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Laser & Photonics Review

Breaking the Exponential: Decoherence‐Driven Power‐Law Spontaneous Emission in Waveguide Quantum Electrodynamics

Stefano Longhi

Published Jan 15, 2026• 0 citations
Publisher

Abstract

ABSTRACT We investigate the spontaneous emission of a two‐level system coupled to a photonic waveguide, showing that dynamical dephasing in the photon modes profoundly alters the decay law. In the absence of dephasing, the emitter displays conventional exponential decay followed by a long‐time power‐law tail – observable only at extremely low survival probabilities. Strikingly, when dephasing is introduced, a robust power‐law decay emerges already at short times, driven by photon diffusion in the dynamically disordered environment rather than spectral edge effects. These results reveal a novel, decoherence‐induced mechanism for non‐exponential spontaneous emission in waveguide QED platforms.

DOI
10.1002/lpor.202501986

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ABSTRACT We investigate the spontaneous emission of a two‐level system coupled to a photonic waveguide, showing that dynamical dephasing in the photon modes profoundly alters the decay law. In the absence of dephasing, the emitter displays conventional exponential decay followed by a long‐time power‐law tail – observable only at extremely low survival probabilities. Strikingly, when dephasing is introduced, a robust power‐law decay emerges already at short times, driven by photon diffusion in the dynamically disordered environment rather than spectral edge effects. These results reveal a novel, decoherence‐induced mechanism for non‐exponential spontaneous emission in waveguide QED platforms.
We investigate the spontaneous emission of a two-level system coupled to a photonic waveguide, showing that dynamical dephasing in the photon modes profoundly alters the decay law. In the absence of dephasing, the emitter displays conventional exponential decay followed by a long-time power-law tail -- observable only at extremely low survival probabilities. Strikingly, when dephasing is introduced, a robust power-law decay emerges already at short times, driven by photon diffusion in the dynamically disordered environment rather than spectral edge effects. These results reveal a novel, decoherence-induced mechanism for non-exponential spontaneous emission in waveguide QED platforms.
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 spontaneous decay of an impurity coupled to a linear array of bosonic cavities forming a single-band photonic waveguide. The average frequency of the emitted photon is different from the frequency for single-photon resonant scattering, which perfectly matches the bare frequency of the excited state of the impurity. We study how the energy of the excited state of the impurity influences the spatial profile of the emitted photon. The farther the energy is from the middle of the photonic band, the farther the wave packet is from the causal limit. In particular, if the energy lies in the middle of the band, the wave packet is localized around the causal limit. Besides, the occupation of the excited state of the impurity presents a rich dynamics: it shows an exponential decay up to intermediate times, this is followed by a power-law tail in the long-time regime, and it finally reaches an oscillatory stationary regime. Finally, we show that this phenomenology is robust under the presence of losses, both in the impurity and in the cavities.
The decay of an unstable system is usually described by an exponential law. Quantum mechanics predicts strong deviations of the survival probability from the exponential: Indeed, the decay is initially quadratic, while at very large times it follows a power law, with superimposed oscillations. The latter regime is particularly elusive and difficult to observe. Here we employ arrays of single-mode optical waveguides, fabricated by femtosecond laser direct inscription, to implement quantum systems where a discrete state is coupled and can decay into a continuum. The optical modes correspond to distinct quantum states of the photon, and the temporal evolution of the quantum system is mapped into the spatial propagation coordinate. By injecting coherent light states in the fabricated photonic structures and by measuring a small scattered fraction of such light with an unprecedented dynamic range, we are able to experimentally observe not only the exponential decay regime, but also the quadratic Zeno region and the power-law decay at long evolution times.
Abstract Waveguide quantum electrodynamics (QED) system manifests an ideal platform for studying many-body physics. When multiple emitters are coupled to a common waveguide, subradiant states may arise because of the waveguide-mediated interaction, leading to a long lifetime because of their immunity to the waveguide mode-induced dissipation. However, they can still be influenced by local environments, which are incoherent for different emitters and cannot be canceled out through interference. Herein, a new mechanism termed energy quantum confinement effect (EQCE) is proposed in a non-Markovian waveguide QED system to suppress the local dissipation. The energy quantum is confined in the waveguide by emitters, suppressing spontaneous decay of the emitters. The EQCE makes the system partly free from local dissipation of emitters, leading to a total decay rate lower than the local decay rate. We further show that similar effect occurs spontaneously by self-interference and can be stressed by cooperative coupling, relaxing the requirement for initializing the emitters into a remotely entangled state.
We have theoretically studied the effect of deterministic temporal control of spontaneous emission in a dynamic optical microcavity. We propose a new paradigm in light emission: we envision an ensemble of two-level emitters in an environment where the local density of optical states is modified on a time scale shorter than the decay time. A rate equation model is developed for the excited state population of two-level emitters in a time-dependent environment in the weak coupling regime in quantum electrodynamics. As a realistic experimental system, we consider emitters in a semiconductor microcavity that is switched by free-carrier excitation. We demonstrate that a short temporal increase of the radiative decay rate depletes the excited state and drastically increases the emission intensity during the switch time. The resulting time-dependent spontaneous emission shows a distribution of photon arrival times that strongly deviates from the usual exponential decay: A deterministic burst of photons is spontaneously emitted during the switch event.