Dynamics of entanglement between field modes in a one-dimensional cavity with a vibrating boundary

Abstract

We study the dynamics of the coefficient of quantum separability between resonantly coupled modes of the massless scalar field in a one-dimensional ideal cavity, whose boundary performs small harmonic oscillations at the frequency ω w = pω 1 (where ω 1 is the fundamental field eigenfrequency). A qualitative difference between the cases p = 1 and p = 2 is discovered. In the first case, initially factorized thermal states remain separable in the process of evolution, whereas the dynamics of entanglement of initial entangled states (modelled by two-mode squeezed states) turns out to be more intricate, showing sudden changes from 'classical' to 'nonclassical' regimes. In contrast, in the 'principal resonance case' p = 2 the degree of entanglement changes with time monotonically, and any initially factorized thermal states go asymptotically to mixed quantum states with maximal degree of entanglement. Moreover, for highly thermalized states, the time dependence of the separability coefficient exhibits sharp jumps, which are, nonetheless, not correlated with time dependences of the energies of the field modes.