Geometric Phases due to Used Transitions cause Disturbances in a Hyperfine Qubit

Geometric phases play a key role in the understanding of the dynamics of quantum systems undergoing cyclic evolution. In a multi-state system undergoing multiple phases of evolution, the interplay between various dynamical and geometric phases can create highly nontrivial evolution. We show that adding a fourth state to a three state interferometric scheme can drastically alter the observed phases. We experimentally show that these results are easily seen in the evolution of a hyperfine qubit in an 87Rb Bose condensate.