Vortices in Bose-Einstein Condensates: Theory

Abstract

Vortices are pervasive in nature, representing the breakdown of laminar fluid flow and hence playing a key role in turbulence. The fluid rotation associated with a vortex can be parameterized by the circulation $\Gamma=\oint {\rm d}{\bf r}\cdot{\bf v}({\bf r})$ about the vortex, where ${\bf v}({\bf r})$ is the fluid velocity field. While classical vortices can take any value of circulation, superfluids are irrotational, and any rotation or angular momentum is constrained to occur through vortices with quantized circulation. Quantized vortices also play a key role in the dissipation of transport in superfluids. In BECs quantized vortices have been observed in several forms, including single vortices, vortex lattices, and vortex pairs and rings. The recent observation of quantized vortices in a fermionic gas was taken as a clear signature of the underlying condensation and superfluidity of fermion pairs. In addition to BECs, quantized vortices also occur in superfluid Helium, nonlinear optics, and type-II superconductors.Comment: 17 pages, 2 figures. Book chapter to appear in "Emergent Nonlinear Phenomena in Bose-Einstein condensates: Theory and Experiment" (Springer-Verlag)

Rotating trapped Bose-Einstein condensates

“…The current article will emphasize those aspects most relevant to rotating trapped gases and the associated quantized vortices (Aftalion, 2006;Fetter and Svidzinsky, 2001;Kasamatsu and Tsubota, 2007;Parker et al, 2007). In particular, I will emphasize the regime of regular vortex arrays, both the "mean-field Thomas-Fermi" limit when the vortex cores remain small and the "lowest-Landau-level" limit when the cores are comparable to the intervortex spacing (Baym, 2005;Ho, 2001).…”

Stable giant vortex annuli in microwave-coupled atomic condensates

“…Vortices in BEC are essential for simulating various effects from condensed matter [20], and as building blocks of quantum turbulence [21]. They also help to emulate gravitational physics [22], and find applications, such as phase qubits [23] and matter-wave Sagnac interferometers for testing the rotational-equivalence principle [25,26]. As mentioned above, atomic-matter vortices can store and release information delivered by optical vortex beams [2].…”

Deep learning based quantum vortex detection in atomic Bose-Einstein condensates

“…The vortices are clearly defined through a density dip at their cores and through the characteristic 2π phase winding in the phase. Note that the detailed structure of the vortex core depends on the trapping potential [4,6]: in a homogeneous BEC, the width of a vortex core is fixed by the balance between the kinetic and interaction energy, with a typical core size given by the healing length ξ = √ 8πna s , where n corresponds to the density. In trap systems, the size of the vortex core depends also on the local chemical potential, which gives rise to slightly larger sizes in low density regions.…”