Multidimensional high-harmonic echo spectroscopy: Resolving coherent electron dynamics in the EUV regime.

We theoretically propose a multidimensional high-harmonic echo spectroscopy technique which utilizes strong optical fields to resolve coherent electron dynamics spanning an energy range of multiple electronvolts. Using our recently developed semi-perturbative approach, we can describe the coherent valence electron dynamics driven by a sequence of phase-matched and well-separated short few-cycle strong infrared laser pulses. The recombination of tunnel-ionized electrons by each pulse coherently populates the valence states of a molecule, which allows for a direct observation of its dynamics via the high harmonic echo signal. The broad bandwidth of the effective dipole between valence states originated from the strong-field excitation results in nontrivial ultra-delayed partial rephasing echo, which is not observed in standard two-dimensional optical spectroscopic techniques in a two-level molecular systems. We demonstrate the results of simulations for the anionic molecular system and show that the ultrafast valence electron dynamics can be well captured with femtosecond resolution.

Multidimensional four-wave mixing signals detected by quantum squeezed light.

Four-wave mixing (FWM) of optical fields has been extensively used in quantum information processing, sensing, and memories. It also forms a basis for nonlinear spectroscopies such as transient grating, stimulated Raman, and photon echo where phase matching is used to select desired components of the third-order response of matter. Here we report an experimental study of the two-dimensional quantum noise intensity difference spectra of a pair of squeezed beams generated by FWM in hot Rb vapor. The measurement reveals details of the [Formula: see text] susceptibility dressed by the strong pump field which induces an AC Stark shift, with higher spectral resolution compared to classical measurements of probe and conjugate beam intensities. We demonstrate how quantum correlations of squeezed light can be utilized as a spectroscopic tool which unlike their classical counterparts are robust to external noise.

Detecting electronic coherences by time-domain high-harmonic spectroscopy.

Ultrafast spectroscopy is capable of monitoring electronic and vibrational states. For electronic states a few eV apart, an X-ray laser source is required. We propose an alternative method based on the time-domain high-order harmonic spectroscopy where a coherent superposition of the electronic states is first prepared by the strong optical laser pulse. The coherent dynamics can then be probed by the higher-order harmonics generated by the delayed probe pulse. The high nonlinearity typically modeled by the three-step mechanism introduced by Lewenstein and Corkum can serve as a recipe for generation of the coherent excitation with broad bandwidth. The main advantage of the method is that only optical (non-X-ray) lasers are needed. A semiperturbative model based on the Liouville space superoperator approach is developed for the bookkeeping of the different orders of the nonlinear response for the high-order harmonic generation using multiple pulses. Coherence between bound electronic states is monitored in the harmonic spectra from both first- and second-order responses.

Quantum phase-sensitive diffraction and imaging using entangled photons.

We propose a quantum diffraction imaging technique whereby one photon of an entangled pair is diffracted off a sample and detected in coincidence with its twin. The image is obtained by scanning the photon that did not interact with matter. We show that when a dynamical quantum system interacts with an external field, the phase information is imprinted in the state of the field in a detectable way. The contribution to the signal from photons that interact with the sample scales as [Formula: see text], where [Formula: see text] is the source intensity, compared with [Formula: see text] of classical diffraction. This makes imaging with weak fields possible, providing high signal-to-noise ratio, avoiding damage to delicate samples. A Schmidt decomposition of the state of the field can be used for image enhancement by reweighting the Schmidt modes contributions.

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.

Multi-wave mixing in the high harmonic regime: monitoring electronic dynamics.

It has been demonstrated that electronic coherences across many eV can be detected in pump-probe experiments involving high harmonic sources. An additional degree of control over the phase matching can be employed by investigating a more general class of multi-wave mixing. Non-collinear multi-wave mixing of high harmonics with energy (q1ω1 + q2ω2) can be selectively detected along the direction of (q1k1 + q2k2). Simulations based on a recently developed semi-perturbative approach show that only the specific harmonic signals with q1ω1 close to the energy difference between ground state and excited states are observable when the two input pulses are well separated in time. The coherent dynamics between different states can be selectively tracked by detecting the time-delay dependent signals with different q1k1, which can overcome the potential spectral congestion in real experiments. Additionally, such non-collinear geometry can be used to separate the dephasing induced decay and collision induced recovery behaviors of pump-probe high harmonic signal typically observed in the time-resolved high harmonic pump-probe signals.

Interferometric spectroscopy with quantum light: Revealing out-of-time-ordering correlators.

We survey the inclusion of interferometric elements in nonlinear spectroscopy performed with quantum light. Controlled interference of electromagnetic fields coupled to matter can induce constructive or destructive contributions of microscopic coupling sequences (histories) of matter. Since quantum fields do not commute, quantum light signals are sensitive to the order of light-matter coupling sequences. Matter correlation functions are thus imprinted by different field factors, which depend on that order. We identify the associated quantum information obtained by controlling the weights of different contributing pathways and offer several experimental schemes for recovering it. Nonlinear quantum response functions include out-of-time-ordering matter correlators (OTOCs), which reveal how perturbations spread throughout a quantum system (information scrambling). Their effect becomes most notable when using ultrafast pulse sequences with respect to the path difference induced by the interferometer. OTOCs appear in quantum-informatics studies in other fields, including black hole, high energy, and condensed matter physics.

Detection of photon statistics and multimode field correlations by Raman processes.

Glauber's g(2)-function provides a common measure of quantum field statistics through two-photon coincidence counting in Hanbury Brown-Twiss measurements. Here, we propose to use nonlinear optical signals as a tool for the characterization of quantum light. In particular, we show that Raman measurements provide an alternative direct probe for a different component of the four-point correlation function underlying the g(2)-function. We illustrate this capacity for a specific quantum state obtained from a frequency conversion process. Our work points out how the analysis of controlled optical nonlinear processes can provide an alternative window toward the analysis of quantum light sources.

Light absorption by interacting atomic gas in quantum optical regime.

Quantum optical theory of absorption properties of interacting atoms is developed. The concept of local absorptance is introduced as a derivative of the logarithm of intensity with respect to the distance in the vicinity of a given spatial point and a moment of time. The intensity is represented by the quantum and statistically averaged normal product of creation and annihilation operators of the electromagnetic field. The development of an analytical method of the estimation for the kinetic and optical parameters for the system is proposed here. The calculation method of the absorption coefficient includes thermal atomic motion, Doppler effect, and the short-range interaction between atoms. The absorption coefficient explicitly takes into account the quantum nature of the optical field. The ability of the system to absorb or emit quanta is quantitatively expressed through the special form of interaction integrals. The specific form of integrals results from the structure of the quantum brackets. The interplay between the collective (virtual photon exchange) and binary (optically induced inter-particle bonding) processes determines the system behavior. The spectral profile of the local absorption coefficient for different atomic densities and time intervals is simulated for realistic parameters.

Multidimensional photon correlation spectroscopy of cavity polaritons.

The strong coupling of atoms and molecules to radiation field modes in optical cavities creates dressed matter/field states known as polaritons with controllable dynamical and energy transfer properties. We propose a multidimensional optical spectroscopy technique for monitoring polariton dynamics. The response of a two-level atom to the time-dependent coupling to a single-cavity mode is monitored through time-and-frequency-resolved single-photon coincidence measurements of spontaneous emission. Polariton population and coherence dynamics and its variation with cavity photon number and controlled by gating parameters are predicted by solving the Jaynes-Cummings model.

Entangled Two-Photon Absorption Spectroscopy.

The application of quantum states of light such as entangled photons, for example, created by parametric down conversion, has experienced tremendous progress in the almost 40 years since their first experimental realization. Initially, they were employed in the investigation of the foundations of quantum physics, such as the violation of Bell's inequalities and studies of quantum entanglement. They later emerged as basic platforms for quantum communication protocols and, in the recent experiments on single-photon interactions, in photonic quantum computation. These applications aim at the controlled manipulation of the photonic degrees of freedom, and therefore rely on simple models of matter, where the analysis is simpler. Furthermore, quantum imaging with entangled light can achieve enhanced resolution, and quantum metrology can overcome the shot noise limit for classical light. This Account focuses on an entirely different emerging class of applications using quantum light as a powerful spectroscopic tool to reveal novel information about complex molecules. These applications utilize two appealing properties of quantum light: its distinct intensity fluctuations and its nonclassical bandwidth properties. These give rise to new and surprising behavior of nonlinear optical signals. Nonclassical intensity fluctuations can enhance nonlinear optical signals relative to linear absorption. For instance, the two-photon absorption of entangled photon pairs scales linearly (rather than quadratically) in the photon flux, just like a single photon absorption. This enables nonlinear quantum spectroscopy of photosensitive, for example, biological, samples at low light intensities. We will discuss how the two-photon absorption cross section becomes a function of the photonic quantum state, which can be manipulated by properties of the entangled photon pairs. In addition, the quantum correlations in entangled photon states further influence the nonlinear signals in a variety of ways. Apart from affecting the signal's scaling with intensity, they also constitute an entirely new approach to shaping and controlling excitation pathways in molecular aggregates in a way that cannot be achieved with shaped classical pulses. This is because between the two absorption events in entangled two-photon absorption, the light and material system are entangled. Classical constraints for the simultaneous time and frequency resolution can thus be circumvented, since the two are not Fourier conjugates. Here we review the simplest manifestation of quantum light spectroscopy, two-photon absorption spectroscopy with entangled photons. This will allow us to discuss exemplarily the impact of quantum properties of light on a nonlinear optical signal and explore the opportunities for future applications.

Quantum interference and collisional dynamics in excited bounds states revealed by time-resolved pump-high-harmonic-generation-probe spectroscopy.

Ultrafast pump-high-harmonic-generation-probe spectroscopy aims to provide a unique observation window into electronic dynamics while using the infrared or visible light sources. While it is widely accepted that the role of excited bound states in high-harmonic generation is negligible, its dynamics play a significant role in time-resolved pump-probe measurements. Here we show that the time-resolved pump-high-harmonic-generation-probe measurement may reveal a significant (up to 20%) contribution of the quantum interference in electron ionization and recombination with atomic system, with the initial or the final state being an excited bound state. Interplay of two dephasing mechanisms of electron-ion and electron-atom collisions yields decay and recovery of the time-resolved signal, respectively, signifying the role of the quantum interference involving excited bound states in recovery mode. Our theory, based on the density matrix Liouville space formalism, is supported by experimental measurements in argon gas.

Simulating Coherent Multidimensional Spectroscopy of Nonadiabatic Molecular Processes: From the Infrared to the X-ray Regime.

Crossings of electronic potential energy surfaces in nuclear configuration space, known as conical intersections, determine the rates and outcomes of a large class of photochemical molecular processes. Much theoretical progress has been made in computing strongly coupled electronic and nuclear motions at different levels, but how to incorporate them in different spectroscopic signals and the approximations involved are less established. This will be the focus of the present review. We survey a wide range of time-resolved spectroscopic techniques which span from the infrared to the X-ray regimes and can be used for probing the nonadiabatic dynamics in the vicinity of conical intersections. Transient electronic and vibrational probes and their theoretical signal calculations are classified by their information content. This includes transient vibrational spectroscopic methods (transient infrared and femtosecond off-resonant stimulated Raman), resonant electronic probes (transient absorption and photoelectron spectroscopy), and novel stimulated X-ray Raman techniques. Along with the precise definition of what to calculate for predicting the various signals, we outline a toolbox of protocols for their simulation.

Coherent control of long-range photoinduced electron transfer by stimulated X-ray Raman processes.

We show that X-ray pulses resonant with selected core transitions can manipulate electron transfer (ET) in molecules with ultrafast and atomic selectivity. We present possible protocols for coherently controlling ET dynamics in donor-bridge-acceptor (DBA) systems by stimulated X-ray resonant Raman processes involving various transitions between the D, B, and A sites. Simulations presented for a Ru(II)-Co(III) model complex demonstrate how the shapes, phases and amplitudes of the X-ray pulses can be optimized to create charge on demand at selected atoms, by opening up otherwise blocked ET pathways.

Probing electron-atom collision dynamics in gas plasma by high-order harmonic spectroscopy.

Plasma is a complex system involving diverse collisional processes and interactions, such as electron-impact excitation, ionization, recombination, etc. One of the most important methods for studying the properties and dynamics of plasma is to analyze the radiations from plasma. Here, we demonstrate the high-order harmonic (HH) spectroscopy for probing the complex electron-atom collision (EAC) dynamics in a laser-induced gas plasma. These measurements were carried out by using an elliptically polarized pump and a time-delayed linearly polarized probe. The HH spectra from argon and krypton plasmas were recorded by scanning the time delay up to hundreds of picoseconds. We found that the delay-dependent HH yield contains three distinct regions, i.e., the first enhancement, the subsequent suppression, and the final restoration regions. A qualitative analysis shows that these features are clear signatures of the EAC processes and interactions involved in the delay-dependent HH spectroscopy.

Monitoring polariton dynamics in the LHCII photosynthetic antenna in a microcavity by two-photon coincidence counting.

The relaxation dynamics of light-harvesting complex II in an optical cavity is explored theoretically by multidimensional photon coincidence counting spectroscopy. This technique reveals the dynamics in both single (e) and double (f) excitation bands. We study how the polariton dynamics are affected by coupling to photon modes and molecular vibrations described by a realistic spectral density at 77 K. Without the cavity, the e- and f-band energy transfer pathways are not clearly resolved due to the line broadening caused by fast exciton dephasing. The strong coupling to cavity photons results in well-resolved polariton modes. The hybrid nature of polaritons slows down their energy transfer rates.

Photosynthetic reaction center as a quantum heat engine.

Two seemingly unrelated effects attributed to quantum coherence have been reported recently in natural and artificial light-harvesting systems. First, an enhanced solar cell efficiency was predicted and second, population oscillations were measured in photosynthetic antennae excited by sequences of coherent ultrashort laser pulses. Because both systems operate as quantum heat engines (QHEs) that convert the solar photon energy to useful work (electric currents or chemical energy, respectively), the question arises whether coherence could also enhance the photosynthetic yield. Here, we show that both effects arise from the same population-coherence coupling term which is induced by noise, does not require coherent light, and will therefore work for incoherent excitation under natural conditions of solar excitation. Charge separation in light-harvesting complexes occurs in a pair of tightly coupled chlorophylls (the special pair) at the heart of photosynthetic reaction centers of both plants and bacteria. We show the analogy between the energy level schemes of the special pair and of the laser/photocell QHEs, and that both population oscillations and enhanced yield have a common origin and are expected to coexist for typical parameters. We predict an enhanced yield of 27% in a QHE motivated by the reaction center. This suggests nature-mimicking architectures for artificial solar energy devices.

Catching Conical Intersections in the Act: Monitoring Transient Electronic Coherences by Attosecond Stimulated X-Ray Raman Signals.

Conical intersections (CIs) dominate the pathways and outcomes of virtually all photophysical and photochemical molecular processes. Despite extensive experimental and theoretical effort, CIs have not been directly observed yet and the experimental evidence is being inferred from fast reaction rates and some vibrational signatures. We show that short x-ray (rather than optical) pulses can directly detect the passage through a CI with the adequate temporal and spectral sensitivity. The technique is based on a coherent Raman process that employs a composite femtosecond or attosecond x-ray pulse to detect the electronic coherences (rather than populations) that are generated as the system passes through the CI.

On the Resolution Limit of Femtosecond Stimulated Raman Spectroscopy: Modelling Fifth-Order Signals with Overlapping Pulses.

Femtosecond stimulated Raman scattering (FSRS) spectroscopy is a powerful pump-probe technique that can track electronic and vibrational dynamics with high spectral and temporal resolution. The investigation of extremely short-lived species, however, implies deciphering complex signals and is ultimately hampered by unwanted nonlinear effects once the time resolution limit is approached and the pulses overlap temporally. Using the loop diagrams formalism we calculate the fifth-order response of a model system and address the limiting case where the relevant dynamics timescale is comparable to the pump-pulse duration and, consequently, the pump and the probe overlap temporally. We find that in this regime, additional diagrams that do not contribute for temporally well separated pulses need to be taken into account, giving rise to new time-dependent features, even in the absence of photoinduced dynamics and for negative delays.

Stochastic Liouville equations for femtosecond stimulated Raman spectroscopy.

Electron and vibrational dynamics of molecules are commonly studied by subjecting them to two interactions with a fast actinic pulse that prepares them in a nonstationary state and after a variable delay period T, probing them with a Raman process induced by a combination of a broadband and a narrowband pulse. This technique, known as femtosecond stimulated Raman spectroscopy (FSRS), can effectively probe time resolved vibrational resonances. We show how FSRS signals can be modeled and interpreted using the stochastic Liouville equations (SLE), originally developed for NMR lineshapes. The SLE provide a convenient simulation protocol that can describe complex dynamics caused by coupling to collective bath coordinates at much lower cost than a full dynamical simulation. The origin of the dispersive features that appear when there is no separation of timescales between vibrational variations and the dephasing time is clarified.