Colors of entangled two-photon absorption.

Multiphoton absorption of entangled photons offers ways for obtaining unique information about chemical and biological processes. Measurements with entangled photons may enable sensing biological signatures with high selectivity and at very low light levels to protect against photodamage. In this paper, we present a theoretical and experimental study of the excitation wavelength dependence of the entangled two-photon absorption (ETPA) process in a molecular system, which provides insights into how entanglement affects molecular spectra. We demonstrate that the ETPA excitation spectrum can be different from that of classical TPA as well as that for one-photon resonant absorption (OPA) with photons of doubled frequency. These results are modeled by assuming the ETPA cross-section is governed by a two-photon excited state radiative linewidth rather than by electron-phonon interactions, and this leads to excitation spectra that match the observed results. Further, we find that the two-photon-allowed states with highest TPA and ETPA intensities have high electronic entanglements, with ETPA especially favoring states with the longest radiative lifetimes. These results provide concepts for the development of quantum light-based spectroscopy and microscopy that will lead to much higher efficiency of ETPA sensors and low-intensity detection schemes.

Entangled Photon Spectroscopy.

The enhanced interest in quantum-related phenomena has provided new opportunities for chemists to push the limits of detection and analysis of chemical processes. As some have called this the second quantum revolution, a time has come to apply the rules learned from previous research in quantum phenomena toward new methods and technologies important to chemists. While there has been great interest recently in quantum information science (QIS), the quest to understand how nonclassical states of light interact with matter has been ongoing for more than two decades. Our entry into this field started around this time with the use of materials to produce nonclassical states of light. Here, the process of multiphoton absorption led to photon-number squeezed states of light, where the photon statistics are sub-Poissonian. In addition to the great interest in generating squeezed states of light, there was also interest in the formation of entangled states of light. While much of the effort is still in foundational physics, there are numerous new avenues as to how quantum entanglement can be applied to spectroscopy, imaging, and sensing. These opportunities could have a large impact on the chemical community for a broad spectrum of applications.In this Account, we discuss the use of entangled (or quantum) light for spectroscopy as well as applications in microscopy and interferometry. The potential benefits of the use of quantum light are discussed in detail. From the first experiments in porphyrin dendrimer systems by Dr. Dong-Ik Lee in our group to the measurements of the entangled two photon absorption cross sections of biological systems such as flavoproteins, the usefulness of entangled light for spectroscopy has been illustrated. These early measurements led the way to more advanced measurements of the unique characteristics of both entangled light and the entangled photon absorption cross-section, which provides new control knobs for manipulating excited states in molecules.The first reports of fluorescence-induced entangled processes were in organic chromophores where the entangled photon cross-section was measured. These results would later have widespread impact in applications such as entangled two-photon microscopy. From our design, construction and implementation of a quantum entangled photon excited microscope, important imaging capabilities were achieved at an unprecedented low excitation intensity of 107 photons/s, which is 6 orders of magnitude lower than the excitation level for the classical two-photon image. New reports have also illustrated an advantage of nonclassical light in Raman imaging as well.From a standpoint of more precise measurements, the use of entangled photons in quantum interferometry may offer new opportunities for chemistry research. Experiments that combine molecular spectroscopy and quantum interferometry, by utilizing the correlations of entangled photons in a Hong-Ou-Mandel (HOM) interferometer, have been carried out. The initial experiment showed that the HOM signal is sensitive to the presence of a resonant organic sample placed in one arm of the interferometer. In addition, parameters such as the dephasing time have been obtained with the opportunity for even more advanced phenomenology in the future.

Enhancing Entangled Two-Photon Absorption for Picosecond Quantum Spectroscopy.

Entangled two-photon absorption (ETPA) is known to create photoinduced transitions with extremely low light intensity, reducing the risk of phototoxicity compared to classical two-photon absorption. Previous works have predicted the ETPA cross-section, σe, to vary inversely with the product of entanglement time (Te) and entanglement area (Ae), i.e., σe ∼ 1/AeTe. The decreasing σe with increasing Te has limited ETPA to fs-scale Te, while ETPA applications for ps-scale spectroscopy have been unexplored. However, we show that spectral-spatial coupling, which reduces Ae as the SPDC bandwidth (σf) decreases, plays a significant role in determining σe when Te > ∼100 fs. We experimentally measured σe for zinc tetraphenylporphyrin at several σf values. For type-I ETPA, σe increases as σf decreases down to 0.1 ps-1. For type-II SPDC, σe is constant for a wide range of σf. With a theoretical analysis of the data, the maximum type-I σe would occur at σf = 0.1 ps-1 (Te = 10 ps). At this maximum, σe is 1 order of magnitude larger than fs-scale σe and 3 orders of magnitude larger than previous predictions of ps-scale σe. By utilizing this spectral-spatial coupling, narrowband type-I ETPA provides a new opportunity to increase the efficiency of measuring nonlinear optical signals and to control photochemical reactions requiring ps temporal precision.

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.

Two-Photon Fluorescence Microscopy at Extremely Low Excitation Intensity: The Power of Quantum Correlations.

Quantum entanglement has been shown to imply correlations stronger than those allowed by classical models. The possibility of performing tasks that are classically impossible has made quantum entanglement a powerful resource for the development of novel methods and applications in various fields of research such as quantum computing, quantum cryptography, and quantum metrology. There is a great need for the development of next generation instrumentation and technologies utilizing entangled quantum light. Among the many applications of nonclassical states of light, nonlinear microscopy has the potential to make an impact in broad areas of science from physics to biology. Here, the microscopic image created by the fluorescence selectively excited by the process of the entangled two-photon absorption is reported. Entangled two-photon microscopy offers nonlinear imaging capabilities at an unprecedented low excitation intensity 107, which is 6 orders of magnitude lower than the excitation level for the classical two-photon image. The nonmonotonic dependence of the image on the femtosecond delay between the components of the entangled photon pair is demonstrated. This delay dependence is a result of specific quantum interference effects associated with the entanglement and this is not observable with classical excitation light. In combination with novel spectroscopic capabilities provided by a nonclassical light excitation, this is of critical importance for sensing and biological applications.

Efficient Modeling of Organic Chromophores for Entangled Two-Photon Absorption.

The use of a nonclassical light source for studying molecular electronic structure has been of great interest in many applications. Here we report a theoretical study of entangled two-photon absorption (ETPA) in organic chromophores, and we provide new insight into the quantitative relation between ETPA and the corresponding unentangled TPA based on the significantly different line widths associated with entangled and unentangled processes. A sum-over-states approach is used to obtain classical TPA and ETPA cross sections and to explore the contribution of each electronic state to the ETPA process. The transition moments and energies needed for this calculation were obtained from a second linear-response (SLR) TDDFT method [J. Chem. Phys., 2016, 144, 204105], which enables the treatment of relatively large polythiophene dendrimers that serve as two-photon absorbers. In addition, the SLR calculations provide estimates of the excited state radiative line width, which we relate to the entangled two-photon density of states using a quantum electrodynamic analysis. This analysis shows that for the dendrimers being studied, the line width for ETPA is orders of magnitude narrower than for TPA, corresponding to highly entangled photons with a large Schmidt number. The calculated cross sections are in good agreement with the experimentally reported values. We also carried out a state-resolved analysis to unveil pathways for the ETPA process, and these demonstrate significant interference behavior. We emphasize that the use of entangled photons in TPA process plays a critical role in probing the detailed electronic structure of a molecule by probing light-matter interference nature in the quantum limit.

A pyrene-based two-photon excitable fluorescent probe to visualize nuclei in live cells.

The two-photon absorption properties of a pyrene-pyridinium dye (1) were studied for potential application in two-photon spectroscopy. When probe 1 was used in cellular two-photon fluorescence microscopy imaging, it allowed the visualization of nuclei in live cells with a relatively low probe concentration (such as 1 µM). Spectroscopic evidence further revealed that probe 1 interacted with DNA as an intercalator. The proposed DNA intercalation properties of probe 1 were consistent with the experimental findings that suggested that the observed nucleus staining ability is dependent on the substituents on the pyridinium fragment of the probe.

Two-Photon Excitation of Flavins and Flavoproteins with Classical and Quantum Light.

In this contribution, the entangled two-photon absorption (ETPA) process on naturally occurring flavoproteins was studied. Low temperature responsive protein (LOT6P) and b-type dihydroorotate dehydrogenase (DHOD B), which possess flavin mononucleotide (FMN) and flavin adenine dinucleotide (FAD) chromophores embedded in the protein environment, were investigated. The ETPA cross-section was measured, and we found that it increases when going from an aqueous solution of the free flavin chromophore to the chromophore embedded in the protein. This enhancement is particularly evident when entangled photons are used as excitation light compared to classical light. Our results prove the potential of ETPA as a sensing technique for fluorescent proteins even for those whose classical TPA cross-section is small compared to well-known fluorescent proteins.

Enacting Two-Electron Transfer from a Double-Triplet State of Intramolecular Singlet Fission.

A simulation-led strategy enacts two-electron transfer between an intramolecular singlet fission chromophore (tetracyanomethylene quinoidal bithiopehene with ß,ß'-solubilizing groups) and multielectron acceptor (anthraquinone). The thermodynamic plausibility of multielectron transfer from a double-triplet state and the absorption spectra of electron transfer (ET) products were predicted using quantum chemical simulations. These predictions are consistent with experimental observations of reduced lifetimes in time-resolved fluorescence spectroscopy, changes in transmission profile, and appearance of new absorption bands in transient absorption spectroscopy, all of which support multi-ET in the QOT2/AQ mixture. The analysis suggests 2ET is favored over 1ET by a 2.5:1 ratio.

Long-Range Energy Transfer in Protein Megamolecules.

In this investigation, we report evidence for energy transfer in new protein-based megamolecules with tunable distances between donor and acceptor fluorescent proteins. The megamolecules used in this work are monodisperse oligomers, with molecular weights of ∼100-300 kDa and lengths of ∼5-20 nm, and are precisely defined structures of fusion protein building blocks and covalent cross-linkers. Such structures are promising because the study of energy transfer in protein complexes is usually difficult in this long length regime due to synthetic limitations. We incorporated fluorescent proteins into the megamolecule structure and varied the separation distance between donor and acceptor by changing the length of the cross-linker in dimer conjugates and inserting nonfluorescent spacer proteins to create oligomers. Two-photon absorption measurements demonstrated strong coupling between donor and acceptor dipoles in the megamolecules. For the dimer systems, no effect of the cross-linker length on energy transfer efficiency was observed with the steady-state fluorescence investigation. However, for the same dimer conjugates, energy transfer rates decreased upon increasing cross-linker length, as evaluated by fluorescence up-conversion. Molecular dynamics simulations were used to rationalize the results, providing quantitative agreement between measured and calculated energy transfer lengths for steady-state results, and showing that the differences between the time-resolved and steady-state measurements arise from the long time scale for large-scale fluctuations in the megamolecule structure. Our results show an increase in energy transfer length with increasing megamolecule size. This is evidence for long-range energy transfer in large protein megamolecules.

Predicting and Controlling Entangled Two-Photon Absorption in Diatomic Molecules.

The use of nonclassical states of light to probe organic molecules has received great attention due to the possibility of providing new and detailed information regarding molecular excitations. Experimental and theoretical results have been reported which show large enhancements of the nonlinear optical responses in organic materials due to possible virtual-electronic-state interactions with entangled photons. In order to predict molecular excitations with nonclassical light, more detailed investigations of the parameters involved must be carried out. In this report we investigate the details of the state-to-state parameters important in calculating the contribution of particular transitions involved in the entangled two-photon absorption process for diatomic molecules. The theoretical discussion of the entangled two-photon process is described for a set of diatomic molecules. Specifically, we provide detailed quantum chemical calculations which give accurate energies and transition moments for selection-rule allowed intermediate states important in the entangled nonlinear effect for the diatomic molecules. These results are used to estimate in a more accurate manner the nonmonotonic behavior of the entangled two-photon absorption cross-section. We also derive accurate approximations that can be used to predict the period between entanglement-induced transparencies without needing exact values of the transition dipole moments. These results suggest that with the additional parameters allotted by the entangled two-photon absorption (in comparison to the classical case), it may be possible to predict and later control the nonlinear absorption and transparency of a molecule at a constant incident photon frequency.

Enhanced Emission from Single Isolated Gold Quantum Dots Investigated Using Two-Photon-Excited Fluorescence Near-Field Scanning Optical Microscopy.

New approaches in molecular nanoscopy are greatly desired for interrogation of biological, organic, and inorganic objects with sizes below the diffraction limit. Our current work investigates emergent monolayer-protected gold quantum dots (nanoclusters, NCs) composed of 25 Au atoms by utilizing two-photon-excited fluorescence (TPEF) near-field scanning optical microscopy (NSOM) at single NC concentrations. Here, we demonstrate an approach to synthesize and isolate single NCs on solid glass substrates. Subsequent investigation of the NCs using TPEF NSOM reveals that, even when they are separated by distances of several tens of nanometers, we can excite and interrogate single NCs individually. Interestingly, we observe an enhanced two-photon absorption (TPA) cross section for single Au25 NCs that can be attributed to few-atom local field effects and to local field-induced microscopic cascading, indicating their potential for use in ultrasensitive sensing, disease diagnostics, cancer cell therapy, and molecular computers. Finally, we report room-temperature aperture-based TPEF NSOM imaging of these NCs for the first time at 30 nm point resolution, which is a ∼5-fold improvement compared to the previous best result for the same technique. This report unveils the unique combination of an unusually large TPA cross section and the high photostability of Au NCs to (non-destructively) investigate stable isolated single NCs using TPEF NSOM. This is the first reported optical study of monolayer-protected single quantum clusters, opening some very promising opportunities in spectroscopy of nanosized objects, bioimaging, ultrasensitive sensing, molecular computers, and high-density data storage.

Synthesis of Ladder-Type Thienoacenes and Their Electronic and Optical Properties.

A series of ladder-type thienoacenes based on benzo[1,2-b:4,5-b']dithiophene (BDT) have been synthesized and characterized. They were shown to be p-type semiconductors with wide band gaps and able to support multiple stable cationic states. As the conjugation lengthens, these oligomers become more emissive, showing high quantum yields. They were shown to be good two-photon absorbers, exhibiting high two-photon absorption coefficients.

Effect of acceptor strength on optical and electronic properties in conjugated polymers for solar applications.

Four new low-bandgap electron-accepting polymers-poly(4,10-bis(2-butyloctyl)-2-(2-(2-ethylhexyl)-1,1-dioxido-3-oxo-2,3-dihydrothieno[3,4-d]isothiazol-4-yl)thieno[2',3':5,6]pyrido[3,4-g]thieno[3,2-c]isoquinoline-5,11(4H,10H-dione) (PNSW); poly(4,10-bis(2-butyloctyl)-2-(5-(2-ethylhexyl)-4,6-dioxo-5,6-dihydro-4H-thieno[3,4-c]pyrrol-1-yl)thieno[2',3':5,6]pyrido[3,4-g]thieno[3,2-c]isoquinoline-5,11(4H,10H)-dione) (PNTPD); poly(5-(4,10-bis(2-butyloctyl)-5,11-dioxo-4,5,10,11-tetrahydrothieno[2',3':5,6]pyrido[3,4-g]thieno[3,2-c]isoquinolin-2-yl)-2,9-bis(2-decyldodecyl)anthra[2,1,9-def:6,5,10-d'e'f']diisoquinoline-1,3,8,10(2H,9H)-tetraone) (PNPDI); and poly(9,9-bis(2-butyloctyl)-9H-fluorene-bis((1,10:5,6)2-(5,6-dihydro-4H-cyclopenta[b]thiophene-4-ylidene)malonitrile)-2-(2,3-dihydrothieno[3,4-b][1,4]dioxine)) (PECN)-containing thieno[2',3':5',6']pyrido[3,4-g]thieno[3,2-c]isoquinoline-5,11(4H,10H)-dione and fluorenedicyclopentathiophene dimalononitrile, were investigated to probe their structure-function relationships for solar cell applications. PTB7 was also investigated for comparison with the new low-bandgap polymers. The steady-state, ultrafast dynamics and nonlinear optical properties of all the organic polymers were probed. All the polymers showed broad absorption in the visible region, with the absorption of PNPDI and PECN extending into the near-IR region. The polymers had HOMO levels ranging from -5.73 to -5.15 eV and low bandgaps of 1.47-2.45 eV. Fluorescence upconversion studies on the polymers showed long lifetimes of 1.6 and 2.4 ns for PNSW and PNTPD, respectively, while PNPDI and PECN showed very fast decays within 353 and 110 fs. PECN exhibited a very high two-photon absorption cross section. The electronic structure calculations of the repeating units of the polymers indicated the localization of the molecular orbitals in different co-monomers. As the difference between the electron affinities of the co-monomers in the repeating units decreases, the highest occupied and lowest unoccupied molecular orbitals become more distributed. All the measurements suggest that a large difference in the electron affinities of the co-monomers of the polymers contributes to the improvement of the photophysical properties necessary for highly efficient solar cell performance. PECN exhibited excellent photophysical properties, which makes it to be a good candidate for solar cell device applications.

Two-Photon Spectroscopy as a New Sensitive Method for Determining the DNA Binding Mode of Fluorescent Nuclear Dyes.

A new optical strategy to determine the binding modes (intercalation vs groove binding) of small fluorescent organic molecules with calf thymus DNA was developed using two-photon absorption (TPA) spectroscopy. Two-photon excited emission was utilized to investigate a series of fluorescent nuclear dyes. The results show that TPA cross-sections are able to differentiate the fine details between the DNA binding modes. Groove binding molecules exhibit an enhanced TPA cross-section due to the DNA electric field induced enhancement of the transition dipole moment, while intercalative binding molecules exhibit a decrease in the TPA cross-section. Remarkably, the TPA cross-section of 4,6-bis(4-(4-methylpiperazin-1-yl)phenyl) pyrimidine is significantly enhanced (13.6-fold) upon binding with DNA. The sensitivity of our TPA methodology is compared to circular dichroism spectroscopy. TPA demonstrates superior sensitivity by more than an order of magnitude at low DNA concentrations. This methodology can be utilized to probe DNA interactions with other external molecules such as proteins, enzymes, and drugs.

An ultrafast look at Au nanoclusters.

In the past 20 years, researchers studying nanomaterials have uncovered many new and interesting properties not found in bulk materials. Extensive research has focused on metal nanoparticles (>3 nm) because of their potential applications, such as in molecular electronics, image markers, and catalysts. In particular, the discovery of metal nanoclusters (<3 nm) has greatly expanded the horizon of nanomaterial research. These nanosystems exhibit molecular-like characteristics as their size approaches the Fermi-wavelength of an electron. The relationships between size and physical properties for nanomaterials are intriguing, because for metal nanosystems in this size regime both size and shape determine electronic properties. Remarkably, changes in the optical properties of nanomaterials have provided tremendous insight into the electronic structure of nanoclusters. The success of synthesizing monolayer protected clusters (MPCs) in the condensed phase has allowed scientists to probe the metal core directly. Au MPCs have become the "gold" standard in nanocluster science, thanks to the rigorous structural characterization already accomplished. The use of ultrafast laser spectroscopy on MPCs in solution provides the benefit of directly studying the chemical dynamics of metal nanoclusters (core), and their nonlinear optical properties. In this Account, we investigate the optical properties of MPCs in the visible region using ultrafast spectroscopy. Based on fluorescence up-conversion spectroscopy, we propose an emission mechanism for these nanoclusters. These clusters behave differently from nanoparticles in terms of emission lifetimes as well as two-photon cross sections. Through further investigation of the transient (excited state) absorption, we have found many unique phenomena of nanoclusters, such as quantum confinement effects and vibrational breathing modes. In summary, based on the differences in the optical properties, the distinction between nanoclusters and nanoparticles appears at a size near 2.2 nm. This is consistent with simulations from a free-electron model proposed for MPCs. The use of ultrafast techniques on these nanoclusters can answer many of the fundamental questions about the nature of these exciting nanomaterials and their applications.

Isolation and characterization of precise dye/dendrimer ratios.

Fluorescent dyes are commonly conjugated to nanomaterials for imaging applications using stochastic synthesis conditions that result in a Poisson distribution of dye/particle ratios and therefore a broad range of photophysical and biodistribution properties. We report the isolation and characterization of generation 5 poly(amidoamine) (G5 PAMAM) dendrimer samples containing 1, 2, 3, and 4 fluorescein (FC) or 6-carboxytetramethylrhodamine succinimidyl ester (TAMRA) dyes per polymer particle. For the fluorescein case, this was achieved by stochastically functionalizing dendrimer with a cyclooctyne "click" ligand, separation into sample containing precisely defined "click" ligand/particle ratios using reverse-phase high performance liquid chromatography (RP-HPLC), followed by reaction with excess azide-functionalized fluorescein dye. For the TAMRA samples, stochastically functionalized dendrimer was directly separated into precise dye/particle ratios using RP-HPLC. These materials were characterized using (1)H and (19)F NMR spectroscopy, RP-HPLC, UV/Vis and fluorescence spectroscopy, lifetime measurements, and MALDI.

Impact of Classical and Quantum Light on Donor-Acceptor-Donor Molecules.

Investigations of entangled and classical two-photon absorption have been carried out for six donor (D)-acceptor (A)-donor (D) compounds containing the dithieno pyrrole (DTP) unit as donor and acceptors with systematically varied electronic properties. Comparing ETPA (quantum) and TPA (classical) results reveals that the ETPA cross section decreases with increasing TPA cross section for molecules with highly off-resonant excited states for single-photon excitation. Theory (TDDFT) results are in semiquantitative agreement with this anticorrelated behavior due to the dependence of the ETPA cross section but not TPA on the two-photon excited state lifetime. The largest cross section is found for a DTP derivative that has a single photon excitation energy closest to resonance with half the two-photon excitation energy. These results are important for the possible use of quantum light for low-intensity energy-conversion applications.