Entanglement of resonantly coupled field modes in cavities with vibrating boundaries

Abstract

We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropic coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered: a three-dimensional cavity possessing eigenfrequencies $\omega_3=3\omega_1$, whose wall oscillates at the frequency $\omega_w=2\omega_1$, and a one-dimensional (Fabry--Perot) cavity with an equidistant spectrum $\omega_n= n\omega_1$, when the distance between perfect mirrors oscillates at the frequencies $\omega_1$ and $2\omega_1$. The behaviour of entanglement measures in these cases turns out to be completely different, although all three coefficients demonstrate qualitatively similar time dependences in each case (except for some specific situations, where the covariance entanglement coefficient, based on traces of covariance submatrices, seems to be essentially more sensitive to entanglement than other measures, which are based on determinants of covariance submatrices). Different initial states of the field are considered: vacuum, squeezed vacuum, thermal, Fock, and even/odd coherent states.