# Bound state and non-Markovian dynamics of a quantum emitter around a surface plasmonic nanostructure

## TL;DR

This paper introduces a new theoretical framework to analyze the bound states and non-Markovian decay dynamics of quantum emitters near plasmonic nanostructures, enabling more efficient predictions of their long-term behavior.

## Contribution

It presents a general approach for calculating energy level shifts and excited-state populations without eigenfrequency calculations, advancing understanding of quantum emitter dynamics near plasmonic structures.

## Key findings

- Bound states can be identified using the proposed criterion.
- The formalism accurately predicts long-time excited-state populations.
- Numerical demonstrations validate the approach for nanosphere and nanocavity systems.

## Abstract

A bound state between a quantum emitter (QE) and surface plasmon polaritons (SPPs) can be formed, where the QE is partially stabilized in its excited state. We put forward a general approach for calculating the energy level shift at a negative frequency $\omega$, which is just the negative of the nonresonant part for the energy level shift at positive frequency $-\omega$. We also propose an efficient formalism for obtaining the long-time value of the excited-state population without calculating the eigenfrequency of the bound state or performing a time evolution of the system, in which the probability amplitude for the excited state in the steady limit is equal to one minus the integral of the evolution spectrum over the positive frequency range. With the above two quantities obtained, we show that the non-Markovian decay dynamics in the presence of a bound state can be obtained by the method based on the Green's function expression for the evolution operator. A general criterion for identifying the existence of a bound state is presented. These are numerically demonstrated for a QE located around a nanosphere and in a gap plasmonic nanocavity. These findings are instructive in the fields of coherent light-matter interactions.