Superfluid Vortices in Four Spatial Dimensions

Abstract

Quantum vortices in superfluids have been an important research area for many decades. Naturally, research on this topic has focused on two and three-dimensional superfluids, in which vortex cores form points and lines, respectively. Very recently, however, there has been growing interest in the quantum simulation of systems with four spatial dimensions; this raises the question of how vortices would behave in a higher-dimensional superfluid. In this paper, we begin to establish the phenomenology of vortices in 4D superfluids under rotation, where the vortex core can form a plane. In 4D, the most generic type of rotation is a "double rotation" with two angles (or frequencies). We show, by solving the Gross-Pitaesvkii equation, that the simplest case of equal-frequency double rotation can stabilise a pair of vortex planes intersecting at a point. This opens up a wide number of future research topics, including unequal-frequency double rotations; the stability and reconnection dynamics of intersecting vortex surfaces; and the possibility of closed vortex surfaces.

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Cited by in corpus (6)

• Realization of an atomic quantum Hall system in four dimensions
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations
• Curved vortex surfaces in four-dimensional superfluids: II. Equal-frequency double rotations
• Motion groupoids and mapping class groupoids
• Liouville Fock state lattices and potential simulators