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

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.

The proposed research fits into the EPSRC portfolio of Quantum Fluids and Solids, a research area that EPSRC has decided to maintain due to its UK world leading research quality. It is sensible to regard our project as pure research one and for this reason short term impacts are mainly of academic nature. We will make use of standard methods to disseminate the project results. We aim to publish in high-impact international journals at least four papers, one for each research question (Q1)-(Q4) addressed, see the Proposed Research document for details. Possible journals are Proceedings of the National Academy of Sciences, Physical Review Letters, Physical Review B, Physical Review A, Physical Review Fluids, Journal of Physics A, and Journal of Low Temperature Physics; whenever possible we will make the article open access. Project costs include fundings to participate to conferences and workshops all along the 2-year project time. Main international events like LT28, ETC16, FINESS 2017, QFS2018 will be attended by the PI or the PDRA. We will also invite researchers working in Bose-Einstein condensate and superfluid Helium communities to give research seminars at UEA and, possibly, spend some days with the UEA Quantum Fluids group.

Aside from academic impact, we can definitely foresee knowledge and economy advances in the medium and long term. Due to the unprecedented level of experimental control, Bose-Einstein condensates are nowadays used to carry fundamental physics studies in quantum field and many-body theories, wave turbulence, and fluid mechanics. The proposed research will advance our understanding on how to control those systems, making BECs more robust when applied to future technologies. This may also lead experimentalists to develop novel experimental setups involving new procedures, protocols and technologies that might be applied elsewhere in the future. Our findings will also contribute to a better understanding of superfluid turbulence, and eventually to turbulence in classical fluids that is essential in domains like engineering, aerodynamics, biology, and medicine. Finally, some results could be extended to other physics fields and related applications, including nonlinear optics, and superconductors.

The proposed research will also contribute also to career and skills development. It will give a major boost to the career of the PDRA, who will learn cutting edge new science and gain international experience and exposure. The PI will include the project results in the material of the course on Introduction to Superfluids and Turbulence he teaches for MAGIC, a consortium involving 20 UK universities that is designed to deliver postgraduate-level courses. PhD students of the MAGIC group, but also the UK students of non-member institutions, will have access to the lectures and consequently have a chance to improve their skills.

We also aim to impact on the society and general public by improving the general perception towards the importance of pure science research. We will participate to science festivals and disseminate our research results online using podcast-like instruments. The former activity will involve designing a science stand to explain notions of superfluidity, vortices, sound radiation, coherent structures, and vortex reconnections using everyday concepts (see Pathways to Impact for details). The latter activity encompasses to record a short video every time that we will submit a new research paper to a journal; our aim is to explain there the main research questions we were able to answer and the results we obtained in a way that is comprehensible for non-academics. Videos will then be made available on the most common websites like YouTube and Facebook, and disseminated as podcast-like format throughout the dedicated research project webpage.