The search for methods to create and maintain entanglement has led to the idea of environmentally induced entanglement. Roughly speaking, the usually detrimental effect of coupling a non-interacting bipartite system to an environment is turned into an advantage by using the environment to mediate an indirect interaction, which can result in entanglement of the two parts of the system under certain conditions. Of course, care has to be taken to properly evaluate the conflicting influences of the environment. Only if the indirect interaction overcompensates for the decoherence, entanglement creation can be expected.
It has been suggested that entanglement creation can be achieved in bosonic heat baths even over finite spatial separations with only a moderate polynomial decay of entanglement with distance. In this work, we look more closely at the distance dependence, for the first time employing an oscillator model that is both exactly solvable and includes dissipation. We numerically prove that entanglement creation is, in fact, extremely distance-sensitive and it is not possible to entangle objects which are further apart than approximately their own size.
Additionally, we suggest an approach how to mitigate the distance dependence. It comes at the cost of geometrically modifying the bath modes by imposing physical boundary conditions resulting in a gap in the spectrum. This is implemented by placing the system inside of an infinitely long superconducting cavity. An experimental implementation of this could be feasible
