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

Quantum entanglement maintained by virtual excitations in an ultrastrongly-coupled-oscillator system