Abstract
Vorticity in two-dimensional superfluids is subject to intense research efforts due to its role in quantum turbulence, dissipation and the BKT phase transition. Interaction of sound and vortices is of broad importance in Bose–Einstein condensates and superfluid helium. However, both the modelling of the vortex flow field and of its interaction with sound are complicated hydrodynamic problems, with analytic solutions only available in special cases. In this work, we develop methods to compute both the vortex and sound flow fields in an arbitrary two-dimensional domain. Further, we analyse the dispersive interaction of vortices with sound modes in a two-dimensional superfluid and develop a model that quantifies this interaction for any vortex distribution on any two-dimensional bounded domain, possibly non-simply connected, exploiting analogies with fluid dynamics of an ideal gas and electrostatics. As an example application we use this technique to propose an experiment that should be able to unambiguously detect single circulation quanta in a helium thin film.
Highlights
Superfluidity in two dimensions, first systematically investigated in the 70’s in helium thin films [5,6,7,8], has sparked major research efforts in recent years, culminating in the 2016 Nobel Prize, awarded for understanding the nature of superfluidity in two dimensions [9,10,11]
To give an experimentally relevant example, in the following we study the interaction of a quantized vortex with sound modes in a disk-shaped resonator with a free (‘Neumann’) boundary condition. This analysis is applicable to geometries used in superfluid helium experiments [33,45,46] with a microtoroidal optomechanical resonator of R ∼ 30 μm radius (see Fig. 3(a)), those of refs. [3, 56, 60, 61], and experiments with two-dimensional Bose-Einstein-condensates, which are confined by a hard-walled trap [1]
From symmetry arguments the overlap between sound and vortex flow fields is maximized for a centered vortex
Summary
Superfluidity in two dimensions, first systematically investigated in the 70’s in helium thin films [5,6,7,8], has sparked major research efforts in recent years, culminating in the 2016 Nobel Prize, awarded for understanding the nature of superfluidity in two dimensions [9,10,11]. -called third-sound waves, become the primary form of sound wave [31] Both observation of temperature-wave propagation in a two-dimensional BoseEinstein condensate [32], and real-time measurement and control of third sound on a superfluid helium thin film [33] have been demonstrated. We discuss the interaction of sound Bessel modes on a disk-shaped domain with quantized vortices, which is relevant for a number of experiments on superfluid thin films [3, 33, 45, 46] and two-dimensional Bose-Einstein-condensates [32, 47, 48]. Drawing on the finite element model, we discuss how, in this geometry, the interaction with sound can be maximized, so that these steps could be clearly resolved This would enable the first direct detection of quantized circulation in two-dimensional superfluid helium
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