Quantum theory for spatial motion of polaritons in inhomogeneous fields

TL;DR

This paper develops a quantum theoretical framework describing the spatial motion of polaritons in inhomogeneous fields, revealing their anisotropic behavior and light-bending effects akin to particle trajectories in varying media.

Contribution

It introduces an effective Schrödinger equation for polaritons in inhomogeneous fields, highlighting their anisotropic motion and the resulting light-bending phenomena.

Findings

Polaritons exhibit anisotropic motion with relativistic and non-relativistic characteristics.

External field inhomogeneity causes light ray bending in EIT media.

The theory demonstrates the particle-like properties of polaritons in spatially varying fields.

Abstract

Polaritons are the collective excitations of many atoms dressed by resonant photons, which can be used to explain the slow light propagation with the mechanism of electromagnetically induced transparency. As quasi-particles, these collective excitations possess the typical feature of the matter particles, which can be reflected and deflected by the inhomogeneous medium in its spatial motion with some velocity. In this paper we develop a quantum theory to systematically describe the spatial motion of polaritons in inhomogeneous magnetic and optical fields. This theoretical approach treats these quasi-particles through an effective Schr\"{o}dinger equation with anisotropic depression that the longitudinal motion is like a ultra-relativistic motion of a "slow light velocity" while the transverse motion is of non-relativity with certain effective mass. We find that, after passing through the EIT medium, the light ray bends due to the spatial-dependent profile of external field. This phenomenon explicitly demonstrates the exotic corpuscular property of polaritons with anisotropic nature.