Interests

Entanglement Theory

The ultimate goal of this project is to declare if a given quantum state, namely a density matrix in a finite Hilbert space, is separable or entangled. Beside the intrinsic physical worth, this problem is an exciting direction of research where geometry unveil where there is entanglement. I am particular fascinating to explore how the set of the quantum states is organized and which are the technique to detect entanglement. In the case of pure states, via Schmidt decomposition or equivalently with singular value decomposition we can answer to the problem. We know also that for the Hilbert space of qubit-qubit and qubit-qutrit the answer via the partial transposition. But, with tripartite qubit or bipartite qutrit, we have no a general answer which solve the problem. Futhermore, for higher dimension, the problem turns out to be NP hard.

Light-Matter interaction

We want to grasp the idea of light and matter. In particular, can we better understand the role of the quantum fluctuations of the vacuum in quantum theory which carries on the spontaneous emission of a quantum system? We studied a two-level quantum system embedded in a dispersive environment and coupled with the electromagnetic field of the vacuum. We expand the theory of light-matter interactions to include the spatial extension of the atomic system, taken into account through its wave–functions, thanks to which we solve the divergence problem related to the Green tensor propagator. In particular, the inclusion of the spatial structure of the atomic system allows us to build interesting application as nanoantennas and other cool devices. Moreover, we can better understand the role of the asymmetry of atomic states with respect to spatial inversion in these quantities. Future researches should better explain the connection between the phenomenological equantion with the commutation relation rules.

Other interesting projects will be update soon.