Generation of entanglement in quantum parametric oscillators using phase control

Agradecimentos: The authors wish thank Prof. F.T. Arecchi for helpful discussion and revision of the manuscript. R.M. also thanks Fondazione Ente Cassa di Risparmio di Firenze for financial support. This work was supported by Capes (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior). We thank also the finacial support by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnologico - INCT of Quantum Information), FAPESP (Fundação de Amparo a Pesquisa do Estado de São Paulo - CePOF of Optics and Photonics) Abstract: The control of quantum entanglement in systems in contact with environment plays an important role in information processing, cryptography and quantum computing. However, interactions with the environment, even when very weak, entail decoherence in the system with consequent loss of entanglement. Here we consider a system of two coupled oscillators in contact with a common heat bath and with a time dependent oscillation frequency. The possibility to control the entanglement of the oscillators by means of an external sinusoidal perturbation applied to the oscillation frequency has been theoretically explored. We demonstrate that the oscillators become entangled exactly in the region where the classical counterpart is unstable, otherwise when the classical system is stable, entanglement is not possible. Therefore, we can control the entanglement swapping from stable to unstable regions by adjusting amplitude and phase of our external controller. We also show that the entanglement rate is approximately proportional to the real part of the Floquet coefficient of the classical counterpart of the oscillators. Our results have the intriguing peculiarity of manipulating quantum information operating on a classical system COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIOR - CAPES CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP Aberto