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We are most familiar with the four conventional phases of matter: solid, liquid, gas, and plasma. Changes between two phases, known as phase transitions, are marked by abrupt changes in material properties such as density. In recent decades a wide body of physics research has been devoted to discovering new unconventional phases of matter, which typically emerge at ultra-low temperatures or in specially-structured materials. Exotic "topological" phases exhibit properties that can only change in a quantized (stepwise) manner, making them intrinsically robust against impurities and defects.

In addition to topological states of matter, topological phases of can emerge in certain such as photonic crystals and optical waveguide arrays. Topological states of light are of interest as they can form the basis for future energy-efficient light-based communication technologies such as lasers and integrated optical circuits.

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