  The relationship among the entanglement creation within coherently pumped and
closely spaced two-level emitters longitudinally coupled with a single-mode
boson field, and the subsequent quantum cooling of the boson mode is
investigated. Even though the two-level qubits are resonantly driven, we have
demonstrated an efficient cooling mechanism well below limits imposed by the
thermal background. Furthermore, the cooling effect is accompanied by
entanglement of the qubit pair components when the dipole-dipole frequency
shift is close to the frequency of the boson mode. The maximum boson mode
cooling efficiency realizes on the expense of the entanglement creation.
Importantly, this occurs for rather weak external pumping fields protecting the
sample from the deteriorations. Finally, the conditions to effectively optimize
these effects are described as well.
