Turbulence in quantum gases: setting the framework

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At extremely low temperatures, matter behaves differently to what we are used to: its constituent particles are not independent but behave collectively as one entity, known as the Bose-Einstein Condensate (BEC). The condensate appears in solids, liquids, or gases, leading to some of the most fundamental physical phenomena. Historically the condensate has been studied extensively in liquid helium. At very low temperatures helium exhibits strange properties, which we can understand by describing helium as a combination of a usual liquid (the 'normal fluid') and a new 'quantum' liquid, called the 'superfluid', which can flow without the friction which a normal fluid would experience.Everybody is familiar with the jittery motion of an aeroplane due to the irregular motion of the turbulent air through which it flies. Turbulence is one of nature's most ubiquitous phenomenon: turbulent eddies and swirls occur in flows ranging from the aortic blood stream, to water and gas pipes, to winds in the atmosphere. Turbulence in superfluid helium has a new feature: it consists of discrete vortices, all with the same circulation and core structures, unlike the eddies of arbitrary shapes and strengths of ordinary fluids. This distinction arises because the superfluid consists of a condensate of many atoms, and is mathematically described by a single wavefunction: any rotational motion of the superfluid is constrained to vortices which are quantised, i.e. the flow around them is restricted by the laws of quantum mechanics.Recent experiments with superfluid helium have highlighted many remarkable similarities (e.g. energy spectra) and differences (e.g. velocity statistics) between ordinary turbulence and superfluid turbulence (also called quantum turbulence). Experimentalists have reported the existence of different regimes of quantum turbulence (e.g. random vs. structured), characterised by different temporal evolution (decay laws); theoreticians have proposed new mechanisms (e.g. the Kelvin wave cascade) for energy transfer and decay. The natural big question is whether ordinary turbulence is, in some sense, the classical limit of quantum turbulence: can the complexity of eddies and swirls in a turbulent stream be better understood in terms of the dynamics of a large number of discrete vortex filaments, each carrying one unit of circulation ?Parallel to this development, the last 15 years have seen the emergence of new physical systems for studying quantum effects on a macroscopic scale. Instead of working with liquid helium, whose constituent particles interact strongly, experimentalists have now created weakly-interacting trapped condensates of atoms in gases, known as quantum gases. Such systems provide an ideal context for the study of quantum turbulence, because they allow unprecedented experimental control of a vast range of parameters, such as the geometry and the effective dimensionality of the system, and the strength and the type of interactions (which can be tuned, rather than be given by nature as for helium). The first experimental evidence of turbulence in BEC ultracold gases was announced only last year. This proposal timely combines the above concepts in order to investigate turbulence in quantum gases. We think that, by promoting the study of more controllable atomic gases, the different forms of turbulence arising in classical and quantum systems can be better understood, particularly since quantum gases can be theoretically described very precisely. We plan to establish the framework for studying turbulence in atomic condensates, and address crucial questions in this new emerging field such as: how can we produce turbulence in a quantum gas in a controlled way ? what are the main features classifying the produced turbulent structure ? which experimental schemes are likely to produce the optimal results?