Ehrenfest modeling of cavity vacuum fluctuations and how to achieve emission from a three-level atom.

A much-needed solution for the efficient modeling of strong coupling between matter and optical cavity modes is offered by mean-field mixed quantum-classical dynamics, where a classical cavity field interacts self-consistently with quantum states of matter through Ehrenfest's theorem. We previously introduced a modified mean-field approach, referred to as decoupled mean-field (DC-MF) dynamics, wherein vacuum fluctuations of the cavity field are decoupled from the quantum-mechanical ground state as a means to resolve an unphysical drawing of energy from the vacuum fluctuations by a two-level atom. Here, we generalize DC-MF dynamics for an arbitrary number of (nondegenerate) atomic levels and show that it resolves an unphysical lack of emission from a three-level atom predicted by conventional mean-field dynamics. We furthermore show DC-MF to provide an improved description of reabsorption and (resonant) two-photon emission processes.

Ab Initio Prediction of Excited-State and Polaron Effects in Transient XUV Measurements of α-Fe2O3.

Transient X-ray and extreme ultraviolet (XUV) spectroscopies have become invaluable tools for studying photoexcited dynamics due to their sensitivity to carrier occupations and local chemical or structural changes. One of the most studied materials using transient XUV spectroscopy is α-Fe2O3 because of its rich photoexcited dynamics, including small polaron formation. The interpretation of carrier and polaron effects in α-Fe2O3 is currently carried out using a semi-empirical method that is not transferrable to most materials. Here, an ab initio, Bethe-Salpeter equation (BSE) approach is developed that can incorporate photoexcited-state effects into arbitrary material systems. The accuracy of this approach is proven by calculating the XUV absorption spectra for the ground, photoexcited, and polaron states of α-Fe2O3. Furthermore, the theoretical approach allows for the projection of the core-valence excitons and different components of the X-ray transition Hamiltonian onto the band structure, providing new insights into old measurements. From this information, a physical intuition about the origins and nature of the transient XUV spectra can be built. A route to extracting electron and hole energies is even shown possible for highly angular momentum split XUV peaks. This method is easily generalized to K, L, M, and N edges to provide a general approach for analyzing transient X-ray absorption or reflection data.

A reciprocal-space formulation of surface hopping.

Surface hopping has seen great success in describing molecular phenomena where electronic excitations tend to be localized, but its application to materials with band-like electronic properties has remained limited. Here, we derive a formulation of fewest-switches surface hopping where both the quantum and classical equations of motion are solved entirely in terms of reciprocal-space coordinates. The resulting method is directly compatible with band structure calculations and allows for the efficient description of band-like phenomena by means of a truncation of the Brillouin zone. Using the Holstein and Peierls models as examples, we demonstrate the formal equivalence between real-space and reciprocal-space surface hopping and assess their accuracy against mean-field mixed quantum-classical dynamics and numerically exact results. Having very similar equations of motion, reciprocal-space surface hopping can be straightforwardly incorporated in existing (real-space) surface hopping implementations.

A reciprocal-space formulation of mixed quantum-classical dynamics.

We derive a formulation of mixed quantum-classical dynamics for modeling electronic carriers interacting with phonons in reciprocal space. For dispersionless phonons, we start by expressing the real-space classical coordinates in terms of complex variables. Taking these variables as a Fourier series then yields the reciprocal-space coordinates. Evaluating the electron-phonon interaction term through Ehrenfest's theorem, we arrive at a reciprocal-space formalism that is equivalent to mean-field mixed quantum-classical dynamics in real space. This equivalence is numerically verified for the Holstein and Peierls models, for which we find the reciprocal-space Hellmann-Feynman forces to involve momentum-derivative contributions in addition to the position-derivative terms commonly seen in real space. To illustrate the advantage of the reciprocal-space formulation, we present a proof of concept for the inexpensive modeling of low-momentum carriers interacting with phonons using a truncated reciprocal-space basis, which is not possible within a real-space formulation.

A Mean-Field Treatment of Vacuum Fluctuations in Strong Light-Matter Coupling.

Mean-field mixed quantum-classical dynamics could provide a much-needed means to inexpensively model quantum electrodynamical phenomena by describing the optical field and its vacuum fluctuations classically. However, this approach is known to suffer from an unphysical transfer of energy out of the vacuum fluctuations when the light-matter coupling becomes strong. We highlight this issue for the case of an atom in an optical cavity and resolve it by introducing an additional set of classical coordinates to specifically represent vacuum fluctuations whose light-matter interaction is scaled by the instantaneous ground-state population of the atom. This not only rigorously prevents the aforementioned unphysical energy transfer but is also shown to yield a radically improved accuracy in terms of the atomic population and the optical field dynamics, generating results in excellent agreement with full quantum calculations. As such, the resulting method emerges as an attractive solution for the affordable modeling of strong light-matter coupling phenomena involving macroscopic numbers of optical modes.

Quantum Ensembles of Silicon Nanoparticles: Discrimination of Static and Dynamic Photoluminescence Quenching Processes.

Porous silicon photoluminescence is characterized by a broad emission band that displays unusually long (tens to hundreds of micro-seconds), wavelength-dependent emissive lifetimes. The photoluminescence is associated with quantum confinement of excitons in silicon nanocrystallites contained within the porous matrix, and the broad emission spectrum derives from the wide distribution of nanocrystallite sizes in the material. The longer emissive lifetimes in the ensemble of quantum-confined emitters correspond to the larger nanocrystallites, with their longer wavelengths of emission. The quenching of this photoluminescence by aromatic, redox-active molecules aminochrome (AMC), dopamine, adrenochrome, sodium anthraquinone-2-sulfonate, benzyl viologen dichloride, methyl viologen dichloride hydrate, and ethyl viologen dibromide is studied, and dynamic and static quenching mechanisms are distinguished by the emission lifetime analysis. Because of the dependence of the emission lifetime on emission wavelength from the silicon nanocrystallite ensemble, a pronounced blue shift is observed in the steady-state emission spectrum upon exposure to dynamic-type quenchers. Conversely, static-type quenching systems show uniform quenching across all emission wavelengths. Thus, the difference between static and dynamic quenching mechanisms is readily distinguished by ratiometric photoluminescence spectroscopy. The application of this concept to imaging of AMC, the oxidized form of the neurotransmitter dopamine that is of interest for its role in neurodegenerative diseases, is demonstrated. It is found that static electron acceptors result in no ratiometric contrast, while AMC shows a strong contrast, allowing ready visualization in a 2-D imaging experiment.