Eur. Phys. J. D (2014) 68: 238
https://doi.org/10.1140/epjd/e2014-50294-0

Regular Article

Effect of squeezing and Planck constant dependence in short time semiclassical entanglement

¹ Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
² Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore, Republic of Singapore

^a e-mail: miguel.sanjuan@urjc.es

Received: 10 April 2014
Published online: 14 August 2014

Abstract

In this paper, we investigate into the short time semiclassical entanglement of a general class of two-coupled harmonic oscillator system that includes additional nonlinear terms in the potential of the form λx^myⁿ, such that the sum of the degree m and n equals to a fixed constant. An analytical expression of the short time linear entropy is derived and it shows a clear relationship between the single mode squeezing and the entanglement dynamics. In addition to that, our theoretical analysis has shown that the short time semiclassical entanglement entropy displays a dependence on the Planck constant ħ of the form ħ^{m + n − 2} for this class of systems. By applying our results to the linearly coupled harmonic oscillator, the Barbanis-Contopoulos, the Hénon-Heiles and the Pullen-Edmonds Hamiltonian, we have found a good correspondence between the numerical and analytical results in the short-time regime. Interestingly, our results have demonstrated both analytically and numerically that an appropriate manipulation of initial squeezing can have the significant effect of enhancing the short time semiclassical entanglement between the two subsystems.