Numerical simulation of Kerr nonlinear systems; analyzing non-classical dynamics

Abstract

We simulate coherent driven free dissipative Kerr nonlinear system numerically using Euler’s method by solving Heisenberg equation of motion and time evolving block decimation (TEBD) algorithm, and demonstrate how the numerical results are analogous to classical bistability. The comparison with analytics show that the TEBD numerics follow the quantum mechanical exact solution obtained by mapping the equation of motion of the density matrix of the system to a Fokker-Plank equation. Comparing between two different numerical techniques, we see that the semi-classical Euler’s method gives the dynamics of the system field of one among two coherent branches, whereas TEBD numerics generate the superposition of both of them. Therefore, the time dynamics determined by TEBD numerical method undergoes through a non-classical state which is also shown by determining second order correlation function.