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

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 λxmyn, 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 ħm + 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