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Superradiance, in which the collective behavior of emitters can generate enhanced radiative decay, was first predicted by a model, now known as the Dicke model, that contains a collection of two-level systems (the emitters) all interacting with the same photonic mode. In this article, we extend the original Dicke model to elucidate the influence of nuclear motion on superradiant emission. Our dynamical simulations of the combined electronic, nuclear, and photonic system reveal a new time scale attributed to the population leakage of the dark, subradiant states. Furthermore, this dark state emission pathway can be controlled by tuning the nuclear potential energy landscape. These findings impact how superradiant states and molecular degrees of freedom can be leveraged and utilized in quantum optical systems.

Recently developed electronic pre-resonance stimulated Raman scattering (epr-SRS) microscopy, in which the Raman signal of a dye is significantly boosted by setting the incident laser frequency near the electronic excitation energy, has pushed the sensitivity of SRS microscopy close to that offered by confocal fluorescence microscopy. Prominently, the maintained narrow line-width of epr-SRS also offers high multiplexity that breaks the "color barrier" in optical microscopy. However, detailed understandings of the fundamental mechanism in these epr-SRS dyes still remain elusive. Here, we combine experiments with theoretical modeling to investigate the structure-signal relationship, aiming to facilitate the design of new probes and expanding epr-SRS palettes. Our ab initio approach employing the displaced harmonic oscillator (DHO) model provides a consistent agreement between simulated and experimental SRS intensities of various triple-bond bearing epr-SRS probes with distinct scaffolds. We further review two popular approximate expressions for epr-SRS, namely the short-time and Albrecht A-term equations, and compare them to the DHO model. Overall, the theory allows us to illustrate how the observed intensity differences between molecular scaffolds stem from the coupling strength between the electronic excitation and the targeted vibrational mode, leading to a general design strategy for highly sensitive next-generation vibrational imaging probes.

Two-dimensional Raman and hybrid terahertz/Raman spectroscopic techniques provide invaluable insight into molecular structure and dynamics of condensed-phase systems. However, corroborating experimental results with theory is difficult due to the high computational cost of incorporating quantum-mechanical effects in the simulations. Here, we present the equilibrium-nonequilibrium ring-polymer molecular dynamics (RPMD), a practical computational method that can account for nuclear quantum effects on the two-time response function of nonlinear optical spectroscopy. Unlike a recently developed approach based on the double Kubo transformed (DKT) correlation function, our method is exact in the classical limit, where it reduces to the established equilibrium-nonequilibrium classical molecular dynamics method. Using benchmark model calculations, we demonstrate the advantages of the equilibrium-nonequilibrium RPMD over classical and DKT-based approaches. Importantly, its derivation, which is based on the nonequilibrium RPMD, obviates the need for identifying an appropriate Kubo transformed correlation function and paves the way for applying real-time path-integral techniques to multidimensional spectroscopy., Comment: v2: Added a two-dimensional model system (Fig. 4), updated list of authors, other minor improvements; last 10 pages contain the supplementary material

We present a detailed study of the nuclear quantum effects in H/D sticking to graphene, comparing classical, quantum and mixed quantum/classical simulations to results of scattering experiments. Agreement with experimentally derived sticking probabilities is improved when nuclear quantum effects are included using ring polymer molecular dynamics. Specifically, the quantum motion of the carbon atoms enhances sticking, showing that an accurate description of graphene phonons is important to capturing the adsorption dynamics. We also find an inverse H/D isotope effect arising from Newtonian mechanics.

We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that simple application of the stationary-phase approximation (SPA) dramatically improves the performance of the microcanonical rates using RPMD, particularly in the low-energy region where tunneling dominates. Using the SPA as a Bayesian prior, numerically exact RPMD microcanonical rates are then obtained using maximum entropy inversion of the thermal reaction rates, for both electronically adiabatic and non-adiabatic model systems. Finally, the direct-shooting method is revisited using the SPA-determined temperature for the internal ring-polymer modes, leading to a simple, direct-simulation method with improved accuracy in the tunneling regime.

We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced, such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.