Fully quantum mechanical dynamic analysis of single-photon transport in a single-mode waveguide coupled to a traveling-wave resonator

TL;DR

This paper presents a fully quantum mechanical analysis of single-photon transport in a waveguide coupled to a resonator, demonstrating the dynamics, numerical methods, and photon trapping capabilities under various conditions.

Contribution

It introduces a comprehensive quantum model for single-photon transport in coupled waveguide-resonator systems, including numerical techniques and dynamic photon trapping analysis.

Findings

Quantum model reproduces semi-classical results in the appropriate limit.

Adiabatic tuning preserves the invariant of single-photon energy.

Photon trapping is achievable in dynamically tuned coupled cavities.

Abstract

We analyze the dynamics of single photon transport in a single-mode waveguide coupled to a micro-optical resonator using a fully quantum mechanical model. We examine the propagation of a single-photon Gaussian packet through the system under various coupling conditions. We review the theory of single photon transport phenomena as applied to the system and we develop a discussion on the numerical technique we used to solve for dynamical behavior of the quantized field. To demonstrate our method and to establish robust single photon results, we study the process of adiabatically lowering or raising the energy of a single photon trapped in an optical resonator under active tuning of the resonator. We show that our fully quantum mechanical approach reproduces the semi-classical result in the appropriate limit and that the adiabatic invariant has the same form in each case. Finally, we explore the trapping of a single photon in a system of dynamically tuned, coupled optical cavities.