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Quantum Nanophotonic Materials, Devices, and Systems

Non-Markovian dynamics of collective atomic states coupled to a waveguide

Kanu Sinha, Pierre Meystre, Pablo Solano

Published Sep 3, 2019• 5 citations
Publisher

Abstract

When atoms are optically coupled to a one dimensional waveguide, they can interact through macroscopic distances. The retardation effects inherent to field propagation and the associated delay in information backflow between the atoms result in a departure from the familiar Markovian dynamics. We study the case of two two level atoms coupled along a waveguide. One remarkable feature of the dynamics in this regime is the formation of long-lived bound states in the continuum (BIC),30 that refer to a hybrid diatomic molecule bound together by propagating modes of a field. In particular, we study the probability of reaching such a bound states of the system starting in an initially anti-symmetric state of the emitters.

DOI
10.1117/12.2530927

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When atoms are optically coupled to a one dimensional waveguide, they can interact through macroscopic distances. The retardation effects inherent to field propagation and the associated delay in information backflow between the atoms result in a departure from the familiar Markovian dynamics. We study the case of two two level atoms coupled along a waveguide. One remarkable feature of the dynamics in this regime is the formation of long-lived bound states in the continuum (BIC),30 that refer to a hybrid diatomic molecule bound together by propagating modes of a field. In particular, we study the probability of reaching such a bound states of the system starting in an initially anti-symmetric state of the emitters.
We study the collective radiative decay of a system of two two-level emitters coupled to a one-dimensional waveguide in a regime where their separation is comparable to the coherence length of a spontaneously emitted photon. The electromagnetic field propagating in the cavity-like geometry formed by the emitters exerts a retarded backaction on the system leading to strongly non-Markovian dynamics. The collective spontaneous emission rate of the emitters exhibits an enhancement or inhibition beyond the usual Dicke superradiance and subradiance due to self-consistent coherent time-delayed feedback.
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.
Waveguides allow for direct coupling of emitters separated by large distances, offering a path to connect remote quantum systems. However, when facing the distances needed for practical applications, retardation effects due to the finite speed of light are often overlooked. Previous works studied the non-Markovian dynamics of emitters with retardation, but the properties of the radiated field remain mostly unexplored. By considering a toy model of two distant two-level atoms coupled through a waveguide, we study the spectrum of the radiated field that exhibits non-Markovian features such as linewidth broadening beyond standard superradiance, or narrow Fano-resonance-like peaks. We also observe modifications to the energy-exchange dynamics in the presence of retardation. We discuss a proof-of-concept implementation of our results in a superconducting circuit platform.
Quantum emitters coupled to a waveguide are a paradigm of quantum optics, whose essential properties are described by waveguide quantum electrodynamics (QED). We study the possibility of observing the typical features of the conventional waveguide QED scenario in a system where the role of the waveguide is played by a one-dimensional subwavelength atomic array. For the role of emitters, we propose to use antisymmetric states of atomic dimers---a pair of closely spaced atoms---as effective two-level systems, which significantly reduces the effect of free-space spontaneous emission. We solve the dynamics of the system both when the dimer frequency lies inside and when it lies outside the band of modes of the array. Along with well-known phenomena of collective emission into the guided modes and waveguide-mediated long-range dimer-dimer interactions, we uncover significant non-Markovian corrections which arise from both the finiteness of the array and through retardation effects.
The non-Markovian effects of open quantum systems subjected to external environments are deemed to be valuable resources in quantum optics and quantum information processing. In this work, we construct the model Hamiltonian of three-level giant atom with multiple coupling points in the semi-infinite photonic waveguide via complex coupling coefficients and investigate the non-Markovian dynamics of the three-level giant atom driven by a classical laser field. In the non-Markovian regime, the traveling time of a photon between different coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the giant atom. We derive the analytical expressions for the probability amplitudes of the driven three-level giant atom by solving a set of delay differential equations and obtain two independent conditions of bound states' formation that can inhibit the dissipation. We find two different types of bound states (including the static bound states and the periodic equal-amplitude oscillating bound states) and discuss the physical origins of the bound states' formation. Moreover, we discuss the case of the driven three-level giant atom interacting with the infinite photonic waveguide, where there is only one purely imaginary solution (i.e., only one bound-state condition exists) for its complex frequency (coming from the absence of mirror at one end of the waveguide) compared to that of a driven three-level giant atom coupling with a semi-infinite photonic waveguide. With this, we also find two different types of bound states, including the static bound state and the periodic equal-amplitude oscillating bound states. We study the influences of the phase in the coupling strength on the bound states in semi-infinite and infinite photonic waveguides. The presented protocol might open a way to better understand exactly the non-Markovian dynamics of driven multilevel giant atoms interacting with semi-infinite (or infinite) photonic waveguides.
Non‐Markovian Dynamics with ΛΛ\LambdaΛ‐Type Atomic Systems in a Single‐End Photonic Waveguide
Abstract In this work, the non‐Markovian dynamical evolution of a ‐type atom interacting with a semi‐infinite 1D photonic waveguide via two atomic transitions is investigated. The waveguide terminates at a perfect mirror, which reflects the light and introduces boundary effects. Exact analytical expressions are derived and it is shown 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, the output field intensity is analyzed and it is demonstrated that blocking one of the coupling channels forces the atomic system to emit photons of a single frequency. Finally, the model is extened to a two‐atom system and the disentanglement dynamics of the two spatially separated atoms are examined. 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.