Exploring Non-Abelian Geometric Phases in Spin-1 Ultracold Atoms.

The spin vector of a spin-1 system, unlike that of a spin-1/2 system, can lie anywhere on or inside the Bloch sphere representing the phase space. As a consequence, the geometrical and topological properties of the spin-1 phase space of quantum states are richer and require a generalization of Berry's phase. For special trajectories passing through the center of the Bloch sphere (singular loops), the geometric phase has a non-Abelian nature.

Adiabatic quenches and characterization of amplitude excitations in a continuous quantum phase transition.

Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian.

Quantum Kibble-Zurek Mechanism in a Spin-1 Bose-Einstein Condensate.

The dynamics of a quantum phase transition are explored using slow quenches from the polar to the broken-axisymmetry phases in a small spin-1 ferromagnetic Bose-Einstein condensate. Measurements of the evolution of the spin populations reveal a power-law scaling of the temporal onset of excitations versus quench speed as predicted from quantum extensions of the Kibble-Zurek mechanism. The satisfactory agreement of the measured scaling exponent with the analytical theory and numerical simulations provides experimental confirmation of the quantum Kibble-Zurek model.