Visualizing and controlling vibrational wave packets of single molecules

Merging Vibrational Spectroscopy with Fluorescence Microscopy: Combining the Best of Two Worlds

Vibrational spectroscopy and fluorescence spectroscopy have historically been two established but separate fields of molecular spectroscopy. While vibrational spectroscopy provides exquisite chemical information, fluorescence spectroscopy often offers orders of magnitude higher detection sensitivity. However, they each lack the advantages of each other. In recent years, a series of novel nonlinear optical spectroscopy studies have been developed that merge both spectroscopies into a single double-resonance process. These techniques combine the chemical specificity of Raman or infrared (IR) spectroscopy with the superb detection sensitivity and spatial resolution of fluorescence microscopy. Many facets have been explored, including Raman transition versus IR transition, time domain versus frequency domain, and spectroscopy versus microscopy. Notably, single-molecule vibrational spectroscopy has been achieved at room temperature without the need for plasmonics. Even superresolution vibrational imaging beyond the diffraction limit was demonstrated. This review summarizes the growing field of vibrational-encoded fluorescence microscopy, including key technical developments, emerging applications, and future prospects.

Time-resolved Coulomb explosion imaging of vibrational wave packets in alkali dimers on helium nanodroplets

Vibrational wave packets are created in the lowest triplet state 13Σu+ of K2 and Rb2 residing on the surface of helium nanodroplets, through non-resonant stimulated impulsive Raman scattering induced by a moderately intense near-infrared laser pulse. A delayed, intense 50-fs laser pulse doubly ionizes the alkali dimers via multiphoton absorption and thereby causes them to Coulomb explode into a pair of alkali ions Ak+. From the kinetic energy distribution P(Ekin) of the Ak+ fragment ions, measured at a large number of delays, we determine the time-dependent internuclear distribution P(R, t), which represents the modulus square of the wave packet within the accuracy of the experiment. For both K2 and Rb2, P(R, t) exhibits a periodic oscillatory structure throughout the respective 300 and 100 ps observation times. The oscillatory structure is reflected in the time-dependent mean value of R, ⟨R⟩(t). The Fourier transformation of ⟨R⟩(t) shows that the wave packets are composed mainly of the vibrational ground state and the first excited vibrational state, in agreement with numerical simulations. In the case of K2, the oscillations are observed for 300 ps, corresponding to more than 180 vibrational periods with an amplitude that decreases gradually from 0.035 to 0.020 Å. Using time-resolved spectral analysis, we find that the decay time of the amplitude is ∼260 ps. The decrease is ascribed to the weak coupling between the vibrating dimers and the droplet.

Fluorescence-Detected Two-Dimensional Electronic Spectroscopy of a Single Molecule

Single-molecule fluorescence spectroscopy is a powerful method that avoids ensemble averaging, but its temporal resolution is limited by the fluorescence lifetime to nanoseconds at most. At the ensemble level, two-dimensional spectroscopy provides insight into ultrafast femtosecond processes, such as energy transfer and line broadening, even beyond the Fourier limit, by correlating pump and probe spectra. Here, we combine these two techniques and demonstrate coherent 2D spectroscopy of individual dibenzoterrylene (DBT) molecules at room temperature. We excite the molecule in a confocal microscope with a phase-modulated train of femtosecond pulses and detect the emitted fluorescence with single-photon counting detectors. Using a phase-sensitive detection scheme, we were able to measure the nonlinear 2D spectra of most of the DBT molecules that we studied. Our method is applicable to a wide range of single emitters and opens new avenues for understanding energy transfer in single quantum objects on ultrafast time scales.

Deuterium Isotope Effect in Single Molecule Photophysics and Photochemistry of Hypericin

The peripherical protons of the dye molecule hypericin can undergo structural interconversion (tautomerization) between different isomers separated by a low energy barrier with rates that depends sensitively on the interaction with local chemical environment defined by the nature of host material. We investigate the deuterium (D) isotope effect of hypericin tautomerism at the single-molecule level to avoid ensemble averaging in different polymer matrices by a combined spectroscopic and computational approach. In the 'innocent' PMMA matrix only intramolecular isotope effects on the internal conversion channel and tautomerization are observed; while PVA specifically interacts with the probe via H- and D-bonding. This establishes a single molecular picture on intra- and intermolecular nano-environment effects to control chromophore photophysics and -chemistry.

Interconnection between Polarization-Detected and Population-Detected Signals: Theoretical Results and Ab Initio Simulations

Most of spectroscopic signals are specified by the nonlinear laser-induced polarization. In recent years, population-detection of signals becomes a trend in femtosecond spectroscopy. Polarization-detected (PD) and population-detected signals are fundamentally different, because they are determined by photoinduced processes acting on disparate time scales. In this work, we consider the fluorescence-detected (FD) N-wave-mixing (NWM) signal as a representative example of population-detected signals, derive a rigorous expression for this signal, and discuss its approximate variants suitable for numerical simulations. This leads us to the definition of the phenomenological FD (PFD) signal, which contains as a special case all definitions of FD signals available in the literature. Then we formulate and prove the population-polarization equivalence (PPE) theorem, which states that PFD NWM signals produced by (possibly strong) laser pulses can be evaluated as conventional PD signals in which the effective polarization is determined by the PFD transition dipole moment operator. We use the PPE theorem for the construction of the ab initio protocol for the simulation of PFD 4WM signals. As an example, we calculate electronic two-dimensional (2D) PFD spectra of the gas-phase pyrazine and compare them with the corresponding PD 2D spectra.

Active fluorescent modulation for low-noise super-resolution microscopy

Extracting the position of individual molecular probes with high precision is the basis and core of super-resolution microscopy. However, with the expectation of low-light conditions in life science research, the signal-to-noise ratio (SNR) decreases and signal extraction faces a great challenge. Here, based on temporally modulating the fluorescence emission at certain periodical patterns, we achieved super-resolution imaging with high sensitivity by largely suppressing the background noise. We propose simple bright-dim (BD) fluorescent modulation and delicate control by phase-modulated excitation. We demonstrate that the strategy can effectively enhance signal extraction in both sparsely and densely labeled biological samples, and thus improve the efficiency and precision of super-resolution imaging. This active modulation technique is generally applicable to various fluorescent labels, super-resolution techniques, and advanced algorithms, allowing a wide range of bioimaging applications.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Nonadiabatic excited-state dynamics of ReCl(CO)3(bpy) in two different solvents

We present a study of excited-states relaxation of the complex ReCl(CO)₃(bpy) (bpy = 2,2-bipyridine) using a nonadiabatic TD-DFT dynamics on spin-mixed potential energy surfaces in explicit acetonitrile (ACN) and dimethylsulfoxide (DMSO) solutions up to 800 fs. ReCl(CO)₃(bpy) belongs to a group of important photosensitizers which show ultrafast biexponential subpicosecond fluorescence decay kinetics. The choice of solvents was motivated by the different excited-state relaxation dynamics observed in subpicosecond time-resolved IR (TRIR) experiments. Simulations of intersystem crossing (ISC) showed the development of spin-mixed states in both solvents. Transformation of time-dependent populations of spin-mixed states enabled to monitor the temporal evolution of individual singlet and triplet states, fitting of bi-exponential decay kinetics, and simulating the time-resolved fluorescence spectra that show only minor differences between the two solvents. Analysis of structural relaxation and solvent reorganization employing time-resolved proximal distribution functions pointed to the factors influencing the fluorescence decay time constants. Nonadiabatic dynamics simulations of time-evolution of electronic, molecular, and solvent structures emerge as a powerful technique to interpret time-resolved spectroscopic data and ultrafast photochemical reactivity.

Trajectory Ensemble Methods Provide Single-Molecule Statistics for Quantum Dynamical Systems

The emergence of experiments capable of probing quantum dynamics at the single-molecule level requires the development of new theoretical tools capable of simulating and analyzing these dynamics beyond an ensemble-averaged description. In this article, we present an efficient method for sampling and simulating the dynamics of the individual quantum systems that make up an ensemble and apply it to study the nonequilibrium dynamics of the ubiquitous spin-boson model. We generate an ensemble of single-system trajectories, and we analyze this trajectory ensemble using tools from classical statistical mechanics. Our results demonstrate that the dynamics of quantum coherence is highly heterogeneous at the single-system level due to variations in the initial bath configuration, which significantly affects the transient exchange of coherence between the system and its bath. We observe that single systems tend to retain coherence over time scales longer than that of the ensemble. We also compute a novel thermodynamic entanglement entropy that quantifies a thermodynamic driving force favoring system-bath entanglement.

Observation of robust energy transfer in the photosynthetic protein allophycocyanin using single-molecule pump-probe spectroscopy

Photosynthetic organisms convert sunlight to electricity with near unity quantum efficiency. Absorbed photoenergy transfers through a network of chromophores positioned within protein scaffolds, which fluctuate due to thermal motion. The resultant variation in the individual energy transfer steps has not yet been measured, and so how the efficiency is robust to this variation has not been determined. Here, we describe single-molecule pump-probe spectroscopy with facile spectral tuning and its application to the ultrafast dynamics of single allophycocyanin, a light-harvesting protein from cyanobacteria. We disentangled the energy transfer and energetic relaxation from nuclear motion using the spectral dependence of the dynamics. We observed an asymmetric distribution of timescales for energy transfer and a slower and more heterogeneous distribution of timescales for energetic relaxation, which was due to the impact of the protein environment. Collectively, these results suggest that energy transfer is robust to protein fluctuations, a prerequisite for efficient light harvesting.

Nonequilibrium Work Relations and Response Theories in Ensemble Quantum Systems

We develop a nonequilibrium response theory for macroscopic quantum systems that separates the contributions of ensemble heterogeneity and intrinsic quantum uncertainty. To accomplish this, we describe systems with a quantum P-ensemble, which goes beyond the standard density matrix description by explicitly specifying the classical heterogeneity between individual quantum systems in an ensemble. We use the P-ensemble formalism to present quantum generalizations of linear response theory and the Jarzynski nonequilibrium work relation. We derive these generalizations from a Bochkov-Kuzovlev generating functional for quantum P-ensembles, which can be further utilized to derive all orders of response theory that apply to ensemble quantum systems. We contrast these developments with their ρ-ensemble analogs, and we discuss how these P-ensemble theories provide a guide for an effective application of single molecule experiments.

Time-Resolved Excited-State Analysis of Molecular Electron Dynamics by TDDFT and Bethe-Salpeter Equation Formalisms

In this work, a theoretical and computational set of tools to study and analyze time-resolved electron dynamics in molecules, under the influence of one or more external pulses, is presented. By coupling electronic-structure methods with the resolution of the time-dependent Schrödinger equation, we developed and implemented the time-resolved induced density of the electronic wavepacket, the time-resolved formulation of the differential projection density of states (ΔPDOS), and of transition contribution map (TCM) to look at the single-electron orbital occupation and localization change in time. Moreover, to further quantify the possible charge transfer, we also defined the energy-integrated ΔPDOS and the fragment-projected TCM. We have used time-dependent density-functional theory (TDDFT), as implemented in ADF software, and the Bethe-Salpeter equation, as provided by MolGW package, for the description of the electronic excited states. This suite of postprocessing tools also provides the time evolution of the electronic states of the system of interest. To illustrate the usefulness of these postprocessing tools, excited-state populations have been computed for HBDI (the chromophore of GFP) and DNQDI molecules interacting with a sequence of two pulses. Time-resolved descriptors have been applied to study the time-resolved electron dynamics of HBDI, DNQDI, LiCN (being a model system for dipole switching upon highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) electronic excitation), and Ag22. The computational analysis tools presented in this article can be employed to help the interpretation of fast and ultrafast spectroscopies on molecular, supramolecular, and composite systems.

Few-Molecule Strong Coupling with Dimers of Plasmonic Nanoparticles Assembled on DNA

Hybrid nanostructures, in which a known number of quantum emitters are strongly coupled to a plasmonic resonator, should feature optical properties at room temperature such as few-photon nonlinearities or coherent superradiant emission. We demonstrate here that this coupling regime can only be reached with dimers of gold nanoparticles in stringent experimental conditions, when the interparticle spacing falls below 2 nm. Using a short transverse DNA double-strand, we introduce five dye molecules in the gap between two 40 nm gold particles and actively decrease its length down to sub-2 nm values by screening electrostatic repulsion between the particles at high ionic strengths. Single-nanostructure scattering spectroscopy then evidence the observation of a strong-coupling regime in excellent agreement with electrodynamic simulations. Furthermore, we highlight the influence of the planar facets of polycrystalline gold nanoparticles on the probability of observing strongly coupled hybrid nanostructures.

Spectrally-tunable femtosecond single-molecule pump-probe spectroscopy

Single-molecule spectroscopy has been extensively used to investigate heterogeneity in static and dynamic behaviors on millisecond and second timescales. More recently, single-molecule pump-probe spectroscopy emerged as a method to access heterogeneity on the femtosecond and picosecond timescales. Here, we develop a single-molecule pump-probe apparatus that is easily tunable across the visible region and demonstrate its utility on the widely-used fluorescent dye, Atto647N. A spectrally-independent, bimodal distribution of energetic relaxation time constants is found, where one peak corresponds to electronic dephasing (∼ 100 fs) and the other to intravibrational relaxation (∼ 300 fs). The bimodal nature indicates that relaxation within each individual molecule is dominated by only one of these processes. Both peaks of the distribution are narrow, suggesting little heterogeneity is present for either process. As illustrated here, spectrally-tunable single-molecule pump-probe spectroscopy will enable investigation of the heterogeneity in a wide range of biological and material systems.

Enhanced Exciton Quantum Coherence in Single CsPbBr3 Perovskite Quantum Dots using Femtosecond Two-Photon Near-Field Scanning Optical Microscopy

Cesium-halide perovskite quantum dots (QDs) have gained tremendous interest as quantum emitters in quantum information processing applications due to their optical and photophysical properties. However, engineering excitonic states in quantum dots requires a deep knowledge of the coherent dynamics of their excitons at a single-particle level. Here, we use femtosecond time-resolved two-photon near-field scanning optical microscopy (NSOM) to reveal coherences involving a single cesium lead bromide perovskite QD (CsPbBr₃) at room temperature. We show that, compared to other nonperovskite nanoparticles, the electronic coherence on a single perovskite QD has a relatively long lifetime of ca. 150 fs, whereas CdSe QDs have exciton coherence times shorter than 75 fs at room temperature. One possible explanation for the longer coherence time observed for the CsPbBr₃ perovskite system is related to the exciton fine structure of these perovskite QDs compared to other nanoparticles. These perovskite QDs exhibit interesting optical properties that differ from those of the traditional QDs including bright triplet exciton states. In fact, due to the small amplitude of the energy gap fluctuations of dipole-allowed triplet states in perovskite QDs, the coherent superposition could be preserved for longer times. Furthermore, single-particle excitation approach implemented in this work allows us to remove effects of heterogeneity that are usually present in ensemble averaging experiments at room temperature. The realization of quantum-mechanical phase-coherence of a charge carrier that can operate at room temperature is an issue of great importance for the potential application of coherent electronic phenomena in electronic and optoelectronic devices. These interesting findings provide further evidence of the great potential of these perovskite QDs as candidates for quantum computing and information processing applications.

Laser-Driven Anharmonic Oscillator: Ground-State Dissociation of the Helium Hydride Molecular Ion by Midinfrared Pulses

The vibrational motion of molecules represents a fundamental example of an anharmonic oscillator. Using a prototype molecular system, HeH^{+}, we demonstrate that appropriate laser pulses make it possible to drive the nuclear motion in the anharmonic potential of the electronic ground state, increasing its energy above the potential barrier and facilitating dissociation by purely vibrational excitation. We find excellent agreement between the frequency-dependent response of the helium hydride molecular cation to both classical and quantum mechanical simulations, thus removing any ambiguities through electronic excitation. Our results provide access to the rich dynamics of anharmonic quantum oscillator systems and pave the way to state-selective control schemes in ground-state chemistry by the adequate choice of the laser parameters.

Visualizing Quantum Coherence Based on Single-Molecule Coherent Modulation Microscopy

Massive magical phenomena in nature are closely related to quantum effects at the microscopic scale. However, the lack of straightforward methods to observe the quantum coherent dynamics in integrated biological systems limits the study of essential biological mechanisms. In this work, we developed a single-molecule coherent modulation (SMCM) microscopy by combining the superior features of single-molecule microscopy with ultrafast spectroscopy. By introducing the modem technology and defining the coherent visibility, we realized visualization and real-time observation of the decoherence process of a single molecule influenced by the microenvironment for the first time. In particular, we applied this technique to observe the quantum coherent properties of the entire chlorella cells and found the correlation between the coherent visibility and metabolic activities, which may have potential applications in molecular diagnostics and precision medicine.

Investigating ultrafast two-pulse experiments on single DNQDI fluorophores: a stochastic quantum approach

Ultrafast two-pulse experiments on single molecules are invaluable tools to investigate the microscopic dynamics of a fluorophore. The first pulse generates electronic or vibronic coherence and the second pulse probes the time-evolution of the coherence. A protocol that is able to simulate ultrafast experiments on single molecules is applied in this study. It is based on a coupled quantum-mechanical description of the fluorophore and real-time dynamics of the system vibronic wave packet interacting with an electric field, described by means of the stochastic Schrödinger equation within the Markovian limit. This approach is applied to the DNQDI fluorophore, previously investigated experimentally [D. Brinks et al., Nature, 2010, 465, 905-908]. We find this to be in good agreement with the experimental outcomes and provide microscopic and atomistic interpretation.

Pulsed two-photon coherent control of channelrhodopsin-2 photocurrent in live brain cells

Channelrhodopsin-2 (ChR2) is an ion channel activated by the absorption of light. A recent experiment demonstrated that the current emanating from neurons in live brain cells expressing ChR2 can be controlled using two-photon phase control. Here, we propose an experimentally testable coherent control mechanism for this phenomenon. Significantly, we describe how femtosecond, quantum coherent processes arising from weak-field ultrafast excitation are responsible for the reported control of the millisecond classical dynamics of the neuronal current.

Super-resolution nanoscopy by coherent control on nanoparticle emission

Super-resolution nanoscopy based on wide-field microscopic imaging provided high efficiency but limited resolution. Here, we demonstrate a general strategy to push its resolution down to ~50 nm, which is close to the range of single molecular localization microscopy, without sacrificing the wide-field imaging advantage. It is done by actively and simultaneously modulating the characteristic emission of each individual emitter at high density. This method is based on the principle of excited state coherent control on single-particle two-photon fluorescence. In addition, the modulation efficiently suppresses the noise for imaging. The capability of the method is verified both in simulation and in experiments on ZnCdS quantum dot-labeled films and COS7 cells. The principle of coherent control is generally applicable to single-multiphoton imaging and various probes.

Improving the SERS signals of biomolecules using a stacked biochip containing Fe2O3/Au nanoparticles and a DC magnetic field

This study proposes a magnetic biochip that uses surface-enhanced Raman scattering (SERS) for antigen detection. The biochip was a sandwich structure containing alternating layers of gold and magnetic Fe₂O₃ nanoparticles. Both single (Au/Fe₂O₃/Au) and multilayer (Au/Fe₂O₃/Au/Fe₂O₃/Au) chips containing Fe₂O₃ nanoparticles were fabricated to detect bovine serum albumin (BSA). The single-layer chip detected the BSA antigen at a signal-to-noise ratio (SNR) of 5.0. Peaks detected between 1000 and 1500 cm^-1 corresponded to various carbon chains. With more Fe₂O₃ layers, bond resonance was enhanced via the Hall effect. The distribution of electromagnetic field enhancement was determined via SERS. The signal from the single-layer chip containing Au nanoparticles was measured in an external magnetic field. Maximum signal strength was recorded in a field strength of 12.5 gauss. We observed peaks due to other carbon-hydrogen molecules in a 62.5-gauss field. The magnetic field could improve the resolution and selectivity of sample observations.

Quantum Coherent Modulation-Enhanced Single-Molecule Imaging Microscopy

In fluorescence imaging and detection, undesired fluorescence interference (such as autofluorescence) often hampers the contrast of the image and even prevents the identification of structures of interest. Here, we develop a quantum coherent modulation-enhanced (QCME) single-molecule imaging microscopy (SMIM) to substantially eliminate the strong fluorescence interference, based on manipulation of the excited-state population probability of a single molecule. By periodically modulating the phase difference between the ultrashort pulse pairs and performing a discrete Fourier transform of the arrival time of emitted photons, the decimation of single molecules from strong interference in QCME-SMIM has been clearly determined, where the signal-to-interference ratio is enhanced by more than 2 orders of magnitude. This technique, confirmed to be universal to organic dyes and linked with biomacromolecules, paves the way to high-contrast bioimaging under unfavorable conditions.

Monitoring of Nonadiabatic Effects in Individual Chromophores by Femtosecond Double-Pump Single-Molecule Spectroscopy: A Model Study

We explore, by theoretical modeling and computer simulations, how nonadiabatic couplings of excited electronic states of a polyatomic chromophore manifest themselves in single-molecule signals on femtosecond timescales. The chromophore is modeled as a system with three electronic states (the ground state and two non-adiabatically coupled excited states) and a Condon-active vibrational mode which, in turn, is coupled to a harmonic oscillator heat bath. For this system, we simulate double-pump single-molecule signals with fluorescence detection for different system-field interaction strengths, from the weak-coupling regime to the strong-coupling regime. While the signals are determined by the coherence of the electronic density matrix in the weak-coupling regime, they are determined by the populations of the electronic density matrix in the strong-coupling regime. As a consequence, the signals in the strong coupling regime allow the monitoring of nonadiabatic electronic population dynamics and are robust with respect to temporal inhomogeneity of the optical gap, while signals in the weak-coupling regime are sensitive to fluctuations of the optical gap and do not contain information on the electronic population dynamics.

Ultrafast cryptography with indefinitely switchable optical nanoantennas

Bistability is widely exploited to demonstrate all-optical signal processing and light-based computing. The standard paradigm of switching between two steady states corresponding to "0" and "1" bits is based on the rule that a transition occurs when the signal pulse intensity overcomes the bistability threshold, and otherwise, the system remains in the initial state. Here, we break with this concept by revealing the phenomenon of indefinite switching in which the eventual steady state of a resonant bistable system is transformed into a nontrivial function of signal pulse parameters for moderately intense signal pulses. The essential nonlinearity of the indefinite switching allows realization of well-protected cryptographic algorithms with a single bistable element in contrast to software-assisted cryptographic protocols that require thousands of logic gates. As a proof of concept, we demonstrate stream deciphering of the word "enigma" by means of an indefinitely switchable optical nanoantenna. An extremely high bitrate ranging from ~0.1 to 1 terabits per second and a small size make such systems promising as basic elements for all-optical cryptographic architectures.

Simulation of Femtosecond Phase-Locked Double-Pump Signals of Individual Light-Harvesting Complexes LH2

Recent phase-locked femtosecond double-pump experiments on individual light-harvesting complexes LH2 of purple bacteria at ambient temperature revealed undamped oscillatory responses on a time scale of at least 400 fs [ Hildner et al. Science 2013 , 340 , 1448 ]. Using an excitonic Hamiltonian for LH2 available in the literature, we simulate these signals numerically by a method that treats excitonic couplings and exciton-phonon couplings in a nonperturbative manner. The simulations provide novel insights into the origin of coherent dynamics in individual LH2 complexes.

Simulating the vibrational quantum dynamics of molecules using photonics

Advances in control techniques for vibrational quantum states in molecules present new challenges for modelling such systems, which could be amenable to quantum simulation methods. Here, by exploiting a natural mapping between vibrations in molecules and photons in waveguides, we demonstrate a reprogrammable photonic chip as a versatile simulation platform for a range of quantum dynamic behaviour in different molecules. We begin by simulating the time evolution of vibrational excitations in the harmonic approximation for several four-atom molecules, including H₂CS, SO₃, HNCO, HFHF, N₄ and P₄. We then simulate coherent and dephased energy transport in the simplest model of the peptide bond in proteins-N-methylacetamide-and simulate thermal relaxation and the effect of anharmonicities in H₂O. Finally, we use multi-photon statistics with a feedback control algorithm to iteratively identify quantum states that increase a particular dissociation pathway of NH₃. These methods point to powerful new simulation tools for molecular quantum dynamics and the field of femtochemistry.

Coherent two-dimensional fluorescence micro-spectroscopy

We have developed coherent two-dimensional (2D) fluorescence micro-spectroscopy which probes the nonlinear optical response at surfaces via fluorescence detection with sub-micron spatial resolution. This enables the investigation of microscopic variations in heterogeneous systems. An LCD-based pulse shaper in 4f geometry is used to create collinear trains of 12-fs visible/NIR laser pulses in the focus of an NA = 1.4 immersion-oil microscope objective. We demonstrate the capabilities of the new method by presenting 2D spectra, analyzed via phase cycling, as a function of position of selected sub-micron regions from a laterally nanostructured polycrystalline thin film of fluorinated zinc phthalocyanine (F₁₆ZnPc).

Minimization of 1/fn phase noise in liquid crystal masks for reliable femtosecond pulse shaping

Liquid-crystal spatial light modulators (LCM) are a common tool to tailor femtosecond laser pulses. The phase stability of 1 kHz, sub-20 fs visible shaped and unshaped pulses are investigated. Our results show that the spectral phase after the LCM varies from pulse to pulse leading to strong deviations from the predicted pulse shapes. This phase instability is generated only by LCM and is strongly temperature dependent. Based on the experimental data, a numerical model for the phase was developed that takes the temperature-dependent phase instability as well as pixel coupling across the LCM into account. Phase stability after the LCM can be improved by an order of magnitude by combining the control the temperature of the LCM and by using rapid-scan averaging. Reliable pulse shapes on a pulse-to-pulse basis are crucial, especially in coherent control experiments, where small differences between pulse shape are important.

Quantum Ensemble Classification: A Sampling-Based Learning Control Approach

Quantum ensemble classification (QEC) has significant applications in discrimination of atoms (or molecules), separation of isotopes, and quantum information extraction. However, quantum mechanics forbids deterministic discrimination among nonorthogonal states. The classification of inhomogeneous quantum ensembles is very challenging, since there exist variations in the parameters characterizing the members within different classes. In this paper, we recast QEC as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). First, a new discrimination method is proposed for two similar quantum systems. Then, an SLC method is presented for QEC. Numerical results demonstrate the effectiveness of the proposed approach for the binary classification of two-level quantum ensembles and the multiclass classification of multilevel quantum ensembles.

Rapid and robust control of single quantum dots

The combination of single particle detection and ultrafast laser pulses is an instrumental method to track dynamics at the femtosecond time scale in single molecules, quantum dots and plasmonic nanoparticles. Optimal control of the extremely short-lived coherences of these individual systems has so far remained elusive, yet its successful implementation would enable arbitrary external manipulation of otherwise inaccessible nanoscale dynamics. In ensemble measurements, such control is often achieved by resorting to a closed-loop optimization strategy, where the spectral phase of a broadband laser field is iteratively optimized. This scheme needs long measurement times and strong signals to converge to the optimal solution. This requirement is in conflict with the nature of single emitters whose signals are weak and unstable. Here we demonstrate an effective closed-loop optimization strategy capable of addressing single quantum dots at room temperature, using as feedback observable the two-photon photoluminescence induced by a phase-controlled broadband femtosecond laser. Crucial to the optimization loop is the use of a deterministic and robust-against-noise search algorithm converging to the theoretically predicted solution in a reduced amount of steps, even when operating at the few-photon level. Full optimization of the single dot luminescence is obtained within ~100 trials, with a typical integration time of 100 ms per trial. These times are faster than the typical photobleaching times in single molecules at room temperature. Our results show the suitability of the novel approach to perform closed-loop optimizations on single molecules, thus extending the available experimental toolbox to the active control of nanoscale coherences.

Theoretical aspects of femtosecond double-pump single-molecule spectroscopy. II. Strong-field regime

We investigate femtosecond double-pump single-molecule signals in the strong-field regime, which is characterized by nonlinear scaling of the signal with the intensity of the pump pulses.

Theoretical aspects of femtosecond double-pump single-molecule spectroscopy. I. Weak-field regime

We present a theoretical description of double-pump femtosecond single-molecule signals with fluorescence detection.

Effect of Pulse Shaping on Observing Coherent Energy Transfer in Single Light-Harvesting Complexes

Recent experimental and theoretical studies have revealed that quantum coherence plays an important role in the excitation energy transfer in photosynthetic light-harvesting (LH) complexes. Inspired by the recent single-molecule two-color double-pump experiment, we theoretically investigate the effect of pulse shaping on observing coherent energy transfer in the single bacterial LH2 complex. It is found that quantum coherent energy transfer can be observed when the time delay and phase difference between the two laser pulses are controlled independently. However, when the two-color pulses are generated using the pulse-shaping method, how the laser pulses are prepared is crucial to the observation of quantum coherent energy transfer in single photosynthetic complexes.

Proposal for probing energy transfer pathway by single-molecule pump-dump experiment

The structure of Fenna-Matthews-Olson (FMO) light-harvesting complex had long been recognized as containing seven bacteriochlorophyll (BChl) molecules. Recently, an additional BChl molecule was discovered in the crystal structure of the FMO complex, which may serve as a link between baseplate and the remaining seven molecules. Here, we investigate excitation energy transfer (EET) process by simulating single-molecule pump-dump experiment in the eight-molecules complex. We adopt the coherent modified Redfield theory and non-Markovian quantum jump method to simulate EET dynamics. This scheme provides a practical approach of detecting the realistic EET pathway in BChl complexes with currently available experimental technology. And it may assist optimizing design of artificial light-harvesting devices.

Broadband single-molecule excitation spectroscopy

Over the past 25 years, single-molecule spectroscopy has developed into a widely used tool in multiple disciplines of science. The diversity of routinely recorded emission spectra does underpin the strength of the single-molecule approach in resolving the heterogeneity and dynamics, otherwise hidden in the ensemble. In early cryogenic studies single molecules were identified by their distinct excitation spectra, yet measuring excitation spectra at room temperature remains challenging. Here we present a broadband Fourier approach that allows rapid recording of excitation spectra of individual molecules under ambient conditions and that is robust against blinking and bleaching. Applying the method we show that the excitation spectra of individual molecules exhibit an extreme distribution of solvatochromic shifts and distinct spectral shapes. Importantly, we demonstrate that the sensitivity and speed of the broadband technique is comparable to that of emission spectroscopy putting both techniques side-by-side in single-molecule spectroscopy.

Single molecule microscopy and spectroscopy: concluding remarks

Chemistry is all about molecules: control, synthesis, interaction and reaction of molecules. All too easily on a blackboard, one draws molecules, their structures and dynamics, to create an insightful picture. The dream is to see these molecules in reality. This is exactly what "Single Molecule Detection" provides: a look at molecules in action at ambient conditions; a breakthrough technology in chemistry, physics and biology. Within the realms of the Royal Society of Chemistry, the Faraday Discussion on "Single Molecule Microscopy and Spectroscopy" was a very appropriate topic for presentation, deliberation and debate. Undoubtedly, the Faraday Discussions have a splendid reputation in stimulating scientific debates along the traditions set by Michael Faraday. Interestingly, back in the 1830's, Faraday himself pursued an experiment that led to the idea that atoms in a compound were joined by an electrical component. He placed two opposite electrodes in a solution of water containing a dissolved compound, and observed that one of the elements of the compound accumulated on one electrode, while the other was deposited on the opposite electrode. Although Faraday was deeply opposed to atomism, he had to recognize that electrical forces were responsible for the joining of atoms. Probably a direct view on the atoms or molecules in his experiment would have convinced him. As such, Michael Faraday might have liked the gathering at Burlington House in September 2015 (). Surely, with the questioning eyes of his bust on the 1st floor corridor, the non-believer Michael Faraday has incited each passer-by to enter into discussion and search for deeper answers at the level of single molecules. In these concluding remarks, highlights of the presented papers and discussions are summarized, complemented by a conclusion on future perspectives.

Shaped and Feedback-Controlled Excitation of Single Molecules in the Weak-Field Limit

Coherent control uses tailored femtosecond pulse shapes to influence quantum pathways and drive a light-induced process toward a specific outcome. There has been a long-standing debate whether the absorption properties or the probability for population to remain in an excited state of a molecule can be influenced by the pulse shape, even if only a single photon is absorbed. Most such experiments are performed on many molecules simultaneously, so that ensemble averaging reduces the access to quantum effects. Here, we demonstrate systematic coherent control experiments on the fluorescence intensity of a single molecule in the weak-field limit. We demonstrate that a delay scan of interfering pulses reproduces the excitation spectrum of the molecule upon Fourier transformation, but that the spectral phase of a pulse sequence does not affect the transition probability. We generalize this result to arbitrary pulse shapes by performing the first closed-loop coherent control experiments on a single molecule.

Multicolour single molecule emission and excitation spectroscopy reveals extensive spectral shifts

We explore the distribution and shape of single molecule spectra at room temperature, when embedded in a polymer host. Multicolour excitation and emission spectroscopy is implemented to capture the full inhomogeneous distribution. We observe dramatic spectral changes in a distribution of single quaterrylene diimide (QDI) molecules isolated in a PMMA matrix. The molecules are strongly blue shifted with respect to the ensemble absorption maximum and spread over a staggering 200 nm range. Despite these strong shifts, the shape of the emission spectra does not differ much between individual molecules. We demonstrate that a considerable number of molecules may be invisible in single molecule experiments, as they typically rely on only a single excitation wavelength, which predetermines which subensemble is probed in the experiment. Lastly, we make a first step towards single molecule excitation spectroscopy under ambient conditions, which allows us to determine the spectral range at which individual molecules absorb light most efficiently. We show how single molecule emission and excitation spectroscopies can complement each other and a combination of both techniques can help in understanding the origin of underlaying spectral properties of individual molecules.

Optimal Energy Transfer in Light-Harvesting Systems

Photosynthesis is one of the most essential biological processes in which specialized pigment-protein complexes absorb solar photons, and with a remarkably high efficiency, guide the photo-induced excitation energy toward the reaction center to subsequently trigger its conversion to chemical energy. In this work, we review the principles of optimal energy transfer in various natural and artificial light harvesting systems. We begin by presenting the guiding principles for optimizing the energy transfer efficiency in systems connected to dissipative environments, with particular attention paid to the potential role of quantum coherence in light harvesting systems. We will comment briefly on photo-protective mechanisms in natural systems that ensure optimal functionality under varying ambient conditions. For completeness, we will also present an overview of the charge separation and electron transfer pathways in reaction centers. Finally, recent theoretical and experimental progress on excitation energy transfer, charge separation, and charge transport in artificial light harvesting systems is delineated, with organic solar cells taken as prime examples.

Communication: atomic force detection of single-molecule nonlinear optical vibrational spectroscopy

Atomic Force Microscopy (AFM) allows for a highly sensitive detection of spectroscopic signals. This has been first demonstrated for NMR of a single molecule and recently extended to stimulated Raman in the optical regime. We theoretically investigate the use of optical forces to detect time and frequency domain nonlinear optical signals. We show that, with proper phase matching, the AFM-detected signals closely resemble coherent heterodyne-detected signals. Applications are made to AFM-detected and heterodyne-detected vibrational resonances in Coherent Anti-Stokes Raman Spectroscopy (χ((3))) and sum or difference frequency generation (χ((2))).

Experimental implementations of two-dimensional fourier transform electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) reveals connections between an optical excitation at a given frequency and the signals it creates over a wide range of frequencies. These connections, manifested as cross-peak locations and their lineshapes, reflect the underlying electronic and vibrational structure of the system under study. How these spectroscopic signatures evolve in time reveals the system dynamics and provides a detailed picture of coherent and incoherent processes. 2DES is rapidly maturing and has already found numerous applications, including studies of photosynthetic energy transfer and photochemical reactions and many-body interactions in nanostructured materials. Many systems of interest contain electronic transitions spanning the ultraviolet to the near infrared and beyond. Most 2DES measurements to date have explored a relatively small frequency range. We discuss the challenges of implementing 2DES and compare and contrast different approaches in terms of their information content, ease of implementation, and potential for broadband measurements.

Evolution of graphene molecules: structural and functional complexity as driving forces behind nanoscience

The evolution of nanoscience is based on the ability of the fields of chemistry and physics to share competencies through mutually beneficial collaborations. With this in mind, in this Perspective, I describe three classes of compounds: rylene dyes, polyphenylene dendrimers, as well as nanographene molecules and graphene nanoribbons, which have provided a superb platform to nurture these relationships. The synthesis of these complex structures is demanding but also rewarding because they stimulate unique investigations at the single-molecule level by scanning tunneling microscopy and single-molecule spectroscopy. There are close functional and structural relationships between the molecules chosen. In particular, rylenes and nanographenes can be regarded as honeycomb-type, discoid species composed of fused benzene rings. The benzene ring can thus be regarded as a universal modular building block. Polyphenylene dendrimers serve, first, as a scaffold for dyes en route to multichromophoric systems and, second, as chemical precursors for graphene synthesis. Through chemical design, it is possible to tune the properties of these systems at the single-molecule level and to achieve nanoscale control over their self-assembly to form multifunctional (nano)materials.