On the perturbative approach to analyse entanglement in two-channel Kerr nonlinear coupler

The intermodal entanglement in a two-channel symmetric nonlinear coupler, operated with Kerr nonlinearity was investigated using the analytical method based on the Heisenberg picture in quantum mechanics. The Heisenberg equations of motion of the propagating modes were solved based on the Baker-Hausdorff (BH) formula. The entanglement expressions were then derived following the Hillery-Zubairy criteria of two-modes state. The time evolution of entanglement was examined at different values of design parameters. Theoretical results from both the HZ-I and HZ-II criteria show that the system exhibits entangled states of light which can be improved by increasing the coupling constants and the initial amplitude of the input field. On the contrary, the increment in frequency mismatch weakens the HZ-I entanglement, while improving the HZ-II entanglement up to a certain mismatch value. The study provides a new theory of entanglement detection in Kerr nonlinear couplers, which opens up the avenues of a new class of applications based on entanglement.