On the interaction between quantum vortices and phonon radiation in Bose-Einstein condensates

在固定温度的盒子里，流体表现出两种运动现象：以密度压力波的形式出现的声音，以及流体速度围绕它们运动的涡流。例如，在一个挤满了人的咖啡馆里，声音是由聊天的人产生和听到的，而热咖啡杯会产生涡流线这样的结构，由于水蒸气的存在，这种结构变得可见。这种漩涡的其他例子包括浴缸里的水、烟圈、海豚在水族馆里玩耍时产生的空气圈，以及龙卷风。声音和漩涡是截然不同的。前者向各个方向扩散，这就是为什么它在物理学中也被称为辐射；涡旋在运动时倾向于保持其局部形状，因此它们被称为连贯结构。这两种运动现象相互作用：例如，强烈的声音可以破坏烟圈，由于声音共振而振荡的物体可以产生漩涡。这个研究项目不是在空气或水等普通流体中研究声涡相互作用，而是在被称为玻色-爱因斯坦凝聚体的超流体中研究。超流体在以无粘度为特征的流体中形成了一个特殊的类别。粘度是任何流体的一种特性，它量化了两个相互靠近的薄流体层之间摩擦力的大小。现在可以在实验室中制造的超流体的例子是低于2开尔文的液态氦和被称为玻色-爱因斯坦凝聚体的稀释碱性气体，它们被冷却到比绝对零度高几百纳米开尔文（十亿分之一）。除了零粘度之外，超流体还有另外一个特点，那就是只允许存在特定类型的涡流，即量子涡流。这些可以被认为是非常细而长的细丝，就像意大利面条一样，它们进入超流体并影响流体运动。像普通流体一样，超流体也有密度波动（声音），称为声子。实验和数值模拟表明，量子涡旋和声子相互作用，但目前尚不清楚如何，在哪个长度尺度上这种相互作用更强，以及这个过程的时间尺度是什么。我们将使用一个叫做Gross-Pitaevskii方程的模型，它描述了玻色-爱因斯坦凝聚体的密度和速度是如何随时间演化的。这是一个没有一般解析解的复杂方程。由于这个原因，我们要么在称为集群的大型计算机上，要么在安装在图形卡上的图形处理单元上，以数字方式解决它。通过自己设计的数值模拟，我们将模拟三种不同的理想情况。第一个将研究一个像意大利面一样的直涡旋，最初像吉他弦一样摇动，是如何产生声音的。第二种情况将处理由两条涡旋线相互靠近并重新连接所产生的声音脉冲，即交换一半的涡旋线。最后一章将重点讨论上述涡旋脉冲如何衰减为声辐射。通过测量这些理想情况下的声音-涡旋相互作用，并应用一些分析和统计技术，我们将对这一过程有新的了解。最后，我们将与玻色-爱因斯坦实验学家一起努力，将我们的理论发现与当前的实验进行比较，并设计新的实验装置。我们的研究将大大影响现有的超流体动力学知识。这将对未来的低温物理技术产生中长期的影响。例如，利用超流体可以建造非常灵敏的探测器来探测重力或电磁场，而超流体的发现可能有助于设计在室温下工作的超导体。其他处理流体湍流的学科，如生物学、医学、航空学和工程学，也可能受益于我们的结果和开发的技术。

A fluid kept in a box at fixed temperature exhibits two types of moving phenomena: sound, in the form of density pressure waves, and vortices, structures where the fluid velocity moves about them. Consider for instance the air in a café full of people: sound is produced and heard by individuals chatting, while hot coffee cups can generate structures like vortex lines that become visible due to the presence of water vapour. Other examples of such vortices are when water drains from a bath, smoke rings, air rings created by dolphins playing in aquariums, and tornadoes. Sound and vortices are drastically different. The former spreads in all directions and that is why it is also called radiation in physics; vortices tend to retain their shapes localised while moving, so they are referred to as coherent structures. Those two moving phenomena interact with each other: for instance, strong sound can destroy smoke rings and an object oscillating due to sound resonance can generate vortices.This research project studies sound-vortex interaction not in ordinary fluids, like air or water, but in superfluids called Bose-Einstein condensates. Superfluids form a particular category among fluids characterised by the absence of viscosity. The viscosity is a property of any fluid and quantifies how much friction there is between two thin fluid layers moving close to each other. Examples of superfluids that can nowadays be created in laboratories are liquid Helium below 2 degrees Kelvin and dilute alkaline gases cooled down to a few hundreds of nano-Kelvin (one over a billion) above the absolute zero called Bose-Einstein condensates. Apart from zero viscosity, superfluids have the other peculiarity that only certain types of vortices, called quantum vortices, are allowed. These can be thought of as very thin and long filaments, something like spaghetti, which move into the superfluid and influence the fluid motion. Like ordinary fluids, superfluids also admit density fluctuations (sound), called phonons. Experiments and numerical simulations have shown that quantum vortices and phonons interact, but it is not clear yet how, at which length scales this interaction is stronger, and what are the time scales of this process.We will use a model called Gross-Pitaevskii equation, which describes how the density and the velocity of a Bose-Einstein condensate evolve in time. This is a complicated equation which has no general analytical solutions. For this reason we solve it numerically either on large computers called clusters or graphic processing units mounted on graphic cards. By using numerical simulations designed by ourselves, we will simulate three different idealised cases. The first will study how a straight spaghetti-like vortex, initially shaken like the string of a guitar, will produce sound. The second case will deal with sound pulses created by two vortex lines approaching each other and reconnecting, that is swapping half of their lines. The last one will focus on how the above-mentioned vortex pulses decay into sound radiation. By measuring the sound-vortex interaction in those idealised cases and by applying some analytical and statistical techniques we will shed new light on this process. Finally, we will spend our efforts with Bose-Einstein experimentalists to compare our theoretical findings with the current experiments and design new experimental setups.Our research will affect considerably the present knowledge of superfluid dynamics. This can have medium and long term impacts on future low temperature physics technologies. For instance, extremely sensitive probes to detect gravity or electro-magnetic fields can be built using superfluids, and superfluid discoveries might help designing superconductors that work at room temperature. Other disciplines dealing with turbulence in fluids like biology, medicine, aeronautics and engineering may also benefit from our results and developed techniques.