The dynamics of a hybrid quantum system, composed by different subsystems, one of them being macroscopic, has been investigated in such a way to preserve genuine quantum effects even in the presence of a macroscopic part. The problem is related with the analysis of the quantum-to-classical crossover, but our approach allows us to take trace of the quantum correlations established between the microscopic and macroscopic components of the device. The specific systems we have considered model the macroscopic subsystem by one or more spin-S objects, with S large, and the actual calculation is made possible by a suitable approximation, valid in the large-S limit, which simplifies the spin-algebra. Two types of applications have been considered so far.

First, a quantum mechanical oscillator coupled to a spin environment has been considered, showing that an insightful expression for the propagator of the whole system can be found, where we can identify an effective ”back-action” term, i.e. an operator acting on the magnetic environment only, and yet missing in the absence of the quantum principal system, which behaves as an effective time-dependent magnetic anisotropy, whose character, whether uniaxial or planar, also depends on the detuning between the frequency of the oscillator and the level-splitting in the spectrum of the free magnetic system, due to the possible presence of an external magnetic field.

The second system we considered is made by two qubits interacting with a spin-S chain, whose internal interactions allow for the propagation of soliton-like excitations. We have found that in the large-S limit the state of the chain can be sensibly described by coherent state products, so that the system dynamics while a soliton propagates through the chain can be numerically investigated. We have shown that in such hybrid devices, despite the large value of S, the spin chain can still act as a medium able to establish quantum correlations (entanglement) between two delicate, distant qubits, but at the same time its dynamical robustness, deriving from its non-linear macroscopic character, makes it possible to protect the qubits from the noisy effects of the outside world.