Manipulating Two-Photon-Absorption of Cavity Polaritons by Entangled Light

Diagrammatic representation and nonperturbative approximations of the exact time-convolutionless master equation

The time-convolutionless master equation provides a general framework to model the non-Markovian dynamics of an open quantum system with a time-local generator. A diagrammatic representation is developed and proven for the perturbative expansion of the exact time-local generator for an open quantum system interacting with arbitrary environments. A truncation of the perturbation expansion leads to perturbative time-convolutionless quantum master equations. We further introduce a general iterative approach to construct nonperturbative approximations for the time-local generator as nested time-ordered exponential operators.

Cavity Control of Molecular Spectroscopy and Photophysics

ConspectusOptical cavities have been established as a powerful platform for manipulating the spectroscopy and photophysics of molecules. Molecules placed inside an optical cavity will interact with the cavity field, even if the cavity is in the vacuum state with no photons. When the coupling strength between matter excitations, either electronic or vibrational, and a cavity photon mode surpasses all decay rates in the system, hybrid light-matter excitations known as cavity polaritons emerge. Originally studied in atomic systems, there has been growing interest in studying polaritons in molecules. Numerous studies, both experimental and theoretical, have demonstrated that the formation of molecular polaritons can significantly alter the optical, electronic, and chemical properties of molecules in a noninvasive manner.This Account focuses on novel studies that reveal how optical cavities can be employed to control electronic excitations, both valence and core, in molecules and the spectroscopic signatures of molecular polaritons. We first discuss the capacity of optical cavities to manipulate and control the intrinsic conical intersection dynamics in polyatomic molecules. Since conical intersections are responsible for a wide range of photochemical and photophysical processes such as internal conversion, photoisomerization, and singlet fission, this provides a practical strategy to control molecular photodynamics. Two examples are given for the internal conversion in pyrazine and singlet fission in a pentacene dimer. We further show how X-ray cavities can be exploited to control the core-level excitations of molecules. Core polaritons can be created from inequivalent core orbitals by exchanging X-ray cavity photons. The core polaritons can also alter the selection rules in nonlinear spectroscopy.Polaritonic states and dynamics can be monitored by nonlinear spectroscopy. Quantum light spectroscopy is a frontier in nonlinear spectroscopy that exploits the quantum-mechanical properties of light, such as entanglement and squeezing, to extract matter information inaccessible by classical light. We discuss how quantum spectroscopic techniques can be employed for probing polaritonic systems. In multimolecule polaritonic systems, there exist two-polariton states that are dark in the two-photon absorption spectrum due to destructive interference between transition pathways. We show that a time-frequency entangled photon pair can manipulate the interference between transition pathways in the two-photon absorption signal and thus capture classically dark two-polariton states. Finally, we discuss cooperative effects among molecules in spectroscopy and possibly in chemistry. When many molecules are involved in forming the polaritons, while the cooperative effects clearly manifest in the dependence of the Rabi splitting on the number of molecules, whether they can show up in chemical reactivity, which is intrinsically local, is an open question. We explore the cooperative nature of the charge migration process in a cavity and show that, unlike spectroscopy, polaritonic charge dynamics is intrinsically local and does not show collective many-molecule effects.

Photoelectron spectroscopy with entangled photons; enhanced spectrotemporal resolution

In this theoretical study, we show how photoelectron signals generated by time-energy entangled photon pairs can monitor ultrafast excited state dynamics of molecules with high joint spectral and temporal resolutions, not limited by the Fourier uncertainty of classical light. This technique scales linearly, rather than quadratically, with the pump intensity, allowing the study of fragile biological samples with low photon fluxes. Since the spectral resolution is achieved by electron detection and the temporal resolution by a variable phase delay, this technique does not require scanning the pump frequency and the entanglement times, which significantly simplifies the experimental setup, making it feasible with current instrumentation. Application is made to the photodissociation dynamics of pyrrole calculated by exact nonadiabatic wave packet simulations in a reduced two nuclear coordinate space. This study demonstrates the unique advantages of ultrafast quantum light spectroscopy.

Generalization of the Tavis-Cummings model for multi-level anharmonic systems: Insights on the second excitation manifold

Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light-matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis-Cummings model in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excitation manifold, of an arbitrary number N of oscillators collectively coupled to a single cavity mode in the rotating-wave approximation. Elaborating on our group-theoretic approach [New J. Phys. 23, 063081 (2021)], we simplify the brute-force diagonalization of N² × N² Hamiltonians to the eigendecomposition of, at most, 4 × 4 matrices for arbitrary N. We thoroughly discuss the eigenstates and the consequences of weak and strong anharmonicities. Furthermore, we find resonant conditions between bipolaritons and anharmonic transitions where two-photon absorption can be enhanced. Finally, we conclude that energy shifts in the polaritonic states induced by anharmonicities become negligible for large N. Thus, calculations with a single or few quantum emitters qualitatively fail to represent the nonlinear optical response of the collective strong coupling regime. Our work highlights the rich physics of multilevel anharmonic systems coupled to cavities absent in standard models of quantum optics. We also provide concise tabulated expressions for eigenfrequencies and transition amplitudes, which should serve as a reference for future spectroscopic studies of molecular polaritons.

Optical Cavity Manipulation and Nonlinear UV Molecular Spectroscopy of Conical Intersections in Pyrazine

Optical cavities provide a versatile platform for manipulating the excited-state dynamics of molecules via strong light-matter coupling. We employ optical absorption and two-multidimensional electronic spectroscopy simulations to investigate the effect of optical cavity coupling in the nonadiabatic dynamics of photoexcited pyrazine. We observe the emergence of a novel polaritonic conical intersection (PCI) between the electronic dark state and photonic surfaces as the cavity frequency is tuned. The PCI could significantly change the nonadiabatic dynamics of pyrazine by doubling the decay rate constant of the S₂ state population. Moreover, the absorption spectrum and excited-state dynamics could be systematically manipulated by tuning the strong light-matter interaction, e.g., the cavity frequency and cavity coupling strength. We propose that a tunable optical cavity-molecule system may provide promising approaches for manipulating the photophysical properties of molecules.

Cavity quantum-electrodynamical time-dependent density functional theory within Gaussian atomic basis. II. Analytic energy gradient

Following the formulation of cavity quantum-electrodynamical time-dependent density functional theory (cQED-TDDFT) models [Flick et al., ACS Photonics 6, 2757–2778 (2019) and Yang et al., J. Chem. Phys. 155, 064107 (2021)], here, we report the derivation and implementation of the analytic energy gradient for polaritonic states of a single photochrome within the cQED-TDDFT models. Such gradient evaluation is also applicable to a complex of explicitly specified photochromes or, with proper scaling, a set of parallel-oriented, identical-geometry, and non-interacting molecules in the microcavity.

Wave Packet Control and Simulation Protocol for Entangled Two-Photon Absorption of Molecules

Quantum light spectroscopy, providing novel molecular information nonaccessible by classical light, necessitates new computational tools when applied to complex molecular systems. We introduce two computational protocols for the molecular nuclear wave packet dynamics interacting with an entangled photon pair to produce an entangled two-photon absorption signal. The first involves summing over transition pathways in a temporal grid defined by two light-matter interaction times accompanied by the field correlation functions of quantum light. The signal is obtained by averaging over the two time distribution characteristics of the entangled photon state. The other protocol involves a Schmidt decomposition of the entangled light and requires summing over the Schmidt modes. We demonstrate how photon entanglement can be used to control and manipulate the two-photon excited nuclear wave packets in a displaced harmonic oscillator model.

Photoisomerization transition state manipulation by entangled two-photon absorption

We demonstrate how two-photon excitation with quantum light can influence elementary photochemical events. The azobenzene trans → cis isomerization following entangled two-photon excitation is simulated using quantum nuclear wave packet dynamics. Photon entanglement modulates the nuclear wave packets by coherently controlling the transition pathways. The photochemical transition state during passage of the reactive conical intersection in azobenzene photoisomerization is strongly affected with a noticeable alteration of the product yield. Quantum entanglement thus provides a novel control knob for photochemical reactions. The distribution of the vibronic coherences during the conical intersection passage strongly depends on the shape of the initial wave packet created upon quantum light excitation. X-ray signals that can experimentally monitor this coherence are simulated.

Experimental requirements for entangled two-photon spectroscopy

Coherently controlling the spectral properties of energy-entangled photons is a key component of future entangled two-photon spectroscopy schemes that are expected to provide advantages with respect to classical methods. We present here an experimental setup based on a grating compressor. It allows for the spectral shaping of entangled photons with a sevenfold increase in resolution, compared to previous setups with a prism compressor. We evaluate the performances of the shaper by detecting sum frequency generation in a nonlinear crystal with both classical pulses and entangled photon pairs. The efficiency of both processes is experimentally compared and is in accordance with a simple model relating the classical and entangled two-photon absorption coefficients. Finally, the entangled two-photon shaping capability is demonstrated by implementing an interferometric transfer function.

Quantum-electrodynamical time-dependent density functional theory within Gaussian atomic basis

Inspired by the formulation of quantum-electrodynamical time-dependent density functional theory (QED-TDDFT) by Rubio and co-workers [Flick et al., ACS Photonics 6, 2757-2778 (2019)], we propose an implementation that uses dimensionless amplitudes for describing the photonic contributions to QED-TDDFT electron-photon eigenstates. This leads to a Hermitian QED-TDDFT coupling matrix that is expected to facilitate the future development of analytic derivatives. Through a Gaussian atomic basis implementation of the QED-TDDFT method, we examined the effect of dipole self-energy, rotating-wave approximation, and the Tamm-Dancoff approximation on the QED-TDDFT eigenstates of model compounds (ethene, formaldehyde, and benzaldehyde) in an optical cavity. We highlight, in the strong coupling regime, the role of higher-energy and off-resonance excited states with large transition dipole moments in the direction of the photonic field, which are automatically accounted for in our QED-TDDFT calculations and might substantially affect the energies and compositions of polaritons associated with lower-energy electronic states.

Investigations of Molecular Optical Properties Using Quantum Light and Hong-Ou-Mandel Interferometry

Entangled photon pairs have been used for molecular spectroscopy in the form of entangled two-photon absorption and in quantum interferometry for precise measurements of light source properties and time delays. We present an experiment that combines molecular spectroscopy and quantum interferometry by utilizing the correlations of entangled photons in a Hong-Ou-Mandel (HOM) interferometer to study molecular properties. We find that the HOM signal is sensitive to the presence of a resonant organic sample placed in one arm of the interferometer, and the resulting signal contains information pertaining to the light-matter interaction. We can extract the dephasing time of the coherent response induced by the excitation on a femtosecond time scale. A dephasing time of 102 fs is obtained, which is relatively short compared to times found with similar methods and considering line width broadening and the instrument entanglement time As the measurement is done with coincidence counts as opposed to simply intensity, it is unaffected by even-order dispersion effects, and because interactions with the molecular state affect the photon correlation, the observed measurement contains only these effects and no other classical losses. The experiments are accompanied by theory that predicts the observed temporal shift and captures the entangled photon joint spectral amplitude and the molecule's transmission in the coincidence counting rate. Thus, we present a proof-of-concept experimental method based of entangled photon interferometry that can be used to characterize optical properties in organic molecules and can in the future be expanded on for more complex spectroscopic studies of nonlinear optical properties.

Optimization of selective two-photon absorption in cavity polaritons

We investigate optimal states of photon pairs to excite a target transition in a multilevel quantum system. With the help of coherent control theory for two-photon absorption with quantum light, we infer the maximal population achievable by optimal entangled vs separable states of light. Interference between excitation pathways as well as the presence of nearby states may hamper the selective excitation of a particular target state, but we show that quantum correlations can help to overcome this problem and enhance the achievable "selectivity" between two energy levels, i.e., the relative difference in population transferred into each of them. We find that the added value of optimal entangled states of light increases with broadening linewidths of the target states.

Manipulating valence and core electronic excitations of a transition-metal complex using UV/Vis and X-ray cavities

We demonstrate how optical cavities can be exploited to control both valence- and core-excitations in a prototypical model transition metal complex, ferricyanide ([Fe(iii)(CN)6]3-), in an aqueous environment. The spectroscopic signatures of hybrid light-matter polariton states are revealed in UV/Vis and X-ray absorption, and stimulated X-ray Raman signals. In an UV/Vis cavity, the absorption spectrum exhibits the single-polariton states arising from the cavity photon mode coupling to both resonant and off-resonant valence-excited states. We further show that nonlinear stimulated X-ray Raman signals can selectively probe the bipolariton states via cavity-modified Fe core-excited states. This unveils the correlation between valence polaritons and dressed core-excitations. In an X-ray cavity, core-polaritons are generated and their correlations with the bare valence-excitations appear in the linear and nonlinear X-ray spectra.

Optical-Cavity Manipulation of Conical Intersections and Singlet Fission in Pentacene Dimers

We demonstrate how the singlet fission process in pentacene dimers mediated by a conical intersection is controlled by coupling the molecule to a confined optical cavity photon mode. By following the polariton quantum dynamics of a conical intersection coupled to a cavity mode taking into account vibrational relaxation and cavity loss, we find that the singlet fission can be significantly suppressed because the polaritonic conical intersection is pushed away from the initial Franck-Condon excitation region.

Manipulating Core Excitations in Molecules by X-Ray Cavities

Core excitations on different atoms are highly localized and therefore decoupled. By placing molecules in an x-ray cavity the core transitions become coupled via the exchange of cavity photons and form delocalized hybrid light-matter excitations known as core polaritons. We demonstrate these effects for the two inequivalent carbon atoms in 1,1-difluoroethylene. Polariton signatures in the x-ray absorption, two-photon absorption, and multidimensional four-wave mixing signals are predicted.