Comparison of Different Classical, Semiclassical, and Quantum Treatments of Light–Matter Interactions: Understanding Energy Conservation

Identifying Differences between Semiclassical and Full-Quantum Descriptions of Plexcitons

Strong light-matter coupling between molecules and plasmonic nanoparticles gives rise to new hybrid eigenstates of the coupled system, commonly referred to as polaritons or, more precisely, plexcitons. Over the past decade, it has been amply shown that molecular electron dynamics and photophysics can be drastically affected by such interactions, thus paving the way for light-induced control of molecular excited state properties and reactivity. Here, by combining the ab initio molecular description and classical or quantum modeling of arbitrarily shaped plasmonic nanostructures within the stochastic Schrödinger equation, we present two approaches, one semiclassical and one full-quantum, to follow in real time the electronic dynamics of plexcitons while realistically taking plasmonic dissipative losses into account. The full-quantum theory is compared with the semiclassical analogue under different interaction regimes, showing (numerically and theoretically) that even in the weak-field and weak-coupling limit a small-yet-observable difference arises.

Modeling the electroluminescence of atomic wires from quantum dynamics simulations

Static and time-dependent quantum-mechanical approaches have been employed in the literature to characterize the physics of light-emitting molecules and nanostructures. However, the electromagnetic emission induced by an input current has remained beyond the realm of molecular simulations. This is the challenge addressed here with the help of an equation of motion for the density matrix coupled to a photon bath based on a Redfield formulation. This equation is evolved within the framework of the driven-Liouville von Neumann approach, which incorporates open boundaries by introducing an applied bias and a circulating current. The dissipated electromagnetic power can be computed in this context from the time derivative of the energy. This scheme is applied in combination with a self-consistent tight-binding Hamiltonian to investigate the effects of bias and molecular size on the electroluminescence of metallic and semiconducting chains. For the latter, a complex interplay between bias and molecular length is observed: there is an optimal number of atoms that maximizes the emitted power at high voltages but not at low ones. This unanticipated behavior can be understood in terms of the band bending produced along the semiconducting chain, a phenomenon that is captured by the self-consistency of the method. A simple analytical model is proposed that explains the main features revealed by the simulations. The methodology, applied here at a self-consistent tight-binding level but extendable to more sophisticated Hamiltonians such as density functional tight binding and time dependent density functional theory, promises to be helpful for quantifying the power and quantum efficiency of nanoscale electroluminescent devices.

Fluorescence in quantum dynamics: Accurate spectra require post-mean-field approaches

Real time modeling of fluorescence with vibronic resolution entails the representation of the light-matter interaction coupled to a quantum-mechanical description of the phonons and is therefore a challenging problem. In this work, taking advantage of the difference in timescales characterizing internal conversion and radiative relaxation-which allows us to decouple these two phenomena by sequentially modeling one after the other-we simulate the electron dynamics of fluorescence through a master equation derived from the Redfield formalism. Moreover, we explore the use of a recent semiclassical dissipative equation of motion [C. M. Bustamante et al., Phys. Rev. Lett. 126, 087401 (2021)], termed coherent electron electric-field dynamics (CEED), to describe the radiative stage. By comparing the results with those from the full quantum-electrodynamics treatment, we find that the semiclassical model does not reproduce the right amplitudes in the emission spectra when the radiative process involves the de-excitation to a manifold of closely lying states. We argue that this flaw is inherent to any mean-field approach and is the case with CEED. This effect is critical for the study of light-matter interaction, and this work is, to our knowledge, the first one to report this problem. We note that CEED reproduces the correct frequencies in agreement with quantum electrodynamics. This is a major asset of the semiclassical model, since the emission peak positions will be predicted correctly without any prior assumption about the nature of the molecular Hamiltonian. This is not so for the quantum electrodynamics approach, where access to the spectral information relies on knowledge of the Hamiltonian eigenvalues.

Tailoring Cooperative Emission in Molecules: Superradiance and Subradiance from First-Principles Simulations

Cooperative optical effects provide a pathway to both the amplification (superradiance) and the suppression (subradiance) of photon emission from electronically excited states. These captivating phenomena offer a rich variety of possibilities for photonic technologies aimed at electromagnetic energy manipulation, including lasers and high-speed emitting devices in the case of superradiance or optical energy storage in that of subradiance. The employment of molecules as the building pieces in these developments requires a precise understanding of the roles of separation, orientation, spatial distribution, and applied fields, which remains challenging for theory and experiments. These questions are addressed here through ab initio quantum dynamics simulations of collective emission on the basis of a novel semiclassical formalism and time-dependent density functional theory. By establishing the configurations leading to decoherence and how the fine-tuning of a pulse can accumulate or release optical energy in H₂ arrays, this report provides fundamental insight toward the design of real superradiant and subradiant devices.

Incorporating Lindblad Decay Dynamics into Mixed Quantum-Classical Simulations

We derive the $\mathcal{L}$-MFE method to incorporate Lindblad jump operator dynamics into the mean-field Ehrenfest (MFE) approach. We map the density matrix evolution of Lindblad dynamics onto pure state coefficients using trajectory averages. We use simple assumptions to construct the $\mathcal{L}$-MFE method that satisfies this exact mapping. This establishes a method that uses independent trajectories which exactly reproduces Lindblad decay dynamics using a wavefunction description, with deterministic changes of the magnitudes of the quantum expansion coefficients, while only adding on a stochastic phase. We further demonstrate that when including nuclei in the Ehrenfest dynamics, the $\mathcal{L}$-MFE method gives semi-quantitatively accurate results, with the accuracy limited by the accuracy of the approximations present in the semiclassical MFE approach. This work provides a general framework to incorporate Lindblad dynamics into semiclassical or mixed quantum-classical simulations.

Noble classical and quantum approach to model the optical properties of metallic nanoparticles to enhance the sensitivity of optoplasmonic sensors

The bright light obtained from the quantum principle has a key role in the construction of optical sensors. Yet, theoretical and experimental work highlights the challenges of overcoming the high cost and low efficiency of such sensors. Therefore, we report a metallic nanoparticle-based metasurface plasmons polariton using quantum and classical models. We have investigated the material properties, absorption cross-section, scattering cross-section, and efficiency of the classical model. By quantizing light-matter interaction, the quantum features of light - degree of squeezing, correlation, and entanglement are quantified numerically and computationally. In addition, we note the penetration depth and propagation length from a hybrid model in order to enhance the optoplasmonic sensor performance for imaging, diagnosing, and early perception of cancer cells with label-free, direct, and real-time detection. Our study findings conclude that the frequency of incident light, size, shape, and type of nanoparticles has a significant impact on the optical properties of metallic nanoparticles and the nonlinear optical properties of metallic nanoparticles are dynamic, enhancing the sensitivity of the optoplasmonic sensor. Moreover, the resulting bright light shows the systematic potential for further medical image processing.

Pulsed vapor cell atomic clock with a differential Faraday rotation angle detection

Laser intensity noise is one of the main limiting factors in pulsed vapor cell clocks. To reduce the contribution of the laser intensity noise to detection signal in the pulsed optically pumped atomic clock, a scheme based on the differential Faraday rotation angle is proposed. Theoretically, the Ramsey fringes, the sensitivity of clock frequency to laser intensity fluctuation and the signal to noise ratio for absorption, differential, and Faraday rotation angle methods are calculated and compared. Using a Wollaston prism rotated 45°relative to the incident polarization, and two photodetectors, Ramsey fringes of three detection methods are obtained simultaneously. In the proposed scheme, the long-term Faraday rotation angle fluctuation is 0.66% at 30000s, which is much smaller than fluctuation of traditional absorption signal 3.9% at 30000s. And the contribution of laser intensity noise to clock instability is also reduced. Using optimized photodetector with high common mode rejection ratio, a better performance should be expected. This proposed scheme is attractive for the development of high performance vapor clock based on pulsed optically pumped.

Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics

We show that a novel, general phase space mapping Hamiltonian for nonadiabatic systems, which is reminiscent of the renowned Meyer-Miller mapping Hamiltonian, involves a commutator variable matrix rather than the conventional zero-point-energy parameter. In the exact mapping formulation on constraint space for phase space approaches for nonadiabatic dynamics, the general mapping Hamiltonian with commutator variables can be employed to generate approximate trajectory-based dynamics. Various benchmark model tests, which range from gas phase to condensed phase systems, suggest that the overall performance of the general mapping Hamiltonian is better than that of the conventional Meyer-Miller Hamiltonian.

Dissipative Equation of Motion for Electromagnetic Radiation in Quantum Dynamics

The dynamical description of the radiative decay of an electronically excited state in realistic many-particle systems is an unresolved challenge. In the present investigation electromagnetic radiation of the charge density is approximated as the power dissipated by a classical dipole, to cast the emission in closed form as a unitary single-electron theory. This results in a formalism of unprecedented efficiency, critical for ab initio modeling, which exhibits at the same time remarkable properties: it quantitatively predicts decay rates, natural broadening, and absorption intensities. Exquisitely accurate excitation lifetimes are obtained from time-dependent DFT simulations for C^{2+}, B^{+}, and Be, of 0.565, 0.831, and 1.97 ns, respectively, in accord with experimental values of 0.57±0.02, 0.86±0.07, and 1.77-2.5 ns. Hence, the present development expands the frontiers of quantum dynamics, bringing within reach first-principles simulations of a wealth of photophysical phenomena, from fluorescence to time-resolved spectroscopies.

Investigating New Reactivities Enabled by Polariton Photochemistry

We perform quantum dynamics simulations to investigate new chemical reactivities enabled by cavity quantum electrodynamics. The quantum light-matter interactions between the molecule and the quantized radiation mode inside an optical cavity create a set of hybridized electronic-photonic states, so-called polaritons. The polaritonic states adapt the curvatures from both the ground and the excited electronic states, opening up new possibilities to control photochemical reactions by exploiting intrinsic quantum behaviors of light-matter interactions. With quantum dynamics simulations, we demonstrate that the selectivity of a model photoisomerization reaction can be controlled by tuning the photon frequency of the cavity mode or the light-matter coupling strength, providing new ways to manipulate chemical reactions via the light-matter interaction. We further investigate collective quantum effects enabled by coupling the quantized radiation mode to multiple molecules. Our results suggest that in the resonance case, a photon is recycled among molecules to enable multiple excited state reactions, thus effectively functioning as a catalyst. In the nonresonance case, molecules emit and absorb virtual photons to initiate excited state reactions through fundamental quantum electrodynamics processes. These results from quantum dynamics simulations reveal basic principles of polariton photochemistry as well as promising reactivities that take advantage of intrinsic quantum behaviors of photons.

Predictive Semiclassical Model for Coherent and Incoherent Emission in the Strong Field Regime: The Mollow Triplet Revisited

We reinvestigate the famous Mollow triplet and show that most of the well-known quantum characteristics of the Mollow triplet-including incoherent emission and a nonstandard dependence of the sidebands on detuning-can be recovered quantitatively using semiclassical dynamics with a classical light field. In fact, by not relying on the rotating wave approximation, a semiclassical model predicts some quantum effects beyond the quantum optical Bloch equation, including higher-order scattering and asymmetric sideband features. This Letter highlights the fact that, with strong intensities, many putatively quantum features of light-matter interactions arise from a simple balance of mean-field electrodynamics and elementary spontaneous emission, which requires minimal computational cost. Our results suggest that the application of semiclassical electrodynamics to problems with strong light-matter coupling in the fields of nanophotonics and superradiance are likely to yield a plethora of new information.