Quantum Reductive Perturbation Method for Photon Propagations in a Cold Atomic Gas

TL;DR

This paper introduces a quantum reductive perturbation method to derive simplified models for photon propagation in cold atomic gases, enabling analysis of quantum nonlinear phenomena like solitons and bound states.

Contribution

It generalizes classical RPM to quantum systems, providing a new tool for analyzing complex quantum nonlinear problems in photon-atom interactions.

Findings

Derivation of quantum nonlinear Schrödinger equation from quantum Heisenberg-Langevin-Maxwell equations.

Discussion of two-photon bound states and optical solitons in cold atomic gases.

Establishment of a general quantum RPM applicable to various quantum nonlinear systems.

Abstract

We develop a quantum reductive perturbation method (RPM), a generalization of classical RPM widely used in nonlinear wave theory, to derive a simplified model (i.e. quantum nonlinear Schrodinger equation) from fully quantum Heisenberg-Langevin-Maxwell equations describingphoton propagations in a coherent cold atomic gas. The result is used to discuss two-photon bound states and optical solitons in the gas. Though a specific system is considered, the quantum RPM established here is very general and can be applied to other complex quantum nonlinear problems.