Experimental Observation of a Topological Phase in the Maximally Entangled State of a Pair of Qubits

TL;DR

This paper experimentally demonstrates a topological phase in a maximally entangled pair of qubits, showing how certain cyclic evolutions in SO(3) space induce a sign change in the quantum state, revealing topological properties.

Contribution

The study provides the first experimental observation of a topological phase associated with the SO(3) group using entangled qubits, linking geometric phases to topological features.

Findings

Cyclic evolutions in SO(3) can induce a sign change in entangled states.

The topological phase depends on the deformability of the trajectory in SO(3).

Experimental verification of topological phases in quantum systems.

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 pairs 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.