He along with other scientists introduced the concept of geometric phase for mixed states.

In physics, these systems are referred to as geometric phases.

He is noted for his discovery of a type of geometric phase sometimes known as Pancharatnam phase for polarized beams passing through crystals.

Analysis and measurement of geometric phases in mesoscopic rings is ongoing.

In general the geometric phase is given by:

An easy explanation in terms of geometric phases is given by von Bergmann and von Bergmann:

This discovery proved for the first time that geometric phase exists in optics.

The angle between the two polarization vectors is called the phase shift, or the geometric phase, or the Berry phase.

The periodic quenching of this tunneling rate in the compound Fe has been observed and explained with geometric phases.

In physics, the evolution of such systems is determined by geometric phases.