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The coupling of matter to the quantized electromagnetic field of a plasmonic or optical cavity can be harnessed to modify and control chemical and physical properties of molecules. In optical cavities, a term known as the dipole self-energy (DSE) appears in the Hamiltonian to assure gauge invariance. The aim of this work is twofold. First, we introduce a method, which has its own merits and complements existing methods, to compute the DSE. Second, we study the impact of the DSE on cavity-induced nonadiabatic dynamics in a realistic system. For that purpose, various matrix elements of the DSE are computed as functions of the nuclear coordinates and the dynamics of the system after laser excitation is investigated. The cavity is known to induce conical intersections between polaritons, which gives rise to substantial nonadiabatic effects. The DSE is shown to slightly affect these light-induced conical intersections and, in particular, break their symmetry.

Placing an atom and a molecule in a cavity opens the door to initialize molecular dynamics by exciting a level of the atom. This approach enlarges the range of choosing the light source to trigger molecular dynamics substantially. The interplay of the atomic, molecular and photonic populations gives rise to rich dynamics. The cavity photon plays the role of a mediator between the atom and the molecule and it is found that the photonic population is rather low throughout and its evolution follows that of the molecule. Cavities are known to be subject to losses. In spite of the losses it is demonstrated that the presence of the atom gives rise to a long-lived dynamics which should be of relevance for experimental investigations. The presence of more atoms and molecules is expected to further enrich the dynamics.

Soft X-ray irradiation of molecules causes electronic core-level vacancies through photoelectronemission. In light elements, such as C, N, or O, which are abundant in the biosphere, these vacancies predominantly decay by Auger emission, leading inevitably to dissociative multiply charged states. It was recently demonstrated that an environment can prevent fragmentation of core-level-ionized small organic molecules through immediate non-local decay of the core hole, dissipating charge and energy to the environment. Here, we present an extended photoelectron-photoion-photoion coincidence (PEPIPICO) study of the biorelevant pyrimidine molecule embedded in a water cluster. It is observed and supported by theoretical calculations that the supposed protective effect of the environment is partially reversed if the vacancy is originally located at a water molecule. In this scenario, intermolecular energy or charge transfer from the core-ionized water environment to the pyrimidine molecule leads to ionization of the latter, however, presumably in non-dissociative cationic states. Our results contribute to a more comprehensive understanding of the complex interplay of protective and harmful effects of an environment in the photochemistry of microsolvated molecules exposed to X-rays.

Low-energy-electron emission from resonant Auger final states via intermolecular Coulombic decay (RA-ICD) has been previously described as a promising scenario for controlling radiation damage for medical purposes, but has so far only been observed in prototypical atomic and molecular van der Waals dimers and clusters. Here, we report the experimental observation of RA-ICD in aqueous solution. We show that for solvated Ca$^{2+}$ ions, the emission can be very efficiently controlled by tuning the photon energy of exciting X-rays to inner-shell resonances of the ions. Our results provide the next step from proving RA-ICD in relatively simple prototype systems to understanding the relevance and potential applications of ICD in real-life scenarios.

Energy-transfer processes can be viewed as being due to the emission of a virtual photon. It is demonstrated that the emission of virtual photons and thus of energy transfer is stimulated by the sheer presence of photons. We concentrate here on interatomic/intermolecular Coulombic decay (ICD) where an excited system relaxes by transferring its excess energy to a neighbor ionizing it. ICD is inactive if this excess energy is insufficiently large. However, in the presence of photons, the long-range interaction between the system and its neighbor can utilize the photon field making ICD active. The properties of this stimulated-ICD mechanism are discussed. The concept can be transferred to other scenarios. We discuss collective-ICD where two excited molecules concertedly transfer their excess energy. Also here, the presence of photons can make the process active if the sum of excess energies were insufficient to do so. Examples with typical molecules and atoms are presented to demonstrate that these stimulated processes can play a role.

The exchange of energy between electronic and nuclear motion is the origin of non-adiabaticity and plays an important role in many molecular phenomena and processes. Conical intersections (CIs) of different electronic potential energy surfaces lead to the most singular non-adiabaticity and have been intensely investigated. The coupling of light and matter induces conical intersections which are termed light-induced conical intersections (LICIs). There are two kinds of LICIs, those induced by classical (laser) light and those by quantum light like that provided by a cavity. The present work reviews the subject of LICIs, discussing the achievements made so far. Particular attention is paid to comparing classical and quantum LICIs, their similarities and differences and their relationship to naturally occurring CIs. In contrast to natural CIs, the properties of which are dictated by nature, the properties of their light-induced counterparts are controllable by choosing the frequency and intensity (or coupling to the cavity) of the external light source. This opens the door to inducing and manipulating various kinds of non-adiabatic effects. Several examples of diatomic and polyatomic molecules are presented covering both dynamics and spectroscopy. The computational methods employed are discussed as well. To our opinion, the young field of LICIs and their impact show much future potential.

The use of cavities to impact molecular structure and dynamics has become popular. As cavities, in particular plasmonic nanocavities, are lossy and the lifetime of their modes can be very short, their lossy nature must be incorporated into the calculations. The Lindblad master equation is commonly considered as an appropriate tool to describe this lossy nature. This approach requires the dynamics of the density operator and is thus substantially more costly than approaches employing the Schr\"odinger equation for the quantum wave function when several or many nuclear degrees of freedom are involved. In this work we compare numerically the Lindblad and Schr\"odinger descriptions discussed in the literature for a molecular example where the cavity is pumped by a laser. The laser and cavity properties are varied over a range of parameters. It is found that the Schr\"odinger description adequately describes the dynamics of the polaritons and emission signal as long as the laser intensity is moderate and the pump time is not much longer than the lifetime of the cavity mode. Otherwise, it is demonstrated that the Schr\"odinger description gradually fails. We also show that the failure of the Schr\"odinger description can often be remedied by renormalizing the wave function at every step of the time propagation. The results are discussed and analyzed.

Many-body properties of a fermionic impurity embedded in a Bose-Einstein condensate are analyzed analytically using a solvable model, the harmonic-interaction model for Bose-Fermi mixtures. The one-particle and two-particle densities, reduced density matrices, and correlation functions of the fermions and bosons, both in position and momentum spaces, are prescribed in closed form. The various coherence lengths are analyzed. We show that the first-order coherence lengths in position and momentum spaces are equal whereas the second-order quantities can differ substantially. Illustrative examples where the sole interaction is between the impurity and the condensate are presented. Implications are briefly discussed., Comment: 13 pages, 1 figure

An exactly solvable model of a trapped interacting Bose-Einstein condensate (BEC) coupled in the dipole approximation to a quantized light mode in a cavity is presented. The model can be seen as a generalization of the harmonic-interaction model for a trapped BEC coupled to a bosonic bath. After obtaining the ground-state energy and wavefunction in closed form, we focus on computing the correlations in the system. The reduced one-particle density matrices of the bosons and the cavity are constructed and diagonalized analytically, and the von Neumann entanglement entropy of the BEC and the cavity is also expressed explicitly as a function of the number and mass of the bosons, frequencies of the trap and cavity, and the cavity-boson coupling strength. The results allow one to study the impact of the cavity on the bosons and vice versa on an equal footing. As an application we investigate a specific case of basic interest for itself, namely, non-interacting bosons in a cavity. We find that both the bosons and the cavity develop correlations in a complementary manner while increasing the coupling between them. Whereas the cavity wavepacket broadens in Fock space, the BEC density saturates in real space. On the other hand, while the cavity depletion saturates, and hence does the BEC-cavity entanglement entropy, the BEC becomes strongly correlated and eventually increasingly fragmented. The latter phenomenon implies single-trap fragmentation of otherwise ideal bosons, where their induced long-range interaction is mediated by the cavity. Finally, as a complimentary investigation, the mean-field equations for the BEC-cavity system are solved analytically as well, and the breakdown of mean-field theory for the cavity and the bosons with increasing coupling is discussed. Further applications are envisaged., Comment: 28 pages, 4 figures

Ionization phenomena are widely studied for decades. With the advent of cavity technology, the question arises how quantum light affects molecular ionization. As the ionization spectrum is recorded from the neutral ground state, it is usually possible to choose cavities which exert negligible effect on the neutral ground state, but have significant impact on the ion and the ionization spectrum. Particularly interesting are cases where the ion exhibits conical intersections between close-lying electronic states, which gives rise to substantial nonadiabatic effects. Assuming single-molecule strong coupling, we demonstrate that vibrational modes irrelevant in the absence of cavity play a decisive role when the molecule is in the cavity. Here, dynamical symmetry breaking is responsible for the ion-cavity coupling and high symmetry enables control of the coupling via molecular orientation relative to the cavity field polarization. Significant impact on the spectrum by the cavity is found and shown to even substantially increase for less symmetric molecules.

We show the laser-driven acceleration of unprecedented, collimated ($ 2 \ \mathrm{mrad} $ divergence), and quasi-monoenergetic ($ 25 \ \% $ energy spread) electron beams with energy up to $ 50 \ \mathrm{MeV} $ at $ 1 \ \mathrm{kHz} $ repetition rate. The laser driver is a multi-cycle ($ 15 \ \mathrm{fs} $) $ 1 \ \mathrm{kHz} $ optical parametric chirped pulse amplification (OPCPA) system, operating at $ 26 \ \mathrm{mJ} $ ($ 1.7 \ \mathrm{TW} $). The scalability of the driver laser technology and the electron beams reported in this work pave the way towards developing high-brilliance x-ray sources for medical imaging, innovative devices for brain cancer treatment, and represent a step towards the realization of a kHz GeV electron beamline., Comment: 6 pages, 3 figures, 1 table

The interaction of atoms and molecules with quantum light as realized in cavities has become a highly topical and fast growing field of research. This interaction leads to the formation of hybrid light-matter states giving rise to new phenomena and opening up new pathways to control and to manipulate properties of the matter. In this work, we substantially extend the scope of the interaction by allowing free electrons to enter the cavity and merge and unify the two active fields of electron scattering and quantum-light-matter interaction. In the presence of matter, a new kind of metastable states are formed which exist at a large range of electron energies. The properties of these states depend strongly on the frequency and on the light-matter coupling of the cavity. The incoming electrons can be captured by the matter inside the cavity solely due to the presence of the cavity. The findings are substantiated by an explicit example and general striking consequences are discussed.

Fragmentation of bosons and pairs in a trapped imbalanced bosonic mixture is investigated analytically using an exactly solvable model, the generic harmonic-interaction model for mixtures. Closed-form expressions for the eigenvalues and eigenfunctions of the reduced one-particle and two-particle density matrices as a function of all parameters, the masses, numbers of bosons, and the intraspecies and interspecies interactions, are obtained and analyzed. As an application, we consider a system made of $N_1=100$ non-interacting species $1$ bosons embedded in a bath made of $N_2=10^6$ non-interacting species $2$ bosons, and show how fragmentation of the system's bosons and pairs emerges from the system--bath interaction only. Interestingly, the lighter the bosons comprising the bath are the stronger is the system's fragmentation. Further applications are briefly discussed., Comment: 12 pages, 2 figures

After ionization of an inner-valence electron of molecules, the resulting cation-radicals store substantial internal energy which, if sufficient, can trigger ejection of an additional electron in an Auger decay usually followed by molecule fragmentation. In the environment, intermolecular Coulombic decay (ICD) and electron-transfer mediated decay (ETMD) are also operative, resulting in one or two electrons being ejected from a neighbor, thus preventing the fragmentation of the initially ionized molecule. These relaxation processes are investigated theoretically for prototypical heterocycle-water complexes of imidazole, pyrrole, and pyridine. It is found that the hydrogen-bonding site of the water molecule critically influences the nature and energetics of the electronic states involved, opening or closing certain relaxation processes of the inner-valence ionized system. Our results indicate that the relaxation mechanisms of biologically relevant systems with inner-valence vacancies on their carbon atoms can strongly depend on the presence of the electron-density donating or accepting neighbor, either water or another biomolecule.

Polaritons - hybrid light-matter states formed in cavity - strongly change the properties of the underlying matter. In optical or plasmonic nanocavities, polaritons decay by radiative emission of the cavity, which is accessible experimentally. Due to the interaction of a molecule with the quantized radiation field, polaritons exhibit light-induced conical intersections (LICIs) which dramatically influence the nuclear dynamics of molecular polaritons. We show that ultrafast radiative emission from the lower polariton is controlled by the geometric phase imposed by the LICI. This finding provides insight into the process of emission and, furthermore, allows one to compute these signals by augmenting the Born-Oppenheimer approximation for polaritons with a geometric phase term.

An ensemble of identical, intrinsically non-interacting molecules exposed to quantum light is discussed. Their interaction with the quantum light induces interactions between the molecules. The resulting hybrid light-matter states exhibit complex structure even if only a single vibrational coordinate per molecule is considered. Since all molecules are identical, it is appealing to start from the uniform situation where all molecules possess the same value of this vibrational coordinate. Then, polaritons and dark states follow like in atoms, but are functions of this coordinate, and this vibrational degree of freedom makes the physics different from that of atoms. However, in spite of all molecules being identical, each molecule does have its own vibrational coordinate. It is thus a vital issue to understand the meaning of the uniform situation and how to depart from it, and enable one to realistically investigate the ensemble. A rigorous and physically relevant meaning of the polariton energy curves in the uniform situation has been found. It is proven that any point on a polariton curve is a minimum or maximum for departing from the uniform situation. It is shown how to explicitly compute the energetic impact of departing from the uniform situation using solely properties of a single free molecule. The dark states and their behavior upon departing from the uniform situation are analyzed as well. Useful techniques not used in this topical domain are introduced and general results on, e.g., minimum energy path, symmetry breaking and restoration, are obtained. It is shown how to transfer the findings to include several or even many nuclear degrees of freedom per molecule and thus to address the problem of quantum light interacting with many complex molecules. The interplay of several degrees of freedom in a single molecule of the ensemble leads to qualitatively different physics.

The predominant reason for the damaging power of high-energy radiation is multiple ionization of a molecule, either direct or via the decay of highly excited intermediates, as e.g., in the case of X-ray irradiation. Consequently, the molecule is irreparably damaged by the subsequent fragmentation in a Coulomb explosion. In an aqueous environment, however, it has been observed that irradiated molecules may be saved from fragmentation presumably by charge and energy dissipation mechanisms. Here, we show that the protective effect of the environment sets in even earlier than hitherto expected, namely immediately after single inner-shell ionization. By combining coincidence measurements of the fragmentation of X-ray-irradiated microsolvated pyrimidine molecules with theoretical calculations, we identify direct intermolecular electronic decay as the protective mechanism, outrunning the usually dominant Auger decay. Our results demonstrate that such processes play a key role in charge delocalization and have to be considered in investigations and models on high-energy radiation damage in realistic environments., Comment: 18 pages, 4 figures

The interaction of quantum light with matter like that inside a cavity is known to give rise to mixed light-matter states called polaritons. We discuss the impact of rotation of the cavity on the polaritons. It is shown that the number of polaritons increases due to this rotation. The structure of the original polaritons is modified and new ones are induced by the rotation that strongly depend on the angular velocity and the choice of axis of rotation. In molecules the rotation can change the number of light-induced conical intersections and their dimensionality and hence strongly impact their quantum dynamics. General consequences are discussed.

This review explores the dynamics and the low-energy excitation spectra of Bose-Einstein condensates (BECs) of interacting bosons in external potential traps putting particular emphasis on the emerging many-body effects beyond mean-field descriptions. To do so, methods have to be used that, in principle, can provide numerically exact results for both the dynamics and the excitation spectra in a systematic manner. Numerically exact results for the dynamics are presented employing the well-established multicongurational time-dependent Hartree for bosons (MCTDHB) method. The respective excitation spectra are calculated utilizing the more recently introduced linear-response theory atop it (LR-MCTDHB). The latter theory gives rise to an, in general, non-hermitian eigenvalue problem. The theory and its newly developed implementation are described in detail and benchmarked towards the exactly-solvable harmonic-interaction model. Several applications to BECs in one- and two-dimensional potential traps are discussed. With respect to dynamics, it is shown that both the out-of-equilibrium tunneling dynamics and the dynamics of trapped vortices are of many-body nature. Furthermore, many-body effects in the excitation spectra are presented for BECs in different trap geometries. It is demonstrated that even for essentially-condensed systems, the spectrum of the lowest-in-energy excitations computed at the many-body level can differ substantially from the standard mean-field description. In general, it is shown that bosons carrying angular momentum are more sensitive to many-body effects than bosons without. These effects are present in both the dynamics and the excitation spectrum.

The coupling of a molecule and a cavity induces non-adiabaticity in the molecule which makes the description of its dynamics complicated. For polyatomic molecules, reduced-dimensional models and the use of the Born-Oppenheimer approximation (BOA) may remedy the situation. It is demonstrated that contrary to expectation, BOA may even fail in a one-dimensional model and generally expected to fail in two- or more-dimensional models due to the appearance of conical intersections induced by the cavity.

It is shown that a molecule can dissociate by the energy transferred from a remote neighbor. This neighbor can be an excited neutral or ionic atom or molecule. If it is an atom, the transferred energy is, of course, electronic and in the case of molecules it can also be vibrational. Explicit examples are given which demonstrate that the transfer can be highly efficient at distances where there is no bonding between the transmitter and the dissociating molecule.

To maximize the light yield of the liquid scintillator (LS) for the Jiangmen Underground Neutrino Observatory (JUNO), a 20 t LS sample was produced in a pilot plant at Daya Bay. The optical properties of the new LS in various compositions were studied by replacing the gadolinium-loaded LS in one antineutrino detector. The concentrations of the fluor, PPO, and the wavelength shifter, bis-MSB, were increased in 12 steps from 0.5 g/L and <0.01 mg/L to 4 g/L and 13 mg/L, respectively. The numbers of total detected photoelectrons suggest that, with the optically purified solvent, the bis-MSB concentration does not need to be more than 4 mg/L. To bridge the one order of magnitude in the detector size difference between Daya Bay and JUNO, the Daya Bay data were used to tune the parameters of a newly developed optical model. Then, the model and tuned parameters were used in the JUNO simulation. This enabled to determine the optimal composition for the JUNO LS: purified solvent LAB with 2.5 g/L PPO, and 1 to 4 mg/L bis-MSB., Comment: 13 pages, 8 figures

Nonadiabaticity, i.e., the effect of mixing electronic states by nuclear motion, is a central phenomenon in molecular science. The strongest nonadiabatic effects arise due to the presence of conical intersections of electronic energy surfaces. These intersections are abundant in polyatomic molecules. Laser light can induce in a controlled manner new conical intersections, called light-induced conical intersections, which lead to strong nonadiabatic effects similar to those of the natural conical intersections. These effects are, however, controllable and may even compete with those of the natural intersections. In this work we show that the standard low-energy vibrational spectrum of the electronic ground state can change dramatically by inducing nonadiabaticity via a light-induced conical intersection. This generic effect is demonstrated for an explicit example by full-dimensional high-level quantum calculations using a pump-probe scheme with a moderate-intensity pump laser and a weak probe laser.