Entropy and negativity of Fermi-resonance coupling vibrations in a spectroscopic Hamiltonian

Abstract

The entanglement dynamics of Fermi resonance coupling vibrations in a spectroscopic Hamiltonian for molecules $\mathrm{C}\mathrm{H}{\mathrm{D}}_{3}$, $\mathrm{C}\mathrm{H}{\mathrm{Cl}}_{3}$, and $\mathrm{C}\mathrm{H}{\mathrm{F}}_{3}$ is studied in terms of the von Neumann entropy and negativity with three kinds of initial states that are direct products of coherent states, thermal states, and squeezed states of each mode. It is demonstrated that the increasing rate of entanglement in the early-time evolution is the largest for the squeezed states, while that is the smallest for the coherent states. For small parameters in the coherent and thermal states, entanglement displays a quasiperiodicity with the quasiperiod in $\mathrm{C}\mathrm{H}{\mathrm{F}}_{3}$ being the longest. Furthermore, the dynamical correlation between the von Neumann entropy and negativity shows that positively correlated or anticorrelated behaviors of both measures strongly depend on initial states and molecules. For those states with small parameters, both measures exhibit dominantly positive correlation. These are useful for molecular quantum computing and information processing.