Abstract
Quantum mechanical phase factors can be related to dynamical effects or to the geometrical properties of a trajectory in a given space--either parameter space or Hilbert space. Here, we experimentally investigate a quantum mechanical phase factor that reflects the topology of the SO(3) group: since rotations by {pi} around antiparallel axes are identical, this space is doubly connected. Using a pair of nuclear spins in a maximally entangled state, we subject one of the spins to a cyclic evolution. If the corresponding trajectory in SO(3) can be smoothly deformed to a point, the quantum state at the end of the trajectory is identical to the initial state. For all other trajectories the quantum state changes sign.
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