Quantum Fluids Group

Department of Applied Mathematics and Theoretical Physics (DAMTP)

University of Cambridge

The Quantum Fluids Group is a research group in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge.

Quantum fluids have been studied experimentally for many years and have by now become a major focus of cryogenic physics. Applications of the subject are wide-ranging, from engineering (where, for instance, helium is used as a coolant for superconducting magnets and infrared detectors) to astrophysics (where it is invoked to explain glitches in the rotation of neutron stars). Superfluid turbulence may also provide insights into classical fluid turbulence, especially at high Reynolds numbers, where the vorticity has an intermittent, fractal character.

Even though the superfluid is inviscid, there are significant differences between classical turbulence at large Reynolds number and superfluid turbulence. The most significant is that vorticity is continuously distributed in a classical (Navier-Stokes) fluid, but is quantised in a superfluid in units of h/M, where M is the mass of the boson. Turbulence in the superfluid therefore resembles a tangle of vortex filaments, whose dynamics differs from that of the chaotic but continuous vorticity of classical turbulence.

We are interested in modelling, developing analytical approaches (asymptotic and perturbation methods) and applying numerical simulations in order to elucidate motions in Bose-Einstein condensates and superfluid helium. Some of our work is aimed at explaining and quantifying the experimental results that have been emerging in unprecedented amounts since the discovery of atomic Bose condensates in 1995.

Helium-3-centric Universe according to Grigori Volovik.

Outline of available PhD projects:

Superfluid vortex dynamics incorporated in Landau two-fluid equations.

The aim of this work is to relate and improve different mathematical models of superfluid turbulence by developing hierarchies of new stochastic models of vortex motion and turbulence. Mathematical models of superfluidity and superfluid turbulence have used four approaches: (1) the phenomenological Landau two-fluid model, (2) the phenomenological Hall-Vinen-Bekherevich-Khalatnikov (HVBK) model, (3) classical inviscid model of vortex motion with ad hoc reconnections, and (4) the Gross-Pitaevskii (GP) semi-classical model. The first of these was designed to describe the superfluid motion at all temperatures at which superfluidity exists. It requires modification when the vorticity is present. The HVBK model is intended for situations in which superfluid lines are dense. The GP model is applicable at very low temperatures where normal fluid is absent; it has proved its worth especially recently in describing dilute condensates.

Superfluid turbulence in BECs.

The aim of this research is to model and investigate the fundamental processes of superfluid turbulence in Bose-Einstein condensates (BEC). The central idea is to develop a hierarchy of new models of vortex motion in which the action of sound waves on the large-scale superfluid motion is parametrised in terms of simple random dynamic forces representing sound acting on nonlinear `reduced' dynamic equations with relatively few degrees of freedom representing the vortex motion. Spatially inhomogeneous parameters of the random forcing will be estimated from the statistics diagnosed from the Gross-Pitaevskii (GP) equation. There are three major tasks to achieve this goal: (A) To use GP theory to study the reconnection process in order to evaluate quantitatively the associated radiation of sound and Kelvin waves and to define the reconnection rules for the vortex dynamics; (B) To develop a new method of decomposing the superfluid turbulence into the time-dependent large-scale vortex motion and sound components which makes transparent the sound/sound and vortex/sound nonlinear interactions and allows us to understand the fundamental dynamics involved; (C) To repeat (A) and (B) for nonlocal and dissipative GP models that have different acoustic properties. Finally, there is a hope that the random-forcing parameters can be expressed in terms of the large-scale flow characteristics -- this would be a new turbulent closure.

Exciton-polariotn condensates

Microcavity exciton-polaritons are quasi-particles that result from the hybridisation of excitons and photons confined inside semiconductor microcavities. At low enough densities, they behave as bosons according to Bose-Einstein statistics, and so one may investigate Bose-Einstein condensation of these quasi-particles. Because of the imperfect confinement of the photon component, exciton-polaritons have a finite lifetime, and have to be continuously re-populated. Therefore, exciton-polariton condensates lie somewhere between equilibrium Bose-Einstein condensates and lasers. Similar to other laser systems nonequlibrium nature of the polariton condensates gives rise to different kinds of interesting pattern formation. Specific to polariton condensates, the mechanism responsible for pattern formation is an intricate interplay between nonlinear interactions, forcing, dissipation, dispersion and intrincic disorder in the material. The key to understanding the universal behaviour of pattern-forming systems lies in a common description obtained when particular microscopic models reduced to an order parameter equation. This project concerns with development of such models in close interaction with experimental groups.