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Superfluid states of matter: from superfluid helium to polariton condensates

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When in 1937 liquid helium was first observed to flow with negligible viscosity through a narrow gap, it was clear that, at low temperatures, helium was different from ordinary fluids. The attemps to understand this phenomenon (called superfluidity by Pyotr Kapitza) led to the development of a two-fluid theory by Lev Landau. In this theory the fluid is modelled as an interacting mixture of superfluid and normal fluid components. In more recent times, an aspect of superfluidity that has been emphasized as most central is that the superfluid velocity is associated with the gradient of the phase of the macroscopic classical complex-valued matter field. Such a description impies that the system possesses a Bose–Einstein condensate (a form of matter that emerges when particles collapse into the same lowest-energy state) — with the matter field being the condensate wavefunction — and, therefore, can be described by a nonlinear equation for classical waves, known as the nonlinear Schrodinger equation. This description has the ingredients necessary to produce many of the aspects of superfluidity, such as frictionless flow below the Landau critical velocity, two-fluid hydrodynamics, quantized vortices, and metastable persistent flow in a doughnut-shaped geometry. These features of superfluidity have been experimentally observed not only in liquid helium, but also in ultracold gases and very recently in condensates of semiconductor microcavity polaritons — entities comprising both matter and light. How the condensate model can be modified and applied to study the dynamics of these various superfluid systems is the subject of my talk.

This talk is part of the Trinity Mathematical Society series.

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