Optical Manifestations of Berry’s Topological Phase: Classical and Quantum Aspects

Abstract

Berry’s discovery of a topological phase in quantum mechanics has led to a unified view of many seemingly disconnected topological phenomena in physics, both at the quantum and classical levels.₁ Here we review some recent optical manifestations of this Aharonov-Bohm-like phase. There are now four distinct manifestations of topological phases in optics. All these phases can be thought of as anholonomies. An anholonomy can arise whenever a system is processed through a sequence of changes such that it is returned to its original state; most of the variables characterizing the system obviously return to their original values, but surprisingly certain ones may not. An example is the phase anholonomy which an electron exhibits when it returns to its original state after encircling a solenoid in the Aharonov-Bohm effect. Another example is the age anholonomy which a travelling twin experiences relative to the nontravelling twin when he returns to the Earth after a rocket trip in the twin paradox. When light is cycled through a sequence of states such that it returns to its original state, it can also acquire anholonomies at both the classical and quantum levels.