Quantum chaos in the mesoscopic device for the Josephson flux qubit

Abstract

We study the quantum spectra and eigenfunctions of the three-junction superconducting quantum interference device designed for the Josephson flux qubit at high energies. We analyze the spectral statistics of the parameter region where the system has a mixed classical phase space where regular and chaotic orbits can be found at the same classical energy. We perform a numerical calculation of eigenvalues and eigenstates for different values of the ratio of the Josephson and charging energies, EJ∕EC, which is directly related to an effective ℏ parameter. We find that the nearest-neighbor distributions P(s) of the energy-level spacings are well fitted by the Berry-Robnik theory employing as free parameters the pure classical measures of the chaotic and regular regions of phase space in the different energy regions in the semiclassical case. The phase-space representation of the wave functions is obtained via the Husimi distributions, and the localization of the states of classical structures is analyzed. We discuss for which values of EJ∕EC it can be possible to perform experiments that could be sensitive to the structure of a mixed classical phase space.

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