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arXiv:2306.10682

Dark-state induced trapping law in single-photon emission from multiple quantum emitters

Lei Qiao, Jiangbin Gong

Published Jun 19, 2023• 0 citations
arXivHTMLPDF

Abstract

We study the single-photon collective dynamics in a waveguide system consisting of the photon channel with a finite bandwidth and an ensemble of quantum emitters. The size of the volume of these quantum emitters is ignorable when compared with the wavelength of the radiation photons. Based on the analytical calculations beyond the Wigner-Weisskopf and Markovian theories, we present exact solutions to the time evolution of the excited emitters with collective effects. Different from the trapping effect caused by photon-emitter bound states, we find that the dark states in the systems lead to a universal trapping behavior independent of the bosonic bath and the coupling strength between photons and emitters. Instead, the trapping is solely determined by the number of initially excited emitters and the total number of emitters. We demonstrate that such a trapping law can persist even when there are more than one type of emitters in the system. Our findings lead to the prediction that single-photon collective emissions can be strongly suppressed if the number of excited emitters is much less than the total number of emitters in the system.

DOI
10.48550/arxiv.2306.10682

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Abstract This work introduces a theoretical framework to model the collective dynamics of quantum emitters in highly non-Markovian environments, interacting through the exchange of photons with significant retardations. The formalism consists on a set of coupled delay differential equations for the emitter’s raising/lowering operators σ i ± , supplemented by input–output relations that describe the field mediating the interactions. These equations capture the dynamics of both linear (bosonic) and nonlinear (two-level) emitter arrays. It is exact in some limits—e.g. bosonic emitters or generic systems with up to one collective excitation—and can be integrated to provide accurate results for larger numbers of photons. These equations support a study of collective spontaneous emission of emitter arrays in open waveguide-QED environments. This study uncovers an effect we term cascaded super- and sub-radiance, characterized by light-cone-limited propagation and increasingly correlated photon emission across distant emitters. The collective nature of this dynamics for two-level systems is evident both in the enhancement of collective emission rates, as well as in a superradiant burst with a faster than linear growth. While these effects should be observable in existing circuit QED devices or slight generalizations thereof, the formalism put forward in this work can be extended to model other systems such as network of quantum emitters or the generation of correlated photon states.