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4 Most Common Types of Geometric Phases

Geometric phases are a fascinating concept in physics that describes the accumulated phase of a quantum system due to geometric changes in the system’s parameters. These phases are essential in various fields, including condensed matter physics, quantum computing, and optics. There are several types of geometric phases, and in this article, we will discuss the four most common ones.

Berry Phase

Berry phase is the most well-known geometric phase, named after Sir Michael Berry, who first described it in 1984. Berry phase arises when a quantum system undergoes cyclic evolution in its parameter space. In other words, when the system comes back to its original configuration, it acquires a nontrivial phase shift known as the Berry phase. This phase is an essential property of many physical systems, including superconducting qubits, topological insulators, and spintronics.

Aharonov-Bohm Phase

The Aharonov-Bohm phase is another common geometric phase that arises due to the presence of a magnetic field. In this phase, a charged particle moving in a region of zero magnetic field but non-zero vector potential experiences a phase shift. This phase shift is independent of the particle’s trajectory and is solely determined by the flux of the magnetic field. This effect was first predicted by Yakir Aharonov and David Bohm in 1959 and has since been observed in numerous experiments, including the famous electron interference experiment.

Pancharatnam Phase

The Pancharatnam phase is a geometric phase that arises in polarization optics. It