Magnetic field effect on the dynamics of entanglement for time-dependent harmonic oscillator

Abstract

We investigate the dynamics of entanglement, uncertainty and mixedness by solving time-dependent Schrödinger equation for two-dimensional harmonic oscillator with time-dependent frequency and coupling parameter subject to a static magnetic field. We compute the purities (global/marginal) and then calculate explicitly the linear entropy [Formula: see text] as well as logarithmic negativity [Formula: see text] using the symplectic parametrization of vacuum state. We introduce the spectral decomposition to diagonalize the marginal state and get the expression of von Neumann entropy [Formula: see text] and establish its link with [Formula: see text]. We use the Wigner formalism to derive the Heisenberg uncertainties and show their dependencies on both [Formula: see text] and the coupling parameters [Formula: see text] [Formula: see text] of the quadrature term [Formula: see text]. We graphically study the dynamics of the three features (entanglement, uncertainty, mixedness) and present a similar topology with respect to time. We show the effects of the magnetic field and quenched values of [Formula: see text] and [Formula: see text] on these three dynamics, which lead eventually to control and handle them.