Experimental observation of a topological phase in the maximally entangled state of a pair of qubits

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