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

Souvik Agasti

doi:10.1088/2399-6528/ab4690

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.

Highlights

The Kerr effect was discovered by John Kerr in 1875 [1], which exhibits quadratic electro-optic (QEO) effect, is seen in almost all materials, but certain materials display more strongly than others, for example organic molecules and polymers [2], Se-based chalcogenide glasses [3] and silicon photonic devices [4]
We plot the steady state system field and the second order correlation function in figure 2 which presents both the numerical results determined through time evolving block decimation (TEBD) and the time propagation of the system field using Euler’s method, along with the analytically determined semi-classical and quantum mechanical solution, which shows how the TEBD numerical result is analogous to classical bistability
We have used TEBD numerical technique and Euler’s method successfully for the time propagation of the system field of a Kerr nonlinear system, and studied how the numerical results are analogous to classical bistability

Summary

October 2019

We simulate coherent driven free dissipative Kerr nonlinear system numerically using Euler’s method licence. By solving Heisenberg equation of motion and time evolving block decimation (TEBD) algorithm, Any further distribution of this work must maintain and demonstrate how the numerical results are analogous to classical bistability. The comparison with attribution to the analytics show that the TEBD numerics follow the quantum mechanical exact solution obtained by author(s) and the title of the work, journal citation 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. The time dynamics determined by TEBD numerical method undergoes through a non-classical state which is shown by determining second order correlation function

Introduction

Conclusion