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Physical Review A

Retardation-dependent decaying modes of a single excitation in an atomic array coupled to a one-dimensional waveguide

Lezhi Lo, C. K. Law

Published Mar 3, 2022• 1 citation
Publisher

Abstract

We investigate the effects of retardation on the collective emissions from a linear array of $N\ensuremath{\ge}2$ atoms interacting with a one-dimensional field continuum. Decaying modes consisting of a single excitation in a photon-atom superposition with definite decay rates and frequency shifts are determined as a function of a retardation parameter proportional to the separation between atoms. In particular, the structures of these decaying modes are examined in terms of their photonic and atomic components. In addition to modes that resemble Dicke states in the Markovian limit, higher modes that decay much faster than Dicke superradiance exist. We find that these modes are dominantly photonic with field excitation localized near the edges of the array.

DOI
10.1103/physreva.105.033703

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We investigate the effects of retardation on the collective emissions from a linear array of N\ensuremath≥2N\ensuremath{\ge}2N\ensuremath≥2 atoms interacting with a one-dimensional field continuum. Decaying modes consisting of a single excitation in a photon-atom superposition with definite decay rates and frequency shifts are determined as a function of a retardation parameter proportional to the separation between atoms. In particular, the structures of these decaying modes are examined in terms of their photonic and atomic components. In addition to modes that resemble Dicke states in the Markovian limit, higher modes that decay much faster than Dicke superradiance exist. We find that these modes are dominantly photonic with field excitation localized near the edges of the array.
To build up a collective emission, the atoms in an ensemble must coordinate their behavior by exchanging virtual photons. We study this non-Markovian process in a subwavelength atom chain coupled to a one-dimensional (1D) waveguide and find that retardation is not the only cause of non-Markovianity. The other factor is the memory of the photonic environment, for which a single excited atom needs a finite time, the Zeno regime, to transition from quadratic decay to exponential decay. In the waveguide setup, this crossover has a time scale longer than the retardation, thus impacting the development of collective behavior. By comparing a full quantum treatment with an approach incorporating only the retardation effect, we find that the field memory effect, characterized by the population of atomic excitation, is much more pronounced in collective emissions than that in the decay of a single atom. Our results maybe useful for the dissipation engineering of quantum information processings based on compact atom arrays.
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.
We study the collective spontaneous emission of a linear atomic chain excited by a single photon. The interaction between the atoms and the common vacuum field can significantly change the eigenenergy and the spontaneous emission rate of the system. Due to the dipole-dipole interactions, the system prepared in a single-photon timed Dicke state is the superposition of superradiant and subradiant eigenstates that can have a nonexponential decay dynamics. We can tune the frequency and linewidth of the superradiant and subradiant emission from a timed Dicke state by changing the direction of the atomic dipole moment or the atomic separation. In addition, the emission direction of the superradiant and subradiant photons also depends on the polarization of the atoms.
We present a comprehensive quantum electrodynamical analysis of the interaction between a continuum with photonic band gaps (PBGs) or frequency cut-off and an excited two-level atom, which can be either ‘bare’ or ‘dressed’ by coupling to a near-resonant field mode. A diversity of novel features in the atom and field dynamics is shown to arise from the non-Markovian character of radiative decay into such a continuum of modes. Firstly the excited atom is shown to evolve, by spontaneous decay, into a superposition of non-decaying single-photon dressed states, each having an energy in a different PBG, and a decaying component. This superposition is determined by the atomic resonance shift, induced by the spontaneously emitted photon, into or out of a PBG. The main novel feature exhibited by the decaying excited-state component is the occurrence of beats between the shifted atomic resonance frequency and the PBG cut-off frequencies, corresponding to a non-Lorentzian emission spectrum. Secondly the induced decay of a resonantly driven atom into such a continuum exhibits a cascade of transitions down the ladder of dressed states, which are labelled by decreasing photon numbers of the driving mode. Remarkably, this cascade is terminated at the dressed-state doublet, from which all subsequent transitions to lower doublets are forbidden because they fall within the PBG. This doublet then becomes an attractor state for the populations of higher-lying doublets. As a result, the photon-number distribution of the driving mode becomes strongly sub-Poissonian.
We present a framework to investigate the collective properties of atomic lattices in one, two, and three dimensions. We analyze the single-photon band structure and associated atomic decay rates, revealing a fundamental dependence on dimensionality. One- and two-dimensional arrays are shown to be inherently radiative, exhibiting band gaps and decay rates that oscillate between superradiant and subradiant regimes, as a function of lattice spacing. In contrast, three-dimensional lattices are found to be fundamentally non-radiative due to the inhibition of spontaneous emission, with decay only at discrete Bragg resonances. Furthermore, we demonstrate that this structural difference dictates the system dynamics, which crosses over from dissipative decay in lower dimensions to coherent transport in three dimensions. Our results provide insight into cooperative effects in atomic arrays at the single-photon level.
We study the superradiant decay of a chain of atoms coupled to a chiral waveguide, focusing on the regime of non-negligible photon propagation time. Using an exact master equation description that accounts for delay effects, we obtain evidence to suggest that competition between collective decay and retardation leads to the emergence of an effective maximum number of atoms able to contribute to the superradiant dynamics, resulting in a plateau of the peak emission rate. To develop this analysis further, we investigate the interatomic correlations to find features consistent with the formation of individual superradiant domains. Moreover, we find that retardation can also result in persistent oscillatory atomic dynamics accompanied by a periodic sequence of emission bursts.