Virtual excitations and quantum correlations in ultra-strongly coupled harmonic oscillators under intrinsic decoherence

We study the effect of Milburn intrinsic decoherence in a system of ultra-strongly coupled quantum harmonic oscillators, putting emphasis on the virtual excitations of the ground state and their interconnection with quantum correlations like entanglement and steering. For isotropic (equal frequency) oscillators we derive an analytic expression for the common steady state value of virtual excitations and then show analytically and numerically that the influence of intrinsic decoherence can be delayed by increasing the ultra-strong coupling. When increasing the anisotropy in the oscillator frequencies, we numerically observe an asymmetric redistribution of virtual excitations among the oscillators, which leads to an asymmetry in quantum steering. Furthermore, virtual excitations are increased, causing also the strengthening of entanglement and steering immediately after their generation. For large anisotropy values we observe quantum synchronization between the oscillators, with both excitations and quantum correlations being significantly enhanced. When increasing the ultra-strong coupling in the case of large anisotropy, a considerable reinforcement of quantum correlations is observed, over long simulation times and in spite of the presence of decoherence. This is the most important result of this work, since it suggests how to properly design the experimental parameters of the system in order to delay the effect of intrinsic decoherence.