Multi-level quantum emitter in an optical waveguide: paradoxes and resolutions

TL;DR

This paper explores complex quantum interactions in multi-level emitters within optical waveguides, resolving paradoxes related to photon flux directions and polarization effects, and demonstrating applications like non-destructive photon number measurement.

Contribution

It provides a theoretical framework for understanding paradoxical quantum states and polarization-dependent behaviors in multi-level quantum emitters in waveguides, including a case study on parity measurement.

Findings

Non-orthogonal states can produce opposite photon flux directions without violating quantum mechanics.

An isotropic emitter's transmission or reflection depends on local polarization, changing with infinitesimal polarization rotations.

A four-level system can perform non-destructive parity measurements of photon number.

Abstract

We theoretically investigate the optical dipole interaction between a multi-level quantum system and a single-mode optical waveguide of any local polarisation. We investigate several paradoxical seeming situations, for example we find a situation in which there exist two non-orthogonal quantum states, each of which results in a photon flux in the opposite direction to the other. We show how, despite appearances, this does not break the unitary requirements of quantum mechanics. We also find that an isotropic quantum emitter can be either reflective or transmissive to light depending on the waveguide polarisation at the emitter location, indeed in the zero loss limit such a system changes from 100% transmission to 100% reflection due to an infinitesimal polarisation rotation. An example case for a four level system is also considered, which is found to operate as a non-destructive parity measurement of the photon number.