Coupling polyatomic molecules to lossy nanocavities: Lindblad vs Schrödinger description.

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 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 Schrödinger 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 Schrödinger 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 Schrödinger 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 Schrödinger description gradually fails. We also show that the failure of the Schrödinger description can often be remedied by renormalizing the wave function at every step of time propagation. The results are discussed and analyzed.

Impact of Cavity on Molecular Ionization Spectra.

Ionization phenomena have been 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 a 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.

Light-induced photodissociation in the lowest three electronic states of the NaH molecule.

It has been known that electronic conical intersections in a molecular system can also be created by laser light even in diatomics. The direct consequence of these light-induced degeneracies is the appearance of a strong mixing between the electronic and vibrational motions, which has a strong fingerprint on the ultrafast nuclear dynamics. In the present work, pump and probe numerical simulations are performed with the NaH molecule involving the first three singlet electronic states (X1Σ+(X), A1Σ+(A) and B1Π(B)) and several light-induced degeneracies in the numerical description. To demonstrate the impact of the multiple light-induced non-adiabatic effects together with the molecular rotation on the dynamical properties of the molecule, the dissociation probabilities, kinetic energy release spectra (KER) and the angular distributions of the photofragments were calculated by discussing the role of the permanent dipole moment as well.

Radiative emission of polaritons controlled by light-induced geometric phase.

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.

Probing Light-Induced Conical Intersections by Monitoring Multidimensional Polaritonic Surfaces.

The interaction of a molecule with the quantized electromagnetic field of a nanocavity gives rise to light-induced conical intersections between polaritonic potential energy surfaces. We demonstrate for a realistic model of a polyatomic molecule that the time-resolved ultrafast radiative emission of the cavity enables following both nuclear wavepacket dynamics on, and nonadiabatic population transfer between, polaritonic surfaces without applying a probe pulse. The latter provides an unambiguous (and in principle experimentally accessible) dynamical fingerprint of light-induced conical intersections.

Signatures of light-induced nonadiabaticity in the field-dressed vibronic spectrum of formaldehyde.

Nonadiabatic coupling is absent between the electronic ground X and first excited (singlet) A states of formaldehyde. As laser fields can induce conical intersections between these two electronic states, formaldehyde is particularly suitable for investigating light-induced nonadiabaticity in a polyatomic molecule. The present work reports on the spectrum induced by light-the so-called field-dressed spectrum-probed by a weak laser pulse. A full-dimensional ab initio approach in the framework of Floquet-state representation is applied. The low-energy spectrum, which without the dressing field would correspond to an infrared vibrational spectrum in the X-state, and the high-energy spectrum, which without the dressing field would correspond to the X → A spectrum, are computed and analyzed. The spectra are shown to be highly sensitive to the frequency of the dressing light allowing one to isolate different nonadiabatic phenomena.

Nonadiabatic phenomena in molecular vibrational polaritons.

Nonadiabatic phenomena are investigated in the rovibrational motion of molecules confined in an infrared cavity. Conical intersections (CIs) between vibrational polaritons, similar to CIs between electronic polaritonic surfaces, are found. The spectral, topological, and dynamic properties of the vibrational polaritons show clear fingerprints of nonadiabatic couplings between molecular vibration, rotation, and the cavity photonic mode. Furthermore, it is found that for the investigated system, composed of two rovibrating HCl molecules and the cavity mode, breaking the molecular permutational symmetry, by changing 35Cl to 37Cl in one of the HCl molecules, the polaritonic surfaces, nonadiabatic couplings, and related spectral, topological, and dynamic properties can deviate substantially. This implies that the natural occurrence of different molecular isotopologues needs to be considered when modeling realistic polaritonic systems.

Quantum light-induced nonadiabatic phenomena in the absorption spectrum of formaldehyde: Full- and reduced-dimensionality studies.

The coupling of a molecule to a cavity can induce conical intersections of the arising polaritonic potential energy surfaces. Such intersections give rise to the strongest possible nonadiabatic effects. By choosing an example that does not possess nonadiabatic effects in the absence of the cavity, we can study, for the first time, the emergence of these effects in a polyatomic molecule due to its coupling with the cavity taking into account all vibrational degrees of freedom. The results are compared with those of reduced-dimensionality models, and the shortcomings and merits of the latter are analyzed.

Striking Generic Impact of Light-Induced Non-Adiabaticity in Polyatomic Molecules.

Non-adiabaticity, 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 non-adiabaticity 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.

Robust field-dressed spectra of diatomics in an optical lattice.

The absorption spectra of the cold Na2 molecule dressed by a linearly polarized standing laser wave is investigated with a theoretical model incorporating translational, electronic, vibrational as well as rotational degrees of freedom. In such a situation a light-induced conical intersection (LICI) can be formed (J. Phys. B: At. Mol. Opt. Phys., 2008, 41, 221001). To measure the spectra a weak field is used whose propagation direction is perpendicular to the direction of the dressing field but has identical polarization direction. Although LICIs are present in our model, the simulations demonstrate a very robust absorption spectrum, which is insensitive to the intensity and the wavelength of the dressing field and which does not reflect clear signatures of light-induced nonadiabatic phenomena related to the strong mixing between the electronic, vibrational, rotational and translational motions. However, by widening artificially the very narrow translational energy level gaps, the fingerprint of the LICI appears to some extent in the spectrum.

Born-Oppenheimer approximation in optical cavities: from success to breakdown.

The coupling of a molecule and a cavity induces nonadiabaticity 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 is generally expected to fail in two- or more-dimensional models due to the appearance of conical intersections induced by the cavity.

Communication: Substantial impact of the orientation of transition dipole moments on the dynamics of diatomics in laser fields.

The formation of light-induced conical intersections (LICIs) between electronic states of diatomic molecules has been thoroughly investigated over the past decade. In the case of running laser waves, the rotational, vibrational, and electronic motions couple via the LICI giving rise to strong nonadiabatic phenomena. In contrast to natural conical intersections (CIs) which are given by nature and hard to manipulate, the characteristics of LICIs are easily modified by the parameters of the laser field. The internuclear position of the created LICI is determined by the laser energy, while the angular position is given by the orientation of the transition dipole moment (TDM) with respect to the molecular axis. In the present communication, using MgH+ as a showcase example, we exploit the strong impact of the orientation of the TDMs exerted on the light-induced nonadiabatic dynamics. Comparing the photodissociations induced by parallel or perpendicular transitions, a clear signature of the created LICIs is revealed in the angular distribution of the photofragments.

Conical Intersections Induced by Quantum Light: Field-Dressed Spectra from the Weak to the Ultrastrong Coupling Regimes.

In classical laser fields with frequencies resonant with the electronic excitation in molecules, it is by now known that conical intersections are induced by the field and are called light-induced conical intersections (LICIs). As optical cavities have become accessible, the question arises whether their quantized modes could also lead to the appearance of LICIs. A theoretical framework is formulated for the investigation of LICIs of diatomics in such quantum light. The eigenvalue spectrum of the dressed states in the cavity is studied, putting particular emphasis on the investigation of absorption spectra of the Na2 molecule, that is, on the transitions between dressed states, measured by employing a weak probe pulse. The dependence of the spectra on the light-matter coupling strength in the cavity and on the frequency of the cavity mode is studied in detail. The computations demonstrate strong nonadiabatic effects caused by the appearing LICI.

Direct Signatures of Light-Induced Conical Intersections on the Field-Dressed Spectrum of Na2.

Rovibronic spectra of the field-dressed homonuclear diatomic Na2 molecule are investigated to identify direct signatures of the light-induced conical intersection (LICI) on the spectrum. The theoretical framework formulated allows the computation of the (1) field-dressed rovibronic states induced by a medium-intensity continuous-wave laser light and the (2) transition amplitudes between these field-dressed states with respect to an additional weak probe pulse. The field-dressed spectrum features absorption peaks resembling the field-free spectrum as well as stimulated emission peaks corresponding to transitions not visible in the field-free case. By investigating the dependence of the field-dressed spectra on the dressing-field wavelength, in both full- and reduced-dimensional simulations, direct signatures of the LICI can be identified. These signatures include (1) the appearance of new peaks and the splitting of peaks for both absorption and stimulated emission and (2) the manifestation of an intensity-borrowing effect in the field-dressed spectrum.

Intrinsic and light-induced nonadiabatic phenomena in the NaI molecule.

Nonadiabatic effects play a very important role in controlling chemical dynamical processes. They are strongly related to avoided crossings (AC) or conical intersections (CIs) which can either be present naturally or induced by classical laser light in a molecular system. The latter are named as "light-induced avoided crossings" (LIACs) and "light-induced conical intersections" (LICIs). By performing one or two dimensional quantum dynamical calculations LIAC and LICI situations can easily be created even in diatomic molecules. Applying such calculations for the NaI molecule, which is a strongly coupled diatomic in field free case, significant differences between the impact of the LIAC and LICI on the ground state population dynamics were observed. Moreover, obtained results undoubtedly demonstrate that the effect of the LIAC and LICI on the dynamics strongly depends on the intensity and the frequency of the applied laser field as well as the permanent dipole moments of the molecule.

Competition between Light-Induced and Intrinsic Nonadiabatic Phenomena in Diatomics.

Nonadiabatic effects arise due to avoided crossings or conical intersections that are either present naturally in field-free space or induced by a classical laser field in a molecule. Recently, it was demonstrated that nonadiabatic effects in diatomics can also be created in an optical cavity. Here, the quantized radiation field mixes the nuclear and electronic degrees of freedom. We show the equivalence of using the cavity's quantized field and the classical laser field as usually done for molecules. This is demonstrated for NaI, which exhibits a pronounced natural (intrinsic) avoided crossing that competes with the avoided crossing induced by the field. Furthermore, rotating molecules exhibit light-induced conical intersections (LICIs) in classical laser light, and we also investigate the impact of these intersections. For NaI, we undoubtedly demonstrate a significant difference between the impact of the laser-induced avoided crossing and that of the LICI on the dynamics of the molecule.

Attosecond electronic and nuclear quantum photodynamics of ozone monitored with time and angle resolved photoelectron spectra.

Recently we reported a series of numerical simulations proving that it is possible in principle to create an electronic wave packet and subsequent electronic motion in a neutral molecule photoexcited by a UV pump pulse within a few femtoseconds. We considered the ozone molecule: for this system the electronic wave packet leads to a dissociation process. In the present work, we investigate more specifically the time-resolved photoelectron angular distribution of the ozone molecule that provides a much more detailed description of the evolution of the electronic wave packet. We thus show that this experimental technique should be able to give access to observing in real time the creation of an electronic wave packet in a neutral molecule and its impact on a chemical process.