Geometric Phase of Three-Level Systems in Interferometry

Geometric phase of three-level systems in interferometry.

We present the first scheme for producing and measuring an Abelian geometric phase shift in a three-level system where states are invariant under a non-Abelian group. In contrast to existing experiments and proposals for experiments, based on U(1)-invariant states, our scheme geodesically evolves U(2)-invariant states in a four-dimensional SU(3)/U(2) space and is physically realized via a three...

Geometric Phase in Su(n) Interferometry

The purpose of this contribution is twofold: to review how an SU(N) transformation can be experimentally realized using optical elements, and to show how such an experimental realization can be used to investigate the cyclic evolution of a state over the manifold SU(N)/U(N-1). The bulk of the results will be presented explicitly for SU(3) (see [1] for further details) and SU(4), although it wil...

Superradiant phase transitions with three-level systems

A generalized Pancharatnam geometric phase formula for three-level quantum systems

We describe a recently developed generalization of the Poincaré sphere method, to represent pure states of a three-level quantum system in a convenient geometrical manner. The construction depends on the properties of the group SU(3) and its generators in the defining representation, and uses geometrical objects and operations in an eight-dimensional real Euclidean space. This construction is t...

Spatial Non-Cyclic Geometric Phase in Neutron Interferometry

We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the interferometer and the evolution of the state is controlled by phase shifters and absorbers. A related experiment was reported previously by some of the authors to ve...