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Journal of the Optical Society of America B

Exact approach for spatiotemporal dynamics of spontaneous emissions in waveguide quantum electrodynamic systems

Yuecheng Shen, Zihao Chen, Yu He, Zhaohui Li, Jung‐Tsung Shen

Published Feb 14, 2018• 11 citations
Publisher

Abstract

We propose an exact analytical approach to study the single-photon spontaneous emissions in waveguide quantum electrodynamic (QED) systems. Using the ab initio evolution technique, our approach provides a universal framework to investigate the full spatiotemporal dynamics of the atomic response, the cavity response, and the emitted photonic wave functions. The validity of the analytical approach is numerically confirmed. Our rigorous approach can be extensively applied to more complicated waveguide QED architectures. Moreover, such an approach can readily incorporate the effects of dissipations and has the potential to tremendously facilitate the design of spontaneous emission-driven quantum nanophotonic devices in the dissipative regime.

DOI
10.1364/josab.35.000607

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We propose an exact analytical approach to study the single-photon spontaneous emissions in waveguide quantum electrodynamic (QED) systems. Using the ab initio evolution technique, our approach provides a universal framework to investigate the full spatiotemporal dynamics of the atomic response, the cavity response, and the emitted photonic wave functions. The validity of the analytical approach is numerically confirmed. Our rigorous approach can be extensively applied to more complicated waveguide QED architectures. Moreover, such an approach can readily incorporate the effects of dissipations and has the potential to tremendously facilitate the design of spontaneous emission-driven quantum nanophotonic devices in the dissipative regime.
Understanding transport properties in quantum nanophotonics plays a central role in designing few-photon devices, yet it suffers from a longstanding extensive computational burden. In this work, we propose a statistically driven model with a tremendously eased computational burden, which is based on the deep understanding of the few-photon spontaneous emission process. By utilizing phenomenological, statistically driven inter-photon offset parameters, the proposed model expedites the transport calculation with a three-order-of-magnitude enhancement of speed in contrast to conventional numerical approaches. We showcase the two-photon transport computation benchmarked by the rigorous analytical approach. Our work provides an efficient tool for designing few-photon nano-devices, and it significantly deepens the understanding of correlated quantum many-body physics.
Waveguide quantum electrodynamics platforms have emerged as promising candidates for exploring and implementing non-Markovian quantum phenomena. In this work, we investigate the formation and dynamics of superpositions of bound states in a cavity array waveguide coupled to two spatially separated quantum emitters. By tuning the system parameters, we show that spontaneous emission can drive the system into non-local equilibrium states in which both photonic and emitter populations exhibit persistent oscillations. These states arise from the coexistence of bound states embedded in the energy continuum and bound states outside it, leading to hybrid oscillatory modes. We analytically derive the conditions required for the emergence of these states, numerically simulate their formation through spontaneous emission, and predict their long-time behaviour. Our results demonstrate that such bound-state superpositions enable the generation of emitter-emitter interaction through free evolution, while supporting oscillatory breathing modes of the photon density between the emitters.
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.
Abstract The waveguide quantum electrodynamics (QED) system may have important applications in quantum device and quantum information technology. In this article we review the methods being proposed to calculate photon transport in a one-dimensional (1D) waveguide coupled to quantum emitters. We first introduce the Bethe ansatz approach and the input–output formalism to calculate the stationary results of a single photon transport. Then we present a dynamical time-dependent theory to calculate the real-time evolution of the waveguide QED system. In the longtime limit, both the stationary theory and the dynamical calculation give the same results. Finally, we also briefly discuss the calculations of the multiphoton transport problems.
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 investigate the effects of a nanophotonic boundary on the spontaneous emission properties of an excited two-level atom in cavity quantum electrodynamics (QED) geometry. We show that a boundary provides temporally delayed interference, which can be either constructive or destructive. Consequently, the decay of the atomic excitation can be either increased or greatly inhibited. As a concrete example, we investigate the spontaneous emission process in cavity QED with a terminated line-defect waveguide, and show the rich behavior of the atomic response due to the boundary. We also show that the output photonic wave form is strongly influenced by the boundary.