Perturbative Analysis of Dark State Dynamics in Weakly Anharmonic Photon-Emitter Pairs

TL;DR

This paper investigates how weak anharmonicity affects dark state dynamics in quantum emitter pairs, providing perturbative corrections to understand dissipation mechanisms.

Contribution

It introduces a perturbative approach to analyze the impact of weak anharmonicity on dark states in coupled quantum systems.

Findings

First and second order wavefunction corrections identified.

Dissipation in dark states arises from anharmonic perturbations.

Method enables tracking of dark state dynamics under weak anharmonicity.

Abstract

Dark states are excited quantum states that decouple from their environment in such a way that they do not emit or absorb external photons. These states are found in a variety of different open quantum systems and can be derived from the collective interactions of individual quantum emitters interacting with one another. One of the simplest model where these states exist is in a pair of dissipatively coupled harmonic oscillators described under the Bose-Hubbard model. When on-site interactions are included, these states can no longer be classified as genuine dark states since dissipation is induced in them. In this paper we study the origin of this dissipation in dark states by using weak anharmonicity as a perturbing factor. In our analysis, we find the first and second order corrections to the wavefunction and apply these corrections to the master equation in order to track the dynamics.