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

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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.