Entanglement dynamics in a spin star system

The implementation of more and more efficient nanodevices exploitable in applicative contexts like for example quantum computers often requires a highly challenging miniaturizing process aimed at packing a huge number of point-like basic elements whose dynamics mimics indeed that of a qubit. Stimulated by such a requirement, over the last few years theoretical schemes using the language of the spin frac12 system models have been investigated. The main reason is that besides the simple dynamical behaviour of each elementary constituent these Hamiltonian models do indeed capture basic ingredients of several physical situations differing one another mainly for the numerical values of some relevant parameters appearing in the same model. Examples of physical systems admitting a reasonable description in terms of spin models may be a collection of mutually interacting superconducting flux qubits immersed in appropriate bosonic baths or few electron spins, mutually coupled or not, interacting with a bath of a huge number of nuclear spins. The question deserving the highest interest for quantum computing is the extent at which the quantum coherences essential for any process based on the superposition principle may be protected against the unavoidable degradation of the purity of the state of the small system. In this paper a specific spin model, namely a spin star model, is adopted and its dynamical behaviour is investigated. Particular emphasis has been reserved to the dynamical behaviour of the entanglement get established within the small system or between the system and the bath. The genuine non-Markovian behaviour of the system makes quite challenging to find exact solutions of this problem which therefore is often numerically coped with.