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We show that a squeezed bath, that acts on the central element of a harmonicchain, can drive the whole system to a steady state featuring a series ofnested entangled pairs of oscillators that, ideally, covers the whole chainregardless of its size. We study how to realize this effect in various physicalimplementations, including optomechanical and superconducting devices, usingcurrently available technologies. In these cases no squeezed fields areactually needed, and the squeezed bath is, instead, simulated by quantumreservoir engineering with bichromatic drives.

Steady-state nested entanglement structures in harmonic chains with single-site squeezing manipulation