Phase control of entangled states
The entanglement is a fundamental quantum feature which plays an important role in quantum information and quantum computing. In recent years, many efforts have been done for understanding the survival limits of the quantum behavior in open systems at high temperature.
In this work, we consider a quantum system of two coupled parametric oscillators in contact with a common heat bath and with a time dependent oscillation frequency. We demonstrate that the oscillators become entangled exactly in the region where the classical counterpart, in this case a Mathieu’s oscillator, is unstable.
The instability regions of the system have been theoretically and experimentally explored by means of a weak sinusoidal perturbation, with adjustable amplitude and phase, applied to the oscillation frequency. Such a control method has been frequently used to achieve control of chaos .
We show that if the classical system passes from stable to unstable regions as a consequence of the perturbation, the quantum oscillators become entangled. This means that is possible generate and manipulate entanglement controlling the dynamical behavior of the associated classical system .
 S. Zambrano, J. M. Seoane, I. P. Marino, M. A. F. Sanjuan, R. Meucci “ Phase Control of in Nonlinear Systems” in Recent Progress in Controlling Chaos, Miguel A. F. Sanjuan and C. Grebogi ( Eds.), World Scientific (2010).
 J. Gonzalez-Henao, E. Pugliese, S. Euzzor, S. F. Abdalah, R. Meucci, J. Roversi . “Generation of entanglement in quantum parametric oscillators using phase control” Submitted to Nature Scientific Reports.