Quantized Vortices
Introduction
A quantized vortex is a topological defect exhibited in superfluids and superconductors. The principle behind its formation is rooted in quantum mechanics, specifically quantum field theory. The name "quantized vortex" is derived from the fact that the circulation around the vortex takes on discrete values, typically multiples of a fundamental constant, a phenomenon termed as "quantization".
Quantum Mechanics and Vortices
Quantized vortices are a direct consequence of the principles of quantum mechanics. In quantum mechanics, particles are described by wavefunctions, mathematical functions that provide information about the probability distribution of a particle. When a system of particles is cooled to extremely low temperatures, the wavefunctions of these particles start to overlap and eventually condense into a single, macroscopic wavefunction. This state of matter is called a Bose-Einstein condensate (BEC).
In a BEC, the particles behave as a single entity and exhibit quantum mechanical properties on a macroscopic scale. One such property is superfluidity, the ability of a fluid to flow without viscosity. When a superfluid is stirred, it forms vortices. However, unlike classical vortices, these vortices are quantized, meaning the circulation around the vortex is an integer multiple of a fundamental constant.
Quantization of Vortices
The quantization of vortices is a direct result of the wave nature of particles in quantum mechanics. The wavefunction that describes a particle in a quantum system must be single-valued. In other words, if a particle makes a complete loop around a point, the wavefunction must return to its original value. This requirement leads to the quantization of the circulation around a vortex.
The circulation Γ around a vortex is given by the integral of the velocity field around a closed loop enclosing the vortex. In a quantized vortex, this integral takes on discrete values, typically multiples of the Planck constant divided by twice the mass of the particle, h/2m. This is the fundamental quantum of circulation and is a direct consequence of the single-valuedness of the wavefunction.
Experimental Observation of Quantized Vortices
Quantized vortices have been observed in several quantum systems. The first observation of quantized vortices was in superfluid helium, a BEC made up of helium-4 atoms. When superfluid helium is stirred, it forms a lattice of quantized vortices. These vortices are stable and can persist for long periods of time due to the lack of viscosity in the superfluid.
Quantized vortices have also been observed in atomic BECs and superconductors. In atomic BECs, vortices can be created by rotating the BEC or by using phase imprinting techniques. In superconductors, quantized vortices, also known as fluxons, are formed in the presence of a magnetic field. Each fluxon carries a single quantum of magnetic flux.
Significance and Applications
The study of quantized vortices has significant implications for our understanding of quantum mechanics and quantum field theory. Quantized vortices are topological defects, structures that are stable due to topological constraints rather than energy minimization. The study of these defects provides insights into the nature of phase transitions and symmetry breaking in quantum systems.
Quantized vortices also have potential applications in quantum computing. In a type of quantum computer known as a topological quantum computer, information is stored in the topological properties of a quantum system, such as the number and arrangement of quantized vortices. This makes the information robust against local perturbations, a key requirement for practical quantum computing.