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Symposium on ICT and Energy Efficiency and Workshop on Information Theory and Security (CIICT)

Entanglement dynamics and classical frequency spectrum in an integrable system

Shihui Zhang, Qing Wu Wang, Hongbao Liu

Published Jan 1, 2012• 0 citations
Publisher

Abstract

The role of classical dynamics in entanglement production for an integrable system is analyzed with a model of two coupled oscillators. It is found that the entanglement of an intergrable system is closely connected with the frequency of classical motion. For different classical orbits, the entanglement of the system increases with the classical frequency entropy, which can reveal the frequency spectrum of the classical motion.

DOI
10.1049/cp.2012.1875

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The role of classical dynamics in entanglement production for an integrable system is analyzed with a model of two coupled oscillators. It is found that the entanglement of an intergrable system is closely connected with the frequency of classical motion. For different classical orbits, the entanglement of the system increases with the classical frequency entropy, which can reveal the frequency spectrum of the classical motion.
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We analyze the connections between entanglement dynamics and classical trajectories in a semiclassical regime for two systems: A pair of coupled oscillators and the Jaynes-Cummings model. We find that entanglement production depends on classical invariant tori and such phenomenon is closely related to the power spectra of classical trajectories. Classical power spectrum with a larger number of frequency components corresponds to larger entanglement. We introduce a frequency entropy to describe the classical frequency distribution. It is found that there is good correspondence between the classical frequency entropies and the maximum von Neumann entropies.
We analyze the connections between the dynamical generation of continuous variable entanglement and the underlying classical trajectories in pairs of coupled oscillators. In the quantization of a periodic cycle, we find periodic entanglement which has twice the frequency of the corresponding classical motion. Such frequency doubling continues to hold true in the entanglement dynamics for a second model that exhibits a two-frequency orbit in the classical domain. In addition, the periodicity and the quasiperiodicity of the entanglement are found to be independent of the local classical dynamical behavior. Finally, in our third model, the entanglement production rate is found to be (i) higher in the chaotic regime and (ii) insensitive toward the choice of regular or chaotic initial condition in the mixed regime. In summary, we have illustrated through our sample models that the generation of dynamical pattern of entanglement can depend completely on the global classical dynamical regime without being influenced by the local classical behavior.
Driven nonlinear systems have attracted great interest owing to their applications in quantum technologies such as quantum information. In quantum information, entanglement is a vital resource and can be measured by entropy in bipartite systems. In this paper, we carry out an investigation to study the impact of driving frequency on the entanglement with a bipartite system of two coupled driven nonlinear oscillators. It is numerically found that the time evolution of the entanglement entropy between the subsystems significantly depends on the driving frequency. The dependence curve of the entropy production on the driving frequency exhibits a pronounced peak. This means the entanglement between the subsystems can be greatly increased by tuning the driving frequency. Further analyses show that the enhancement of the entropy production by the driving frequency is closely related to the energy levels involved in the quantum evolution. This is confirmed by the results related to the quantum spectrum and the dispersion of the wave function in the phase space. Our work gives a convenient way to enhance the entanglement in driven nonlinear systems and throws light on the role of driven nonlinear systems in quantum information technologies.
We study harmonic oscillators connected by periodic or quasi-periodic couplings in a common heat bath. Driving frequencies of couplings play an important role in sustaining entanglement among the oscillators, even in high temperature. Driving amplitudes and relative driving frequencies determine whether entanglement would occur, while the base frequency determines characteristic parameters of entanglement dynamics. Frequency properties of ripples in logarithmic entropy are investigated by FFT, in cases with multiple coupling terms. Finally, frequency landscape is given for controlling entanglement dynamics.