Dynamical theory of single photon transport in a one-dimensional waveguide coupled to identical and non-identical emitters

TL;DR

This paper presents a comprehensive dynamical theory for single photon transport in a 1D waveguide coupled to multiple emitters, accounting for waveguide and non-waveguide modes, revealing new effects like narrow transparency windows.

Contribution

It introduces a general dynamical framework that includes non-waveguide vacuum modes and analyzes effects of non-identical emitters on photon transport.

Findings

Dipole-dipole interactions significantly affect emitter dynamics.

Non-identical emitters can create narrow transparency windows.

The theory predicts applications in quantum optical devices.

Abstract

We develop a general dynamical theory for studying a single photon transport in a one-dimensional (1D) waveguide coupled to multiple emitters which can be either identical or non-identical. In this theory, both the effects of the waveguide and non-waveguide vacuum modes are included. This theory enables us to investigate the propagation of an emitter excitation or an arbitrary single photon pulse along an array of emitters coupled to a 1D waveguide. The dipole-dipole interaction induced by the non-waveguide modes, which is usually neglected in the literatures, can significantly modify the dynamics of the emitter system as well as the characteristics of output field if the emitter separation is much smaller than the resonance wavelength. Non-identical emitters can also strongly couple to each other if their energy difference is smaller than or of the order of the dipole-dipole energy shift. Interestingly, if their energy difference is close but non-zero, a very narrow transparency window around the resonance frequency can appear which does not occur for identical emitters. This phenomenon may find important applications in quantum waveguide devices such as optical switch and ultra narrow single photon frequency comb generator.