Canonical quantization of a dissipative system interacting with an anisotropic non-linear absorbing environment

TL;DR

This paper develops a canonical quantization framework for a quantum system interacting with an anisotropic, nonlinear absorbing environment, deriving equations of motion and analyzing effects on spontaneous emission.

Contribution

It introduces a novel quantization scheme for nonlinear, anisotropic environments and derives the nonlinear Langevin-Schrodinger equation for dissipative systems.

Findings

Derived the nonlinear response equation of the environment.

Formulated the nonlinear Langevin-Schrodinger equation.

Analyzed the impact of environmental nonlinearity on spontaneous emission.

Abstract

A canonical quantization scheme is represented for a quantum system interacting with a nonlinear absorbing environment. The environment is taken anisotropic and the main system is coupled to its environment through some coupling tensors of various ranks. The nonlinear response equation of the environment against the motion of the main system is obtained. The nonlinear Langevin-schr\"{o}dinger equation is concluded as the macroscopic equation of motion of the dissipative system. The effect of nonlinearity of the environment is investigated on the spontaneous emission of an initially excited two level-atom imbedded in such an environmrnt.