Demonstration of Geometric Landau-Zener Interferometry in a Superconducting Phase Qubit

Geometric quantum manipulation and Landau-Zener interferometry have been separately explored in many quantum systems. Here we fill this gap by combining these two approaches in the study of the dynamics of a superconducting phase qubit. We propose and then experimentally demonstrate Landau-Zener interferometry based on pure geometric phases in this solid-state qubit. We observe the interference due to geometric phases accumulated in the evolution between two consecutive Landau-Zener transitions, while the dynamical phase is eliminated by a spin-echo pulse. Our numerical simulation results using measured energy relaxation and dephasing times agree well with the experimental results. The full controllability of the qubit population as a function of intrinsically fault-tolerant geometric phases provides a promising approach to fault-tolerant quantum computation.