Study of the Aharonov-Anandan quantum phase by NMR interferometry

Aharonov and Anandan have recently reformulated and generalized Berry’s phase by showing that a quantum system which evolves through a circuit C in projective Hilbert space acquires a geometrical phase β(C) related to the topology of the space and the geometry of the circuit. We present NMR interferometry experiments in a three-level system which demonstrate the Aharonov-Anandan phase and its topological invariance for different circuits.