A quantum vortex is a topological defect in quantum fluids where phase circulation is quantized.A quantum vortex is a topological defect in a quantum fluid, such as a superfluid, a Bose-Einstein condensate, or a superconductor, where the phase of the quantum wavefunction winds around a central point by an integer multiple of 2π. This winding is quantized, meaning the circulation is always a multiple of a fundamental unit, and the vortex core is a region where the fluid density drops to zero. Quantum vortices are the quantum analogs of classical whirlpools, but they are stable and have a fixed strength.
The concept was first proposed by Lars Onsager in 1949 and independently by Richard Feynman in 1955 to explain the rotation properties of superfluid helium. The first experimental observation of quantized vortices in superfluid helium was made in the 1960s, and in superconductors they were predicted by Alexei Abrikosov in 1957, for which he received the Nobel Prize in 2003.
In a superfluid, the entire fluid is described by a single macroscopic wavefunction. When the fluid rotates, it cannot rotate as a solid body; instead, it forms discrete vortices, each carrying one quantum of circulation. The velocity field around a vortex is inversely proportional to the distance from the core, so the fluid moves faster near the core. In superconductors, vortices carry magnetic flux quanta and are called Abrikosov vortices; they appear when a magnetic field penetrates the superconductor above a critical value.
Quantum vortices are exploited in superconducting devices, where they can be used as qubits, and in studies of turbulence in quantum fluids. They also play a role in understanding neutron star interiors and in the development of quantum simulators.
In a rotating superfluid, the vortices arrange themselves into a regular triangular lattice, known as the Abrikosov lattice, which can be directly imaged in superconductors using magnetic force microscopy.
| T_{\mu\nu} | variable | stress-energy tensor — stress energy tensor joule per metre cubed |
| k^\mu | variable | null vector — null vector |
| t | variable | time coordinate — time second |
| f(t) | variable | sampling function — sampling function |
| C | variable | dimensionless constant — dimensionless constant |
| t_0 | variable | characteristic timescale — time second |
| \int_{-\infty}^{\inf | operator | integration over all time — integral |











