Self-Bound Droplets in Two-Component Dilute Bose Gases

在一个极端温度有限的世界里，很难想象高温和低温的系统。然而，在世界各地，有实验能够将物质冷却到几乎绝对零度。在这些温度下，物质开始以许多有趣的方式表现出来，其中一个例子是玻色-爱因斯坦凝聚（BEC）。所有粒子都具有与温度内在相关的波长。在室温下，这个波长可以忽略不计，因此在气体中，粒子碰撞可以模拟为“台球”相互作用。进入超冷状态导致这样的波长变得与粒子之间的距离相当。这可以被认为是粒子经历了一场“身份危机”，导致它们的行为非常一致，就好像步调一致一样。这种物质状态是一种BEC，它是量子物理学的一种表现，具有许多有趣的性质。其中一个性质是超流性，其中流体没有粘度，因此理论上可以永远流动。超冷气体领域是一个不断发展的领域，有许多研究途径，从探索新的物质状态到模拟宇宙学机制。本项目将重点关注一种称为量子液滴的新物质状态。这种状态的第一个预测是在2015年由D.S.Petrov的工作提出的，他认为液滴可以在两种玻色子（即原子）的混合气体中产生。这背后的机制是迫使气体之间的相互作用是有吸引力的。然而，通过使气体之间的相互作用成为主导吸引力，这将导致崩溃，因为没有效果来抵消吸引力。彼得罗夫工作的独创性来自于对量子涨落的研究。量子涨落存在于自然界中，但它们的影响往往太弱而无法被检测到。在彼得罗夫探索的系统中，量子涨落呈现出排斥相互作用。有人认为，通过包括量子涨落，排斥效应可以对抗气体混合物的坍缩。这导致了一个稳定的平衡状态。稳定状态将在中心具有大的恒定密度，在边缘具有低密度尾部，类似于诸如水滴的经典液滴。量子液滴是一种存在于低密度气体中的特殊物体，但它们可以表现为不可压缩的流体。已经有一些实验和理论工作研究量子液滴，但该领域仍然很年轻，还有很多东西需要探索，例如激发和动力学。混合物中的第一个量子液滴是在钾的混合物中产生的，这是成功的，但具有有限寿命的缺点，因此观察到很少的时间依赖性。该项目将与达勒姆大学的实验工作相结合，试图在铯和镱的混合物中产生量子液滴。这种混合物的一个主要好处是延长寿命，因此可以模拟实验结果。在这个项目中采用的技术将主要是数值，并将包括解决Gross-Pitaevskii方程-在建模BEC的支柱-扩展到包括量子涨落的影响。该项目的第一个目标将是使用模拟来帮助实验人员创建液滴。这将包括隔离导致液滴形成的参数值。从那里，该项目预计将与实验结果一起工作，以与已知的理论进行比较。由于量子液滴领域还很年轻，有许多性质需要探索，这项工作将从理论上探索其中的一些性质。此外，量子液滴呈现出一个由量子波动稳定的系统，这种现象如此普遍，但往往很难检测到，使得这个项目既相关

Existing in a world in which temperature extremes are limited, it is difficult to envisage systems of high and low temperatures. However, across the world there are experiments capable of cooling matter down to almost absolute zero. Matter begins to behave in many intriguing ways at these temperatures, one example being the Bose-Einstein Condensate (BEC).All particles possess a wavelength which is intrinsically linked to temperature. At room temperature, this wavelength is negligible and thus within a gas, the particle collisions can be modelled as 'billiard-ball' interactions. Moving into the ultracold regime leads to such wavelengths becoming comparable to the distance between particles. This can be thought of as particles undergoing an 'identity crisis' causing them to act extremely coherently as if in lockstep. This state of matter is a BEC and it is a manifestation of quantum physics with many interesting properties. One such property is superfluidity, in which a fluid possesses no viscosity and hence can theoretically flow forever. The field of ultracold gases is an ever-growing field with many avenues of research from exploring new states of matter through to modelling cosmological mechanisms.This project will focus on a new state of matter called the quantum droplet. The first prediction of this state came in 2015 with the work of D.S.Petrov, who argued that droplets could be created in two mixed gases of bosons (i.e. atoms). The mechanism behind this would be to force the interaction between the gases to be attractive. However, by causing the interactions between the gases to become dominantly attractive, this would lead to a collapse as there would be no effects to counteract the attraction. The ingenuity of Petrov's work arises from the inclusion of quantum fluctuations.Quantum fluctuations are present throughout nature, but their effects are often too weak to be detected. In the system explored by Petrov, quantum fluctuations present a repulsive interaction. It was argued that by including quantum fluctuations, the repulsive effects could counter the collapse of the gas mixture. This leads to a stabilised state in equilibrium. The stabilised state would have a large constant density in the centre, with low density tails at the edges, akin to a classical droplet such as a water droplet. Quantum droplets are peculiar objects as they exist in low density gases, yet they can behave as an incompressible fluid.There has been some experimental and theoretical work looking into quantum droplets, but the field is still young and there is much to explore such as excitations and dynamics. The first quantum droplets in mixtures were created in mixtures of Potassium which were successful but had the drawback of limited lifetimes, thus few time dependent properties were observed. This project will work in conjunction with experimental work at Durham University, attempting to create quantum droplets in mixtures of Caesium and Ytterbium. One major benefit of this mixture will be extended lifetimes and thus it will be possible to model the experimental results. The techniques employed in this project will be largely numerical and will consist of solving the Gross-Pitaevskii equation - a mainstay in modelling BECs - extended to include the effects of quantum fluctuations. The first goal of this project will be using simulations to aid the direction of the experimentalists to create the droplets. This will include isolating parameter values leading to droplet formation. From there, the project is predicted to work alongside the results of the experiments to compare with known theory.With the field of quantum droplets being young, there are many properties to be explored and this work will theoretically explore some of these properties. Furthermore, quantum droplets present a system stabilised by quantum fluctuations, a phenomenon so ubiquitous yet often so difficult to detect, making this project both relevant