Non-Adiabatic Fluctuation in Measured Geometric Phase

We study how the non-adiabatic effect causes the observable fluctuation in the “geometric phase” for a two-level system, which is defined as the experimentally measurable quantity in the adiabatic limit. From the Rabi’s exact solution to this model, we give a reasonable explanation to the experimental discovery of phase fluctuation in the superconducting circuit system [P. J. Leek, $\mathit{\text{et}}\mathit{\text{al}}$., Science $\mathbf{\text{318}}$, 1889 (2007)], which seemed to be regarded as the conventional experimental error.