Ehrenfest+R dynamics. I. A mixed quantum–classical electrodynamics simulation of spontaneous emission

Chen, Hsing-Ta; Li, Tao E.; Sukharev, Maxim; Nitzan, Abraham; Subotnik, Joseph E.

doi:10.1063/1.5057365

Cited by 34 publications

(68 citation statements)

References 74 publications

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“…In contrast to the free-space case, the quantum effects due to fluctuations, such as spontaneous emission, are not negligible here, and the mean-field approximation (shown in subplots a, c and e) fails to capture the dynamics as it can only represent the coherent contribution to the light-matter interaction 27 . In the short-pulse case, Fig.…”

Section: B Cavitymentioning

confidence: 82%

“…Since a n = σ x = σ y = 0 at t = 0 and no external electric field affects the system, no dynamics are predicted. Going beyond mean-field is thus essential to describe spontaneous emission 27,67 . On the other hand, the second-order cumulant expansion (and all higherorder approaches, not shown) already perfectly describes the free-space spontaneous decay of σ + σ − due to the vacuum fluctuations.…”

Section: A Free Space Dynamicsmentioning

confidence: 99%

“…This approach in principle allows for the description of arbitrary photonic structures, but misses all effects due to the quantization of the EM field, such as spontaneous emission. Recently, several groups have extended these approaches to allow for a more complete description, based on, e.g., an Ehrenfest+Relaxation approach 27,28 or cavity quantum electrodynamics with multi-trajectory Ehrenfest dynamics 29 .…”

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confidence: 99%

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Cumulant expansion for the treatment of light–matter interactions in arbitrary material structures

Mónica

Silva

Feist

2020

The Journal of Chemical Physics

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Strong coupling of quantum emitters with confined electromagnetic modes of nanophotonic structures may be used to change optical, chemical and transport properties of materials, with significant theoretical effort invested towards a better understanding of this phenomenon. However, a full theoretical description of both matter and light is an extremely challenging task. Typical theoretical approaches simplify the description of the photonic environment by describing it as a single or few modes. While this approximation is accurate in some cases, it breaks down strongly in complex environments, such as within plasmonic nanocavities, and the electromagnetic environment must be fully taken into account. This requires the quantum description of a continuum of bosonic modes, a problem that is computationally hard. We here investigate a compromise where the quantum character of light is taken into account at modest computational cost. To do so, we focus on a quantum emitter that interacts with an arbitrary photonic spectral density and employ the cumulant or cluster expansion method to the Heisenberg equations of motion up to first, second and third order. We benchmark the method by comparing with exact solutions for specific situations and show that it can accurately represent dynamics for many parameter ranges.Light-matter interaction is of paramount importance for unraveling the laws of nature and its deep understanding allows us to control and manipulate physical and chemical systems. In particular, one can modify the properties of a quantum emitter simply by changing its electromagnetic environment, for example by enclosing it within an optical cavity. This may give rise to a change of the decay rate for spontaneous emission in the weak coupling regime, the so-called Purcell effect 1 , or to the appearance of hybrid light-matter states, socalled polaritons, in the strong-coupling regime 2-5 . Over the last decades, it has been shown that strong light-matter coupling can be achieved using a large variety of physical implementations as the "cavity" that provides the electromagnetic field confinement. These include Fabry-Perot cavities consisting of two mirrors 5 , propagating surface plasmon polaritons 6 , plasmonic hole 7 and nanoparticle arrays 8 , isolated plasmonic nanoparticles 9 and nanoparticle-on-mirror geometries 10,11 , as well as hybrid cavities combining plasmonic and dielectric materials [12][13][14] . In many of these systems, the electromagnetic field modes are not well-described by isolated lossy cavity modes, and a correct treatment demands theoretical approaches that are able to deal with the complexity of the electromagnetic field modes and their spectrum.In principle, to treat the problem of light-matter interaction, one can rely on the most general theory that describes light and matter on equal footing, i.e., quantum electrodynamics (QED) 15 . However, treating all light and matter degrees of freedom in the systems described above in a quantum mechanical way is an intractable problem and approx...

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Section: B Cavitymentioning

confidence: 82%

Section: A Free Space Dynamicsmentioning

confidence: 99%

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confidence: 99%

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Cumulant expansion for the treatment of light–matter interactions in arbitrary material structures

Mónica

Silva

Feist

2020

The Journal of Chemical Physics

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“…In order to address some of these challenges, we have recently shown the potential of the Multi-Trajectory Ehrenfest (MTEF) method to capture the correlated dynamics of a one-dimensional QED cavity-setup with a twolevel atomic system coupled to a large set of cavity photonmodes 29 . Furthermore, we note that in contrast to recent work of Subotnik and co-workers, who investigated light-matter interaction with an adjusted Ehrenfest theory based method to simulate spontaneous emission of classical light [30][31][32] , we focus on the description of quantized light fields. light-matter interactions, and a brief introduction of the class of model systems used in this study.…”

Section: Introductionmentioning

confidence: 99%

Benchmarking semiclassical and perturbative methods for real-time simulations of cavity-bound emission and interference

Hoffmann

Schäfer

Säkkinen

et al. 2019

The Journal of Chemical Physics

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We benchmark a selection of semiclassical and perturbative dynamics techniques by investigating the correlated evolution of a cavity-bound atomic system to assess their applicability to study problems involving strong light-matter interactions in quantum cavities. The model system of interest features spontaneous emission, interference, and strong coupling behaviour, and necessitates the consideration of vacuum fluctuations and correlated light-matter dynamics. We compare a selection of approximate dynamics approaches including fewest switches surface hopping, multi-trajectory Ehrenfest dynamics, linearized semiclasical dynamics, and partially linearized semiclassical dynamics. Furthermore, investigating self-consistent perturbative methods, we apply the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the second Born approximation. With the exception of fewest switches surface hopping, all methods provide a reasonable level of accuracy for the correlated light-matter dynamics, with most methods lacking the capacity to fully capture interference effects.Here we broaden our scope by investigating the performance of a comprehensive class of approximate quantum dynamics methods for simulating spontaneous emission in an optical cavity, including Ehrenfest meanfield theory 33,34 , Tully's surface hopping algorithm 35 , fully linearized 36 and partially linearized 37,38 semilclassical dynamics techniques, and a selection of approximate closures for the quantum mechanical Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. Through benchmark comparisons with exact numerical results, we assess the accuracy and efficiency of each method and highlight the possibilities and theoretical challenges involved with extending these approaches towards realistic systems.The remainder of this work is divided into four sections: Sec. II gives a short overview of general quantum mechanical arXiv:1909.07177v2 [quant-ph]

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“…EM field description, semiclassical electrodynamics cannot fully recover any pure quantum effects for a single electronic system, such as spontaneous emission [15,16]. To date, many techniques have been proposed to account for this issue and this work is still continuing [6,[17][18][19][20].…”

mentioning

confidence: 99%

Understanding the nature of mean-field semiclassical light-matter dynamics: An investigation of energy transfer, electron-electron correlations, external driving, and long-time detailed balance

Chen

Nitzan

et al. 2019

Phys. Rev. A

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Semiclassical electrodynamics [with quantum matter plus classical electrodynamics fields] is an appealing approach for studying light-matter interactions, especially for realistic molecular systems. However, there is no unique semiclassical scheme. On the one hand, intermolecular interactions can be described instantaneously by static two-body interactions connecting two different molecules, while a classical transverse E-field acts as a spectator at short distance; we will call this Hamiltonian #I. On the other hand, intermolecular interactions can also be described as effects that are mediated exclusively through a classical one-body E-field without any quantum effects at all (assuming we ignore electronic exchange); we will call this Hamiltonian #II. Moreover, one can also mix these two different Hamiltonians into a third, hybrid Hamiltonian, which preserves quantum electron-electron correlations for lower excitations but describes higher excitations in a mean-field way. To investigate which semiclassical scheme is most reliable for practical use, here we study the real-time dynamics of a minimalistic many-site model -a pair of identical two-level systems (TLSs) -undergoing either resonance energy transfer (RET) or collectively driven dynamics. While both approaches perform reasonably well (#1 as #2) when there is no strong external excitation, we find that no single approach is perfect for all conditions (and all methods fail when a strong external field is applied). Each method has its own distinct problems: Hamiltonian #I performs best for RET but behaves in a complicated manner for driven dynamics. Hamiltonian #II is always stable, but obviously fails for RET at short distances. One key finding is that, for externally driven dynamics, a full configuration interaction description of Hamiltonian #I (#I-FCI) strongly overestimates the long-time electronic energy, highlighting the not obvious fact that, if one plans to merge quantum molecules with classical light, a full, exact treatment of electron-electron correlations can actually lead to worse results than a simple mean-field electronic structure treatment. Future work will need to investigate (i) how these algorithms behave in the context of more than a pair of TLSs and (ii) whether or not these algorithms can be improved in general by including crucial aspects of spontaneous emission. I. INTRODUCTIONRecent experiments demonstrating collective phenomena with nanoscale light-matter interactions[1-3] have highlighted the need for computational simulations of realistic molecular systems [4][5][6]. Unfortunately, full quantum electrodynamical (QED) calculations scale unfavorably with the number of quantized photonic modes. Moreover, full QED is compatible only with full configuration interactions (CI) for the description of the matter system, such that QED also scales unfavorably with the number of molecules. Thus, mixed quantum-classical electrodynamics are a promising approach with reduced computational cost: one treats electronic/molecular subsystems with ...

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Ehrenfest+R dynamics. I. A mixed quantum–classical electrodynamics simulation of spontaneous emission

Cited by 34 publications

References 74 publications

Cumulant expansion for the treatment of light–matter interactions in arbitrary material structures

Cumulant expansion for the treatment of light–matter interactions in arbitrary material structures

Benchmarking semiclassical and perturbative methods for real-time simulations of cavity-bound emission and interference

Understanding the nature of mean-field semiclassical light-matter dynamics: An investigation of energy transfer, electron-electron correlations, external driving, and long-time detailed balance

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