Quantum Entanglement Oscillations

Haixing Miao, S. L. Danilishin, Yanbei Chen

Quantum entanglement has been actively sought in optomechanical and electromechanical systems. The simplest system is a mechanical oscillator interacting with a coherent optical field, while the oscillator also suffers from thermal decoherence. With a rigorous functional analysis, we develop a mathematical framework for treating quantum entanglement that involves infinite degrees of freedom. We show that the quantum entanglement is always present between the oscillator and continuous optical field---even when the environmental temperature is high and the oscillator is highly classical. Such a universal entanglement is also shown to be able to survive more than one mechanical oscillation period if the characteristic frequency of the optomechanical interaction is larger than that of the thermal noise. In addition, we introduce effective optical modes that are ordered by the entanglement strength to better understand the entanglement structure, analogously to the energy spectrum of an atomic system. In particular, we derive the optical mode that is maximally entangled with the mechanical oscillator, which will be useful for future quantum computing and encoding information into mechanical degrees of freedom.

Shengjun Wu

Hristo Dimov, Stefan Mladenov, Radoslav C. Rashkov +1 more

We study the quantum entanglement of coupled Pais-Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of $N$ coupled Pais-Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. We also make remarks on the appearance of instabilities of higher-derivative oscillators in the context of AdS/CFT correspondence. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.

Dmitry N. Makarov

Quantum entanglement of a system of two coupled quantum harmonic oscillators with a Hamiltonian H[over ̂]=1/2(1/m_{1}p[over ̂]_{1}^{2}+1/m_{2}p[over ̂]_{2}^{2}+Ax_{1}^{2}+Bx_{2}^{2}+Cx_{1}x_{2}) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. Despite this, the quantum entanglement of such a system is still a problem under study. This is primarily due to the fact that the system is multiparametric and the quantum entanglement of such a system is not defined in a simple analytical form. This paper solves this problem and shows that quantum entanglement depends on only one parameter that has a simple physical meaning: the reflection coefficient R∈(0,1). The reflection coefficient R has a simple analytical form and includes all the parameters of the system under consideration. It is shown that for certain values of the coefficient R, the quantum entanglement can be large. The developed theory can be used not only for calculating quantum entanglement, but also for many other applications in physics, chemistry, and biophysics, where coupled harmonic oscillators are considered.