Quantum vortex reconnections in trapped Bose-Einstein condensates

Lead Research Organisation: Newcastle University
Department Name: Sch of Maths, Statistics and Physics

Abstract

Long, almost one dimensional structures (filaments) are ubiquitous in the universe, consisting of chains of atoms (macromolecules) or regions of concentrated field lines (vortex lines in fluids, magnetic flux tubes in electrically conducting plasmas). Filaments occur at the microscopic scale of proteins and DNA, through the intermediate scales of tornadoes, dust devils and the trails behind planes and boats, up to the huge scales of the star-forming clouds in outer space. When two filaments come close to each other, they can split and recombine, having exchanged strands. Such reconnection events not only change the geometry of the filaments themselves but they also change the underlying topology (the property for which two rings which are linked to each other are different from two rings which are separated). A better understanding of reconnections is therefore crucial to many problems in the natural sciences and in engineering (for example, how the energy of a fluid is spread by reconnections).

With reconnections arising across many distinct physical contexts and over many scales, it is natural to ask whether any behaviours are universal, such that a shared framework of understanding can be sought. For example, the loss of energy during a reconnection in a fluid is directly analogous to that which occurs during a reconnection in a plasma despite different physical origins of the loss of energy (viscosity in the fluid and electrical resistivity in the plasma). Other examples debated in the scientific community are whether a measure of the coiling, twisting and linking of the filaments, termed the helicity, is conserved during reconnections, and whether complicated tangled knots of filaments may decay or disentangle in ways which depend on the topology rather than the physical nature of the system. Our understanding of reconnections is still in its infancy and would benefit from detailed quantitative measurements of reconnections, and from comparison of reconnections across different scientific disciplines.

In this context, trapped atomic Bose-Einstein condensates (BECs) provide an ideal testing ground to study reconnections. BECs are gases of atoms, cooled to within a few billionths of a degree above absolute zero. Here the blurry laws of quantum mechanics rule and transform the gas into a quantum fluid. This type of fluid is remarkable in its simplicity: while everyday fluids possess viscosity and can form tornadoes of any size or shape, quantum fluids have no viscosity and their tornadoes have a fixed size and shape. This makes them easier to conceptualise, model and understand. What is more, experimentalists are able to control and manipulate the fluid, and its vortices, to a high level of precision.

Our recent preliminary work in collaboration with an experimental group in Trento, Italy, not only demonstrated reconnections in BECs for the first time, but also revealed new and unexpected forms of reconnections. Motivated by this, we will perform detailed computer simulations of vortex reconnections in the ideal context provided by BECs, determining exactly how reconnections occur and what their consequences are. Then, by comparing to the behaviour in different settings (ordinary fluids, plasmas and macromolecules) we will probe whether universal behaviours do exist (for example, if the distance between reconnecting strands scales with time with a universal power law, or if energy losses relate to the amount of knottedness), probing the relation between energy and topology in different systems.

To disseminate our results across scientific communities, we will organise an interdisciplinary workshop on reconnections with the top experts from atomic physics, astrophysics, fluid dynamics, knot theory, with a view to building a common picture. Close collaboration with the ongoing experiment at Trento will guide our theoretical studies and provide immediate experimental tests of our findings.

Planned Impact

Our project will generate impact in each of the EPSRC-defined areas: Knowledge, People, Economy and Society. The impact on Knowledge will be achieved through both the specific knowledge which will be acquired in the field of atomic physics and the transfer of knowledge to other areas of science and engineering. In parallel, the impact upon People and the Economy will occur via the training of highly skilled individuals, while Society will benefit from our project via the organisation of outreach activities. Our plans to promote these impact issues are described in detail below.

Specific knowledge:
Our proposal is concerned with fundamental aspects of reconnections of quantized vortices in quantum gases. The dynamics of vortices is of central importance for the understanding of transport in quantum gases, which in turn is vital to the design of future atomtronic devices for quantum technologies in precision measurements and quantum information. Our proposal will contribute in making progress in this area, through both our theoretical findings and our impact upon experimental studies via our collaborators at Trento. The impact on atomic physics knowledge will hence be direct, and contribute to the EPSRC Physics Grand Challenge of Quantum Physics for New Quantum Technologies.

Transfer of knowledge:
Our findings will impact beyond the field of atomic physics. Reconnections of coherent filamentary structures are ubiquitous in nature, and take place in systems as disparate as fluids, plasmas, molecules, DNA and optical beams. A major objective of our proposal is to discuss the common, universal behaviours of reconnection events across these physical systems. As a consequence, the findings of our project will contribute to two further EPSRC Physics Grand Challenges: Emergence and Physics far from Equilibrium, and Understanding the Physics of Life.
The dissemination of knowledge across these disparate communities will be promoted by visiting the leading researchers in topological fluid dynamics and organising an Interdisciplinary Workshop on Reconnections in 2020, inviting key researchers across topological fluid dynamics, magnetohydrodynamics, atomic BECs, macromolecules and knot theory, gathering communities which do not normally meet.

Training:
The project will train young researchers with generic quantitative skills and specialist expertise. Galantucci will be the lead researcher, while a School-funded PhD student will work on a related topic. We plan to involve undergraduate students in aspects of the project. The young researchers will gain valuable transferable skills (e.g. to communicate with experimentalists, capture the essential physics and model it) and technical expertise in quantum gases and atomic physics (relevant for a further career in the growing field of quantum technologies).

Outreach:
We plan outreach activities on two levels. Firstly, we will illustrate the physics and importance of reconnecting filamentary structures in systems ranging from fluids to molecules to the general public via open lectures at Newcastle and in the region, including movies and images from our own work and those of our cross-discipline collaborators. Secondly, we will target the interest and curiosity of teenagers with the aim of contributing to enhancing the quality and quantity of students studying STEM subjects in tertiary education. This would help to promote a workforce (particulary teachers) with this in-demand skill-set. This second outreach activity will be implemented in an interactive fashion, through the elaboration of a visual toolkit and ad-hoc videos demonstrating reconnections and vortices, to be presented at stands at local science fairs and university open days. This visual toolkit will be built using sailing/mountain equipment ropes joined together by magnetic connectors. We plan to take part in approximately 10 such events in the north of England, aided by postgraduate demonstrators.

Publications

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Baggaley A (2018) Decay of homogeneous two-dimensional quantum turbulence in Physical Review A

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Cooper Rg (2019) Knot spectrum of turbulence in scientific reports

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Galantucci L (2021) Classical and quantum vortex leapfrogging in two-dimensional channels in Journal of fluid mechanics

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Galantucci L (2020) A new self-consistent approach of quantum turbulence in superfluid helium in The European Physical Journal Plus

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Galantucci L (2019) Crossover from interaction to driven regimes in quantum vortex reconnections. in Proceedings of the National Academy of Sciences of the United States of America

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Haskell Brynmor (2020) Turbulent, pinned superfluids in neutron stars and pulsar glitch recoveries in Mon.Not.Roy.Astron.Soc.

 
Description We have recently discovered universal properties of quantum vortex reconnections in terms of two limiting scaling laws for the minimum distance between the two reconnecting vortex strands. The two laws correspond to a regime of mutual vortex interaction and a regime driven by curvature/density gradients effects. In the first regime the minimum sepration, delta, is proportional to the the square root of the time to/from the reconnection, in the second regime it is linear with time. We can also successfully predict the crossover between the two regimes. This result, published in PNAS,t is fundamental, as it applies to the motion of vortices of quantized vorticity in both superfluid helium and atomic Bose-Einstein condensates.

In a second computational study, we have revealed that quantum turbulence is knotted, that is to say it consists of vortex loops which are knotted and linked. This is the first time that the topology of turbulence has been quantified. The mathematical tool which we used in the Alexander polynomial, which has revealed scaling laws for the probability of finding vortex knots of a given complexity. The creation of knots and links is a consequence of vortex reconnections, the physical significance is that to do and to undo such topology involves an energy cost. Undoing the topology is also linked to dissipation and irreversibility, as sound energy is radiated away. These findings have been published in Scientific Reports.

A third significant study of vortex dynamics has been published in Physical Review Letters and deals with dissipation in a Josephson junction between two trapped atomic Bose-Einstein condensates. The study shows in detail how the creation of a vortex in the weak link between the two condensates dissipates the energy of the Josephson oscillations.
Exploitation Route The result which we have found has many implications for experiments, as the next natural task is to explore the second scaling law (delta proportional to time) and the crossover regime in superfluid helium and atomic BECs. Our result also means that the scaling laws for classical reconnenctions in fluids and plasmas which are not constrained by the quantization need exploring in quantitative detail.

The finding on the topology of turbulence leads to the natural question as to whether ordinary turbulence obeys similar scaling laws for the topology.

Both results have implications for the understanding of ordinary turbulence.
Sectors Other

URL https://www.pnas.org/content/116/25/12204
 
Description Collaboration with group of prof Bagnato at University Sao Paulos, Brazil 
Organisation Universidade de São Paulo
Country Brazil 
Sector Academic/University 
PI Contribution provided analysis of data
Collaborator Contribution provided data
Impact Publication: A. Daniel García-Orozco, L. Madeira, L. Galantucci, C.F. Barenghi, V.S. Bagnato, Intra-scales energy transfer during the evolution of turbulence in a trapped Bose-Einstein condensate, Europhys. Lett. 130, 46001 (2020)
Start Year 2019