Generation of entanglement in quantum parametric oscillators using phase control.

J C Gonzalez-Henao,S Euzzor,S.F Abdalah,E Pugliese,R Meucci,J A Roversi

doi:10.1038/srep13152

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.

Highlights

In this paper, in order to understand how two completely different features such as dynamical instability and entanglement are connected, we introduce a sinusoidal perturbation to the oscillation frequency of a parametric oscillator by a suitable phase modulation, i.e., ω(t) → f(Ω t + φ), where the phase φ is the control parameter
We have found that, for low temperature and small values of dissipation rate, the “+ ” oscillator is unstable and this condition allows entanglement, a result not yet reported in the literature
The logarithmic negativity is not a concave or convex function, it is a monotonous function of entanglement since, in average, it doesn’t increase under Local Operations and Classical Communication (LOCC) operations or operators that conserves PPT19,20

Summary

Results

The connection between classical instabilities and the existence of quantum entanglement relies on the elements of the covariance matrix of the operators {X1, X2, P1, P2} which depend, as stated before, on the solutions of the following differential equations:. 11, it was shown that entanglement of parametric oscillators 1 and 2 strongly depends on the stability of the solutions of Eq (16) which is associated with the position and momentum operators in the Hamiltonian H− It only occurs for values for which the oscillator “− ” is unstable. The dynamical behavior of the oscillator is modified as shown in Fig. 1(b,c) where stability and instability regions are reported in the parameter space m and φ These figures are obtained considering c = 0 .09 and defining a new auxiliary variable ωr = 1 − c. Relationship existing between the classical instability obtained from the Floquet coefficients and the existence of quantum entanglement, for exactly the same parameter values, will be investigated

Discussion

Conclusions

Methods