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arXiv:1811.06256 · Quantum Information Processing

Dynamics of entanglement in three coupled harmonic oscillator system with arbitrary time-dependent frequency and coupling constants

DaeKil Park

Published Jul 31, 2019• 17 citations
arXivHTMLPDF
DOI
10.1007/s11128-019-2393-4

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Abstract The time evolution of the quantum kicked harmonic oscillator (KHO) is described by the Floquet operator which maps the state of the system immediately before one kick onto the state at a time immediately after the next. Quantum KHO is characterized by three parameters: the coupling strength V 0 , the so-called Lamb–Dicke parameter η whose square is proportional to the effective Planck constant ℏ eff , and the ratio T of the natural frequency of the oscillator and the kick frequency. To a given coupling strength and depending on T being a natural or irrational number, the phase space of the classical kicked oscillator can display different behaviors, as for example, stochastic webs or quasicrystal structures, thus showing a chaotic or localized behavior that is mirrored in the quantum phase space. On the other hand, the classical limit is studied letting ℏ eff become negligible. In this paper we investigate how the ratio T , considered as integer, rational or irrational, influences the entanglement dynamics of the quantum KHO and study how the entanglement dynamics behaves when varying either V 0 or ℏ eff parameters.
We investigate the entanglement dynamics of two harmonic oscillators with a weak time-dependent coupling. We find strong connections between the dynamical behaviors of the entanglement and the stability of the normal modes. An abrupt transition of the entanglement dynamics from periodic and bounded to monotonically increasing occurs, when one of the normal modes becomes dynamically unstable as the modulation amplitude crosses the critical value. In particular, when the modulation frequency is roughly twice the oscillator frequency, an explicit critical value for the modulation strength is derived to specify the transition. Moreover, it is found that one can significantly change the dynamical behavior of the entanglement by adding an extremely weak time modulation with specific frequency to a constant coupling.