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Physical Review A

Atom-photon bound states and non-Markovian cooperative dynamics in coupled-resonator waveguides

Lei Qiao, Chang-Pu Sun

Published Dec 4, 2019• 14 citations
Publisher

Abstract

We study the properties of atom-photon bound states and single-photon cooperative dynamics in a waveguide system which consists of a finite-bandwidth channel with model dispersion and an ensemble of two-level atoms whose size is ignorable when compared with the lattice constant. The bound states are formed by all atoms and a localized photonic excitation. We find that the effect of atomic collection is equivalent to the case of one atom by rescaling the coupling strength with the square root of the atom number, as far as the eigenenergy equation is concerned. Besides, it is found there is a quantum phase transition when more than one type of atom are present. The characteristic lengths and wave functions are analyzed near the phase transition point. The exact analytical results for the cooperative dynamics at the single excitation level are obtained and we point out the dark state in this system leads to a universal population trapping in the time evolution process. This type of trapping obeys a simple law that is only associated with the atom number. A direct conclusion that results from the trapping law is that the single-photon cooperative emission is suppressed when the number of atoms is large enough.

DOI
10.1103/physreva.100.063806

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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.
The single-photon cooperative dynamics of an assembly of two-level quantum emitters coupled by a bosonic bath is investigated. The bosonic bath is general and can be anything as long as the exchange of excitations between quantum emitters and bath is present. In these systems it is found that the population on the excited emitter keeps a simple and universal trapping law due to the existence of the system's dark states. Different from the trapping regime caused by photon-emitter dressed states, this type of trapping is only associated with the number of quantum emitters. According to the trapping law, cooperative spontaneous emission at the single-photon level in this kind of system is universally inhibited when the emitter number is large enough.
Non-Markovian dynamics with ΛΛΛ-type atomic systems in a single end photonic waveguide
In this work, we investigate the non-Markovian dynamical evolution of a ΛΛΛ-type atom interacting with a semi-infinite one-dimensional photonic waveguide via two atomic transitions. The waveguide terminates at a perfect mirror, which reflects the light and introduces boundary effects. We derive exact analytical expressions and show that, under suitable conditions, the instantaneous and retarded decay rates reach equilibrium, leading to the formation of an atom-photon bound state that suppresses dissipation. Consequently, the atom retains a long-lived population in the asymptotic time limit. Furthermore, we analyze the output field intensity and demonstrate that blocking one of the coupling channels forces the atomic system to emit photons of a single frequency. Finally, we extend the model to a two-atom system and examine the disentanglement dynamics of the two spatially separated atoms. These findings elucidate the dynamic process of spontaneous emission involving multi-frequency photons from multi-level atoms and provide insights into the complex interference between different decay pathways.
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We investigate one- and two-photon scattering in a one-dimensional waveguide coupled to a giant atom within the non-Markovian regime using the resolvent approach. The non-Markovian behavior gives rise to an atom-photon bound state that cannot be excited by a single incident photon. However, the bound state can be excited via the two-photon scattering process described by multichannel scattering theory, from which an analytical trapping probability of a photon in the bound state can be achieved. Additionally, we analyze the two-photon scattering process, obtaining the analytical expressions for scattered states. As non-Markovian effects strengthen, two peaks appear in the incoherent power spectrum, attributed to the system behaving as a leaky cavity formed by the giant atom's coupling points. Through the analysis of second-order correlation functions, we observe the bunching behavior for transmitted photons, antibunching behavior for reflected photons, and the distinctive retrieval behavior at the coupling points' separation.
Abstract We investigate the quantum dynamics of two two-level atoms coupled to a one-dimensional resonator waveguide. Using the resolvent method, we obtain exact analytical solutions for the atomic evolution and photon scattering processes within the single-excitation subspace. The photonic band structure of the waveguide dictates distinctly different dynamical regimes. For atomic frequencies at the band center and small interatomic separation, the system exhibits Markovian decay and relaxes into a steady-state subradiant Bell entangled state. In contrast, near the band edge, non-Markovian dynamics dominates, leading to the formation of atom-photon bound states that mediate persistent, coherent interactions between the atoms. Furthermore, we demonstrate that the atomic detuning and separation provide effective control over singlephoton scattering, enabling a tunable quantum interface.