Exploring three different indicators of dynamical regimes in a time-dependent two-mode Bose–Hubbard model

Abstract

In this work, we propose three different quantifiers as indicators of manifestation of classical dynamical regimes on the quantum evolution of states in the two-mode Bose–Hubbard model: the Loschmidt echo, generalized purity, and linear entropy. These quantifiers are used to yield bifurcation diagrams and to map phase and parameter spaces. Bifurcation diagrams and mappings of phase and parameter spaces are used to identify boundaries between regions of chaotic, regular, and quasi-regular dynamical regimes. The quantifiers presented a correlation with the Lyapunov exponent, and the generalized purity and linear entropy have shown to be sensible to the complex structure of regular-chaotic borderline. These findings can be employed to classify states and range of parameters eligible to perform control of Josephson oscillations and collapses.