  We study stationary entanglement among three harmonic oscillators which are
dipole coupled to a one-dimensional or a three-dimensional bosonic environment.
The analysis of the open-system dynamics is performed with generalized quantum
Langevin equations which we solve exactly in Fourier representation. The focus
lies on Gaussian bipartite and tripartite entanglement induced by the highly
non-Markovian interaction mediated by the environment. This environment-induced
interaction represents an effective many-parties interaction with a spatial
long-range feature: a main finding is that the presence of a passive oscillator
is detrimental for the stationary two-mode entanglement. Furthermore, our
results strongly indicate that the environment-induced entanglement mechanism
corresponds to uncontrolled feedback which is predominantly coherent at low
temperatures and for moderate oscillator-environment coupling as compared to
the oscillator frequency.
