  Virtual states are a central concept in quantum mechanics. By definition, the
probability of finding a quantum system in a virtual state should be
vanishingly small at all times. In contrast to this notion, we report a
phenomenon occurring in open quantum systems by which virtual states can
acquire a sizable population in the long time limit, even if they are not
directly coupled to any dissipative channel. This means that the situation
where the virtual state remains unpopulated can be metastable. We describe this
effect by introducing a two-step adiabiatic elimination method, that we termed
hierarchical adiabatic elimination, which allows one to obtain analytical
expressions of the timescale of metastability in general open quantum systems.
We show how these results can be relevant for practical questions such as the
generation of stable and metastable entangled states in dissipative systems of
interacting qubits.
