非常有用。例如，原子物理学的精密工具使我们能够调整原子之间相互作用的强度，并将它们捕获在通过干涉激光束形成的不同几何形状的人造晶体中。因此，我们可以用比传统凝聚态系统更灵活的量子模拟复杂的多体哈密顿量。量子模拟的想法最早是由费曼提出的，他指出，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等。最终，我们希望这些用于测量的量子系统将允许我们回答凝聚态物理学中的许多悬而未决的问题，一个突出的例子是未解决的高温超导之谜（HTSC）。这也将允许更系统地设计用于实际应用的新材料。在这项工作中，我们将通过实验解决与设计和探测日益复杂的玻色和费米多体系统有关的几个重要的突出问题。我们将集中讨论低维气体，由于量子和热波动在降维中的重要性日益增加，低维气体非常吸引人。我们将研究的分层二维系统也特别有趣，因为它们的结构与HTSC材料相似。我们还将致力于开发干涉测量方法，该方法允许直接访问多体波函数的相位，从而为粒子之间的复杂相关性提供强大的探测。最后，我们将探索在原子气体中引入远程相互作用的新方法，这是原子系统与电子气体之间通过远程库仑势相互作用的完全类比所缺少的基本成分，并研究具有快速变化的哈密顿量的系统中的非平衡多体物理。除了多体凝聚态物理和材料科学的可能应用之外，我们还将探索使用低维原子气体进行量子模拟的可能性，以解决从统计到高能物理等其他领域的突出问题。这将使超冷气体成为真正意义上的通用量子模拟器，正如费曼所设想的那样。我们在动态变化的哈密顿量上的工作也可能与量子计算的新方法相关。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子小组中进行。

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.