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arXiv:2504.09281 · Physical Review A

Non-Markovian spontaneous emission in a tunable cavity formed by atomic mirrors

Annyun Das, Pablo Solano, Kanu Sinha

Published Sep 30, 2025• 4 citations
arXivHTMLPDF

Abstract

We analyze the non-Markovian spontaneous-emission dynamics of a two-level test atom placed in a cavity formed by two atomic arrays in a waveguide quantum electrodynamics (QED) setup. We demonstrate a crossover from single-mode to multimode strong-coupling cavity QED as the cavity length $\ensuremath{\sim}d$ becomes comparable to the coherence length associated with collective spontaneous emission $\ensuremath{\sim}v/(N\ensuremath{\gamma})$. The resulting non-Markovian dynamics of the test atom and the emergent spectral density of the field are analyzed as a function of various tunable atomic array parameters: the number of atoms, length of the atomic cavity, and resonance frequency of the atoms forming the atomic mirrors. Our results show limitations to cooperatively enhanced light-matter coupling in the presence of time-delayed feedback. We further illustrate that the non-Markovian system dynamics can be efficiently approximated in terms of a few modes of the emergent spectral density of the field.

DOI
10.1103/29yv-12sq

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We analyze the non-Markovian spontaneous-emission dynamics of a two-level test atom placed in a cavity formed by two atomic arrays in a waveguide quantum electrodynamics (QED) setup. We demonstrate a crossover from single-mode to multimode strong-coupling cavity QED as the cavity length \ensuremath∼d\ensuremath{\sim}d\ensuremath∼d becomes comparable to the coherence length associated with collective spontaneous emission \ensuremath∼v/(N\ensuremathγ)\ensuremath{\sim}v/(N\ensuremath{\gamma})\ensuremath∼v/(N\ensuremathγ). The resulting non-Markovian dynamics of the test atom and the emergent spectral density of the field are analyzed as a function of various tunable atomic array parameters: the number of atoms, length of the atomic cavity, and resonance frequency of the atoms forming the atomic mirrors. Our results show limitations to cooperatively enhanced light-matter coupling in the presence of time-delayed feedback. We further illustrate that the non-Markovian system dynamics can be efficiently approximated in terms of a few modes of the emergent spectral density of the field.
Abstract Arrays of atoms coupled to waveguides can behave as mirrors. We consider an array of three-level atoms, with one excited and two ground levels, assuming one of the ground levels to be decoupled from the other two. Preparing the atoms in the coupled or decoupled ground state leads to reflection or transmission of the guided electromagnetic field; a superposition of the two ground states thus corresponds to a coherent superposition of mirror-like and transparent boundary conditions. We analyze the spontaneous emission of an excited two-level atom in the presence of such a quantum mirror, and inside a cavity formed by quantum mirrors, demonstrating that the resulting dynamics of the excited atom can exhibit exotic features, e.g. a superposition of Rabi cycle and exponential decay. Our results pave the way for exploring quantum electrodynamics (QED) phenomena in a paradigm wherein boundary conditions can exhibit quantum superpositions and correlations.
Spontaneous emission of a quantum emitter, such as an excited atom, is a fundamental process in quantum electrodynamics (QED), typically associated with exponential decay to the ground state accompanied by irreversible photon emission. This simple Markovian picture, however, is profoundly modified in the presence of time-delayed feedback, structured continua, or cooperative emission, as occurs when an emitter radiates in front of a mirror, when several emitters radiate collectively, or in the case of a giant atom. In such regimes, strong non-Markovian dynamics arise from photon reabsorption and interference effects, leading to pronounced deviations from exponential decay. Here we demonstrate the emergence of exceptional points (EPs) in these highly non-Markovian waveguide-QED environments, i.e., non-Markovian EPs. These EPs appear directly in the relaxation dynamics as sharp transitions to oscillatory behavior, manifested by the appearance of real zeros in the excited-state amplitude. We analyze in detail the spontaneous emission of giant atoms with two or more coupling points, highlighting the mechanisms leading to non-Markovian EPs, and show that similar phenomena arise in other waveguide-QED settings, such as the collective spontaneous emission of spatially separated point-like emitters. Our results reveal waveguide-QED systems as experimentally accessible platforms for realizing and exploring non-Markovian EP physics.
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.
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.
We introduce a picture to describe and interpret waveguide-QED problems in the non-Markovian regime of long photonic retardation times resulting in delayed coherent feedback. The framework is based on an intuitive spatial decomposition of the waveguide into blocks. Among these, the block directly coupled to the atoms embodies an effective lossy multimode cavity leaking into the rest of the waveguide, in turn embodying an effective white-noise bath. The dynamics can be approximated by retaining only a finite number of cavity modes, which grows with the time delay. This description captures the atomic as well as the field’s dynamics, even with many excitations, in both emission and scattering processes. As an application, we show that the recently identified non-Markovian steady states can be understood by retaining very few or even only one cavity mode.
Here, we report an experimental realization of multimode strong coupling in cavity quantum electrodynamics.This novel regime is achieved when a single artificial atom is simultaneously strongly coupled to a large, but discrete, number of nondegenerate photonic modes of a cavity with coupling strengths comparable to the free spectral range.Our experiment reveals complex quantum multimode dynamics and spontaneous generation of quantum coherence, as evidenced by resonance fluorescence spanning many modes and ultranarrow linewidth emission.This work opens a new avenue for future experiments in light-matter interactions and poses a challenge to current theoretical approaches to its study.