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

在固定温度下保持在盒子中的流体表现出两种类型的运动现象：声音，以密度压力波的形式，以及漩涡，流体速度围绕它们移动的结构。例如，考虑一个充满人的咖啡馆中的空气：声音是由个人聊天产生和听到的，而热咖啡杯可以产生像涡线这样的结构，由于水蒸气的存在而变得可见。其他的例子还有浴缸里的水、烟圈、海豚在水族馆里玩耍时产生的空气圈和龙卷风。声音和漩涡是截然不同的。前者向四面八方传播，这就是为什么它在物理学中也被称为辐射;涡旋在移动时往往会保持其局部形状，因此它们被称为相干结构。这两种运动现象相互作用：例如，强烈的声音可以破坏烟雾环，由于声音共振而振动的物体可以产生漩涡。本研究项目研究的不是普通流体（如空气或水）中的声音-漩涡相互作用，而是称为玻色-爱因斯坦凝聚体的超流体。超流体是流体中的一个特殊类别，其特征是没有粘度。粘度是任何流体的一种属性，它量化了两个相互靠近的薄流体层之间的摩擦力。现在可以在实验室中创造的超流体的例子是低于2开尔文的液态氦和冷却到绝对零度以上几百纳开尔文（十亿分之一）的稀碱性气体，称为玻色-爱因斯坦凝聚。除了零粘度之外，超流体还有另一个特性，即只允许某些类型的涡旋，称为量子涡旋。这些可以被认为是非常细而长的细丝，就像意大利面一样，它们进入超流体并影响流体运动。像普通流体一样，超流体也允许密度波动（声音），称为声子。实验和数值模拟表明，量子涡旋和声子之间存在相互作用，但目前还不清楚这种相互作用是如何发生的，在什么样的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。我们将使用一个称为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如何随时间演化。这是一个复杂的方程，没有一般的解析解。出于这个原因，我们在称为集群的大型计算机或安装在图形卡上的图形处理单元上用数字解决它。通过使用我们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条一样的直漩涡，最初像吉他的琴弦一样摇动，如何产生声音。第二种情况将处理由两条涡旋线彼此接近并重新连接所产生的声音脉冲，即交换它们的一半线。最后一个将集中在如何上述涡旋脉冲衰减成声辐射。通过测量这些理想情况下的声音涡流相互作用，并通过应用一些分析和统计技术，我们将揭示这个过程的新的光。最后，我们将与玻色-爱因斯坦实验学家一起努力，将我们的理论结果与现有的实验进行比较，并设计新的实验装置。我们的研究将对现有的超流体动力学知识产生相当大的影响。这可能对未来的低温物理技术产生中长期影响。例如，可以使用超流体来建造用于检测重力或电磁场的极其敏感的探针，并且超流体的发现可能有助于设计在室温下工作的超导体。处理流体中湍流的其他学科，如生物学，医学，航空学和工程学，也可能从我们的研究结果和开发的技术中受益。

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.