  We study the effect of quantum entanglement maintained by virtual excitations
in an ultrastrongly-coupled harmonic-oscillator system. Here, the quantum
entanglement is caused by the counterrotating interaction terms and hence it is
maintained by the virtual excitations. We obtain the analytical expression for
the ground state of the system and analyze the relationship between the average
excitation numbers and the ground-state entanglement. We also study the
entanglement dynamics between the two oscillators in both the closed- and
open-system cases. In the latter case, the quantum master equation is
microscopically derived in the normal-mode representation of the
coupled-oscillator system. This work will open a route to the study of quantum
information processing and quantum physics based on virtual excitations.
