Parameric representation of open quantum systems and cross-over from quantum to classical environment

Quantum systems with an environment, usually refferred to as Open Quantum Systems (OQS), are tipically treated in terms of reduced density matrices. This approach is a powerful tool but does not allow to keep track of any phase information between the system and the environment and induce an uncontrollable loss of information which prevents some phenomena to be properly described. We have proposed an alternative description of OQS based on a parametric representation of the environment, as obtained in terms of generalized coherent states. One of the major merit of such representation is the possibility to faithfully follow the crossover from a quantum to a classical environment without affecting the full quantum description of the principal system. As a first application of the newly proposed approach, we have considered a prototypical composite system, the so called spin-star, where a central spin-1/2 (the principal system) is surrounded by a ring of other spins (the environment), and the interactions are of Heisenberg type. Besides the specific results for such system, we find that some quantum features of the principal system behaviour are related not only to the fact that an environment exists, but specifically to the condition that the system be entangled with it. In particular, the entanglement between the central spin and its environment is found to be possibly revealed by a quantity that can be measured (the so called Berry’s phase). This result suggests a possible way for obtaining experimental access to entanglement properties and further shows that quantum correlations can be brought up to the surface of our observable world, where they can be used as a resource for understanding and controlling macroscopic phenomena, from quantum communication and computation, to light harvesting and other processes in the realm of quantum biology.