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arXiv:2311.04741 · Physical Review Research

Collective photon emission in solid state environments: Concatenating non-Markovian and Markovian dynamics

Devashish Pandey, Martijn Wubs

Published Jul 10, 2024• 6 citations
arXivHTMLPDF

Abstract

Collective light emission and multiqubit dynamics of solid-state quantum emitters are affected both by their coupling to the light field and to lattice vibrations. The effect of phonons on quantum emitters is twofold: polaron formation is described by ultrafast non-Markovian dynamics, while slower dephasing is well described by exponential decay. Of the two temperature-dependent processes, the effect of the former on the collective emission and the entanglement decay of emitters is usually not modeled, and also the latter is sometimes neglected. Here we propose and compare two methods that are efficient also for several emitters: the first method concatenates the fast and slow phonon dynamics, and the second is the polaron method. For a single quantum emitter, we show that the dynamical equations are identical in both methods, while predictions for two or more emitters also agree very well. Both of our methods incorporate non-Markovian dynamics due to phonons demonstrating the temperature sensitivity of the collective photon emission. Utilizing a simplified Markovian model instead may not be accurate enough especially for quantum information applications: for example, we show how the Markovian model may considerably overestimate the two-emitter concurrence, except at very low temperatures. Our concatenation and polaron methods can be applied to an arbitrary number and type of quantum emitters, and beyond the bulk GaAs environment that we consider here. Especially the concatenation method can take phonon effects into account at the same computational cost as modeling the emitter-photon interaction alone. Finally, we present approximate analytical expressions for the collective emission spectrum for N emitters on a one-dimensional chain. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033044

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Collective light emission and multiqubit dynamics of solid-state quantum emitters are affected both by their coupling to the light field and to lattice vibrations. The effect of phonons on quantum emitters is twofold: polaron formation is described by ultrafast non-Markovian dynamics, while slower dephasing is well described by exponential decay. Of the two temperature-dependent processes, the effect of the former on the collective emission and the entanglement decay of emitters is usually not modeled, and also the latter is sometimes neglected. Here we propose and compare two methods that are efficient also for several emitters: the first method concatenates the fast and slow phonon dynamics, and the second is the polaron method. For a single quantum emitter, we show that the dynamical equations are identical in both methods, while predictions for two or more emitters also agree very well. Both of our methods incorporate non-Markovian dynamics due to phonons demonstrating the temperature sensitivity of the collective photon emission. Utilizing a simplified Markovian model instead may not be accurate enough especially for quantum information applications: for example, we show how the Markovian model may considerably overestimate the two-emitter concurrence, except at very low temperatures. Our concatenation and polaron methods can be applied to an arbitrary number and type of quantum emitters, and beyond the bulk GaAs environment that we consider here. Especially the concatenation method can take phonon effects into account at the same computational cost as modeling the emitter-photon interaction alone. Finally, we present approximate analytical expressions for the collective emission spectrum for N emitters on a one-dimensional chain. Published by the American Physical Society 2024
We consider sub- and superradiance of quantum emitters in a solid-state environment. This collective emission depends on the electromagnetic interaction between the emitters that can be engineered via the environment and described by the classical electromagnetic Green function. But also phonons may affect the collective emission. Phonons produce dephasing, both non-exponential fast initial dephasing and slower exponential dephasing. We compared several ways to account for both types of phonon interactions into the more standard optical master equation for an arbitrary number of quantum emitters that mutually interact via the electromagnetic field. In particular we present a concatenation method that incorporates phonon effects without adding computational complexity, suitable for arrays of emitters. Here we use it to study the effects of detunings on two-emitter spectra and on the corresponding population and entanglement dynamics.
Waveguide quantum electrodynamics constitutes a modern paradigm for the interaction of light and matter, in which strong coupling, bath structure, and propagation delays can break the radiative conditions that quantum emitters typically encounter in free space. These characteristics intertwine the excitations of quantum emitters and guided radiation modes to form complex multiphoton dynamics. So far, combining the collective decay of the emitters with the non-Markovian effects induced by the modes has escaped a full solution and the detailed physics behind these systems remains unknown. Here we analyze such a collective non-Markovian decay in a minimal system of two excited emitters coupled to a one-dimensional single-band waveguide. We develop an exact solution for this system in terms of elementary functions that unveils hidden symmetries and predicts new forms of spontaneous decay. The collective non-Markovian dynamics, which are strongly dependent on the vacuum coupling and the detuning from the center of the band, show exotic features that can be characterized with a simple and readily available criterion. Our analytic methods shed light on the complexity of collective light-matter interactions and open up a pathway for understanding multiparticle open quantum systems. Published by the American Physical Society 2024
Abstract This work introduces a theoretical framework to model the collective dynamics of quantum emitters in highly non-Markovian environments, interacting through the exchange of photons with significant retardations. The formalism consists on a set of coupled delay differential equations for the emitter’s raising/lowering operators σ i ± , supplemented by input–output relations that describe the field mediating the interactions. These equations capture the dynamics of both linear (bosonic) and nonlinear (two-level) emitter arrays. It is exact in some limits—e.g. bosonic emitters or generic systems with up to one collective excitation—and can be integrated to provide accurate results for larger numbers of photons. These equations support a study of collective spontaneous emission of emitter arrays in open waveguide-QED environments. This study uncovers an effect we term cascaded super- and sub-radiance, characterized by light-cone-limited propagation and increasingly correlated photon emission across distant emitters. The collective nature of this dynamics for two-level systems is evident both in the enhancement of collective emission rates, as well as in a superradiant burst with a faster than linear growth. While these effects should be observable in existing circuit QED devices or slight generalizations thereof, the formalism put forward in this work can be extended to model other systems such as network of quantum emitters or the generation of correlated photon states.
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 explore the collective Zeno dynamics of giant artificial atoms that are coupled, via multiple coupling points, to a common photonic or acoustic reservoir. In this regime, the establishment of atomic cooperativity and the revivification of exponential decay are highly intertwined, which is utterly beyond the non-Markovian regime with only retarded backaction. We reveal that giant atoms build up their collective emission smoothly from the decay rate of zero to that predicted by Markovian approximation and show great disparity between different waveguide QED setups. As a comparison, the steplike growth of instantaneous decay rates in the retardation-only picture has also been shown. All of these theoretical pictures predict the same collective behavior in the long time limit. From a phenomenological standpoint, we observe that the atomic superradiance exhibits significant directional property. In addition, the subradiant photons feature prolonged oscillation in the early stage of collective radiance, where the energy is exchanged remarkably between giant emitters and the field. Our results might be probed in state-of-art waveguide QED experiments and fundamentally broaden the fields of collective emission in systems with giant atoms. Published by the American Physical Society 2024
Electron-phonon coupling in semiconductor quantum dots plays a significant role in determining the optical properties of excited excitons, especially the spectral nature of emitted photons. This paper presents a comprehensive theory and analysis of emission spectra from artificial atoms or quantum dots coupled to structured photon reservoirs and acoustic phonons, when excited with incoherent pump fields. As specific examples of structured reservoirs, we chose a Lorentzian cavity and a slow-light coupled-cavity waveguide, which have both been explored experimentally. For the case of optical cavities, we directly compare and contrast the spectra from three well-known and distinct theoretical approaches to treat electron-phonon coupling, including a Markovian polaron master equation, a non-Markovian phonon correlation expansion technique, and a semiclassical linear susceptibility approach, and we point out the limitations of these models. For the cavity-QED polaron master equation, which treats the cavity-mode operator at the level of a system operator, we give closed form analytical solutions to the phonon-assisted scattering rates in the weak excitation approximation, fully accounting for temperature, cavity-exciton detuning, and cavity-dot coupling. We also show explicitly why the semiclassical linear susceptibility approach fails to correctly account for phonon-mediated cavity feeding. For weakly coupled cavities, we calculate the optical spectra using a more general photon reservoir polaron master-equation approach, and explain its differences from the above approaches in the low-QQQ limit of a Lorentzian cavity. We subsequently use this general reservoir approach to calculate the emission spectra from quantum dots coupled to slow-light photonic crystal waveguides, which demonstrate a number of striking photon-phonon coupling effects.