In optics and electromagnetics, the geometric phase originates from the spin–orbit interaction (SOI) of light and describes the relationship between phase change and polarization conversion when light is transmitted or reflected through an anisotropic medium. The general form of the geometric phase was developed by Berry in 1984. He found that when a quantum system in an eigenstate is slowly transported around a circuit C by varying parameters R in its Hamiltonian , it will acquire a geometrical phase factor . Since the pioneering work of Berry, the geometric phase has been applied in various fields of physics and expanded the understanding of state evolutions in different parameter spaces. The most common formulations of the geometric phase are known as the Aharonov–Bohm (AB) phase for electrons and the Pancharatnam–Berry (PB) phase for photons. Figure 1(a) shows a representative case of the AB effect. When a charged particle passes around a long solenoid, the wave function experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being negligible in the region through which the particle passes and the particle’s wave function being negligible inside the solenoid. Subsequently, Chiao et al. considered the manifestations of this phase factor for a photon in a state of adiabatically invariant helicity, and an effective optical activity for a helical optical fiber was predicted. In 1987, Aharonov and Anandan noted that the appearance of the geometric phase did not necessarily go through an adiabatic process, and the geometric phase factor can be defined for any cyclic evolution of a quantum system. Another important manifestation of the geometric phase in solids is known as the Zak phase, which underlies the existence of protected edge states.
Set citation alerts for the article
Please enter your email address