  Two defect particles that couple to a harmonic chain, acting as common
reservoir, can become entangled even when the two defects do not directly
interact and the harmonic chain is effectively a thermal reservoir for each
individual defect. This dynamics is encountered for sufficiently low
temperatures of the chain and depends on the initial state of the two
oscillators. In particular, when each defect is prepared in a squeezed state,
entanglement can be found at time scales at which the steady state of a single
defect is reached. We provide a microscopic description of the coupled quantum
dynamics of chain and defects. By means of numerical simulations, we explore
the parameter regimes for which entanglement is found under the specific
assumption that both particles couple to the same ion of the chain. This model
provides the microscopic setting where bath-induced entanglement can be
observed.
