Confining stationary light: Dirac dynamics and Klein tunneling

TL;DR

This paper explores how tightly confined stationary light pulses in atomic ensembles can be described by a Dirac equation, revealing a fundamental limit to their spatial width due to Klein tunneling, with controllable relativistic effects.

Contribution

It introduces a framework where stationary light in atomic media obeys a Dirac equation, linking optical confinement to relativistic quantum phenomena and identifying a lower spatial limit from Klein tunneling.

Findings

Stationary light pulses obey a Dirac equation with effective parameters.

A fundamental spatial confinement limit arises from Klein tunneling.

Relativistic effects can be observed at macroscopic scales due to controllable parameters.

Abstract

We discuss the properties of 1D stationary pulses of light in atomic ensemble with electromagnetically induced transparency in the limit of tight spatial confinement. When the size of the wavepacket becomes comparable or smaller than the absorption length of the medium, it must be described by a two-component vector which obeys the one-dimensional two-component Dirac equation with an effective mass $m^*$ and effective speed of light $c^*$. Then a fundamental lower limit to the spatial width in an external potential arises from Klein tunneling and is given by the effective Compton length $\lambda_C = \hbar/(m^* c^*)$. Since $c^*$ and $m^*$ can be externally controlled and can be made small it is possible to observe effects of the relativistic dispersion for rather low energies or correspondingly on macroscopic length scales.