# Vortices in Bose-Einstein Condensates: Theory

## TL;DR

This paper reviews the theoretical understanding of vortices in Bose-Einstein Condensates, emphasizing their quantized nature, formation, and significance in superfluidity and related phenomena across various systems.

## Contribution

It provides a comprehensive theoretical overview of vortices in BECs, highlighting their quantization, types, and role in superfluid behavior, with recent experimental observations included.

## Key findings

- Quantized vortices are fundamental in superfluid BECs.
- Vortices include single, lattice, and ring structures.
- Recent detection of vortices in fermionic gases confirms superfluidity.

## 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.