Entangled Photon-Pair Two-Dimensional Fluorescence Spectroscopy (EPP-2DFS)

Two-photon absorption cross sections of pulsed entangled beams

Entangled two-photon absorption (ETPA) could form the basis of nonlinear quantum spectroscopy at very low photon fluxes, since, at sufficiently low photon fluxes, ETPA scales linearly with the photon flux. When different pairs start to overlap temporally, accidental coincidences are thought to give rise to a "classical" quadratic scaling that dominates the signal at large photon fluxes and, thus, recovers a supposedly classical regime, where any quantum advantage is thought to be lost. Here, we scrutinize this assumption and demonstrate that quantum-enhanced absorption cross sections can persist even for very large photon numbers. To this end, we use a minimal model for quantum light, which can interpolate continuously between the entangled pair and a high-photon-flux limit, to analytically derive ETPA cross sections and the intensity crossover regime. We investigate the interplay between spectral and spatial degrees of freedom and how linewidth broadening of the sample impacts the experimentally achievable enhancement.

Observing thermal lensing with quantum light

The introduction of quantum methods in spectroscopy can provide enhanced performance and technical advantages in the management of noise. We investigate the application of quantum illumination in a pump and probe experiment. Thermal lensing in a suspension of gold nanorods is explored using a classical beam as the pump and the emission from parametric downconversion as the probe. We obtain an insightful description of the behavior of the suspension under pumping with a method known to provide good noise rejection. Our findings are a further step toward investigating the effects of quantum light in complex plasmonic media.

Quantum Interferometric Pathway Selectivity in Difference-Frequency-Generation Spectroscopy

Even-order spectroscopies such as sum-frequency generation (SFG) and difference-frequency generation (DFG) can serve as direct probes of molecular chirality. Such signals are usually given by the sum of several interaction pathways that carry different information about matter. Here we focus on DFG, involving impulsive optical-optical-IR interactions, where the last IR pulse probes vibrational transitions in the ground or excited electronic state manifolds, depending on the interaction pathway. Spectroscopy with classical light can use phase matching to select the two pathways. In this theoretical study, we propose a novel quantum interferometric protocol that uses entangled photons to isolate individual pathways. This additional selectivity originates from engineering the state of light using a Zou-Wang-Mandel interferometer combined with coincidence detection.

Multimode vibrational dynamics and orientational effects in fluorescence-encoded infrared spectroscopy. I. Response function theory

Fluorescence-encoded infrared (FEIR) spectroscopy is an emerging technique for performing vibrational spectroscopy in solution with detection sensitivity down to single molecules. FEIR experiments use ultrashort pulses to excite a fluorescent molecule's vibrational and electronic transitions in a sequential, time-resolved manner, and are therefore sensitive to intervening vibrational dynamics on the ground state, vibronic coupling, and the relative orientation of vibrational and electronic transition dipole moments. This series of papers presents a theoretical treatment of FEIR spectroscopy that describes these phenomena and examines their manifestation in experimental data. This first paper develops a nonlinear response function description of Fourier-transform FEIR experiments for a two-level electronic system coupled to multiple vibrations, which is then applied to interpret experimental measurements in the second paper [L. Whaley-Mayda et al., J. Chem. Phys. 159, 194202 (2023)]. Vibrational coherence between pairs of modes produce oscillatory features that interfere with the vibrations' population response in a manner dependent on the relative signs of their respective Franck-Condon wavefunction overlaps, leading to time-dependent distortions in FEIR spectra. The orientational response of population and coherence contributions are analyzed and the ability of polarization-dependent experiments to extract relative transition dipole angles is discussed. Overall, this work presents a framework for understanding the full spectroscopic information content of FEIR measurements to aid data interpretation and inform optimal experimental design.

Photoelectron spectroscopy with entangled photons; enhanced spectrotemporal resolution

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

Controlled Coherent Coupling in a Quantum Dot Molecule Revealed by Ultrafast Four-Wave Mixing Spectroscopy

Semiconductor quantum dot molecules are considered promising candidates for quantum technological applications due to their wide tunability of optical properties and coverage of different energy scales associated with charge and spin physics. While previous works have studied the tunnel-coupling of the different excitonic charge complexes shared by the two quantum dots by conventional optical spectroscopy, we here report on the first demonstration of a coherently controlled interdot tunnel-coupling focusing on the quantum coherence of the optically active trion transitions. We employ ultrafast four-wave mixing spectroscopy to resonantly generate a quantum coherence in one trion complex, transfer it to and probe it in another trion configuration. With the help of theoretical modeling on different levels of complexity, we give an instructive explanation of the underlying coupling mechanism and dynamical processes.

Quantized Fields for Optimal Control in the Strong Coupling Regime

We tailor the quantum statistics of a bosonic field to deterministically drive a quantum system into a target state. Experimentally accessible states of the field achieve good control of multilevel or multiqubit systems, notably also at coupling strengths beyond the rotating-wave approximation. This extends optimal control theory to the realm of fully quantized, strongly coupled control and target degrees of freedom.

Entangled photons enabled time-frequency-resolved coherent Raman spectroscopy and applications to electronic coherences at femtosecond scale

Quantum entanglement has emerged as a great resource for spectroscopy and its importance in two-photon spectrum and microscopy has been demonstrated. Current studies focus on the two-photon absorption, whereas the Raman spectroscopy with quantum entanglement still remains elusive, with outstanding issues of temporal and spectral resolutions. Here we study the new capabilities provided by entangled photons in coherent Raman spectroscopy. An ultrafast frequency-resolved Raman spectroscopy with entangled photons is developed for condensed-phase molecules, to probe the electronic and vibrational coherences. Using quantum correlation between the photons, the signal shows the capability of both temporal and spectral resolutions not accessible by either classical pulses or the fields without entanglement. We develop a microscopic theory for this Raman spectroscopy, revealing the electronic coherence dynamics even at timescale of 50fs. This suggests new paradigms of optical signals and spectroscopy, with potential to push detection below standard quantum limit.

Quantum nonlinear spectroscopy of single nuclear spins

Conventional nonlinear spectroscopy, which use classical probes, can only access a limited set of correlations in a quantum system. Here we demonstrate that quantum nonlinear spectroscopy, in which a quantum sensor and a quantum object are first entangled and the sensor is measured along a chosen basis, can extract arbitrary types and orders of correlations in a quantum system. We measured fourth-order correlations of single nuclear spins that cannot be measured in conventional nonlinear spectroscopy, using sequential weak measurement via a nitrogen-vacancy center in diamond. The quantum nonlinear spectroscopy provides fingerprint features to identify different types of objects, such as Gaussian noises, random-phased AC fields, and quantum spins, which would be indistinguishable in second-order correlations. This work constitutes an initial step toward the application of higher-order correlations to quantum sensing, to examining the quantum foundation (by, e.g., higher-order Leggett-Garg inequality), and to studying quantum many-body physics.

Signals that look the same from their low-order correlations can often be distinguished by looking at higher-order ones. Here, the authors exploit the sensitivity of quantum nonlinear spectroscopy to fourth-order correlations to identify Gaussian noises, random-phased AC fields, and quantum spins.

Experimental Study of the Validity of Entangled Two-Photon Absorption Measurements in Organic Compounds

Entangled two-photon absorption (ETPA) has recently become a topic of lively debate, mainly due to the apparent inconsistencies in the experimentally reported ETPA cross sections of organic molecules obtained by a number of groups. In this work, we provide a thorough experimental study of ETPA in the organic molecules Rhodamine B (RhB) and zinc tetraphenylporphirin (ZnTPP). Our contribution is 3-fold: first, we reproduce previous results from other groups; second, we on the one hand determine the effects of different temporal correlations─introduced as a controllable temporal delay between the signal and idler photons to be absorbed─on the strength of the ETPA signal, and on the other hand, we introduce two concurrent and equivalent detection systems with and without the sample in place as a useful experimental check; third, we introduce, and apply to our data, a novel method to quantify the ETPA rate based on taking into account the full photon-pair behavior rather than focusing on singles or coincidence counts independently. Through this experimental setup we find that, surprisingly, the purported ETPA signal is not suppressed for a temporal delay much greater than the characteristic photon-pair temporal correlation time. While our results reproduce the previous findings from other authors, our full analysis indicates that the signal observed is not actually due to ETPA but simply to linear losses. Interestingly, for higher RhB concentrations, we find a two-photon signal that, contrary to expectations, likewise does not correspond to ETPA.

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.

Bright squeezed vacuum for two-photon spectroscopy: simultaneously high resolution in time and frequency, space and wavevector

Entangled photons offer two advantages for two-photon absorption spectroscopy. One of them, the linear scaling of two-photon absorption rate with the input photon flux, is valid only at very low photon fluxes and is therefore impractical. The other is the overcoming of the classical constraints for simultaneous resolution in time-frequency and in space-wavevector. Here we consider bright squeezed vacuum (BSV) as an alternative to entangled photons. The efficiency increase it offers in comparison with coherent light is modest, but it does not depend on the photon flux. Moreover, and this is what we show in this work, BSV also provides simultaneously high resolution in time and frequency, and in space and wavevector. In our experiment, we measure the widths of the second-order correlation functions in space, time, frequency, and angle and demonstrate the violation of the constraint given by the Fourier transformation, in the case of photon pairs, known as the Mancini criterion of entanglement.

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

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

Photoisomerization transition state manipulation by entangled two-photon absorption

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

Distinguishability and "which pathway" information in multidimensional interferometric spectroscopy with a single entangled photon-pair

Correlated photons inspire abundance of metrology-related platforms, which benefit from quantum (anti-) correlations and outperform their classical counterparts. While these mainly focus on entanglement, the role of photon exchange phase and degree of distinguishability has not been widely used in quantum applications. Using an interferometric setup, we theoretically show that, when a two-photon wave function is coupled to matter, it is encoded with “which pathway?” information even at low-degree of entanglement. An interferometric protocol, which enables phase-sensitive discrimination between microscopic interaction histories (pathways), is developed. We find that quantum light interferometry facilitates utterly different set of time delay variables, which are unbound by uncertainty to the inverse bandwidth of the wave packet. We illustrate our findings on an exciton model system and demonstrate how to probe intraband dephasing in the time domain without temporally resolved detection. The unusual scaling of multiphoton coincidence signals with the applied pump intensity is discussed.

Entangled two-photon absorption by atoms and molecules: A quantum optics tutorial

Two-photon absorption (TPA) and other nonlinear interactions of molecules with time-frequency-entangled photon pairs have been predicted to display a variety of fascinating effects. Therefore, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This Tutorial presents a detailed theoretical study of one- and two-photon absorption by molecules, focusing on how to treat the quantum nature of light. We review some basic quantum optics theory and then we review the density-matrix (Liouville) derivation of molecular optical response, emphasizing how to incorporate quantum states of light into the treatment. For illustration, we treat in detail the TPA of photon pairs created by spontaneous parametric down conversion, with an emphasis on how quantum light TPA differs from that with classical light. In particular, we treat the question of how much enhancement of the TPA rate can be achieved using entangled states. This Tutorial includes a review of known theoretical methods and results as well as some extensions, especially the comparison of TPA processes that occur via far-off-resonant intermediate states only and those that involve off-resonant intermediate states by virtue of dephasing processes. A brief discussion of the main challenges facing experimental studies of entangled two-photon absorption is also given.

Experimental Demonstration of Conjugate-Franson Interferometry

Franson interferometry is a well-known quantum measurement technique for probing photon-pair frequency correlations that is often used to certify time-energy entanglement. We demonstrate, for the first time, the complementary technique in the time basis called conjugate-Franson interferometry. It measures photon-pair arrival-time correlations, thus providing a valuable addition to the quantum toolbox. We obtain a conjugate-Franson interference visibility of 96±1% without background subtraction for entangled photon pairs generated by spontaneous parametric down-conversion. Our measured result surpasses the quantum-classical threshold by 25 standard deviations and validates the conjugate-Franson interferometer (CFI) as an alternative method for certifying time-energy entanglement. Moreover, the CFI visibility is a function of the biphoton's joint temporal intensity, and is therefore sensitive to that state's spectral phase variation: something that is not the case for Franson interferometry or Hong-Ou-Mandel interferometry. We highlight the CFI's utility by measuring its visibilities for two different biphoton states: one without and the other with spectral phase variation, observing a 21% reduction in the CFI visibility for the latter. The CFI is potentially useful for applications in areas of photonic entanglement, quantum communications, and quantum networking.

Achieving two-dimensional optical spectroscopy with temporal and spectral resolution using quantum entangled three photons

Recent advances in techniques for generating quantum light have stimulated research on novel spectroscopic measurements using quantum entangled photons. One such spectroscopy technique utilizes non-classical correlations among entangled photons to enable measurements with enhanced sensitivity and selectivity. Here, we investigate the spectroscopic measurement utilizing entangled three photons. In this measurement, time-resolved entangled photon spectroscopy with monochromatic pumping [A. Ishizaki, J. Chem. Phys. 153, 051102 (2020)] is integrated with the frequency-dispersed two-photon counting technique, which suppresses undesired accidental photon counts in the detector and thus allows one to separate the weak desired signal. This time-resolved frequency-dispersed two-photon counting signal, which is a function of two frequencies, is shown to provide the same information as that of coherent two-dimensional optical spectra. The spectral distribution of the phase-matching function works as a frequency filter to selectively resolve a specific region of the two-dimensional spectra, whereas the excited-state dynamics under investigation are temporally resolved in the time region longer than the entanglement time. The signal is not subject to Fourier limitations on the joint temporal and spectral resolution, and therefore, it is expected to be useful for investigating complex molecular systems in which multiple electronic states are present within a narrow energy range.

Designing high-power, octave spanning entangled photon sources for quantum spectroscopy

Entangled photon spectroscopy is a nascent field that has important implications for measurement and imaging across chemical, biology, and materials fields. Entangled photon spectroscopy potentially offers improved spatial and temporal-frequency resolutions, increased cross sections for multiphoton and nonlinear measurements, and new abilities in inducing or measuring quantum correlations. A critical step in enabling entangled photon spectroscopies is the creation of high-flux entangled sources that can use conventional detectors as well as provide redundancy for the losses in realistic samples. Here, we report a periodically poled, chirped, lithium tantalate platform that generates entangled photon pairs with ∼10^-7 efficiency. For a near watt level diode laser, this results in a near μW-level flux. The single photon per mode limit that is necessary to maintain non-classical photon behavior is still satisfied by distributing this power over up to an octave-spanning bandwidth. The spectral-temporal photon correlations are observed via a Michelson-type interferometer that measures the broadband Hong-Ou-Mandel two-photon interference. A coherence time of 245 fs for a 10 nm bandwidth in the collinear case and a coherence time of 62 fs for a 125 nm bandwidth in the non-collinear case are measured using a CW pump laser and, essentially, collecting the full photon cone. We outline in detail the numerical methods used for designing and tailoring the entangled photons source, such as changing center wavelength or bandwidth, with the ultimate aim of increasing the availability of high-flux UV-Vis entangled photon sources in the optical spectroscopy community.

Quantifying the enhancement of two-photon absorption due to spectral-temporal entanglement

When a low flux of time-frequency-entangled photon pairs (EPP) illuminates a two-photon transition, the rate of two-photon absorption (TPA) can be enhanced considerably by the quantum nature of photon number correlations and frequency correlations. We use a quantum-theoretic derivation of entangled TPA (ETPA) and calculate an upper bound on the amount of quantum enhancement that is possible in such systems. The derived bounds indicate that in order to observe ETPA the experiments would need to operate at a combination of significantly higher rates of EPP illumination, molecular concentrations, and conventional TPA cross sections than are achieved in typical experiments.

Optimization of selective two-photon absorption in cavity polaritons

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

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.

Exploiting chemistry and molecular systems for quantum information science

The power of chemistry to prepare new molecules and materials has driven the quest for new approaches to solve problems having global societal impact, such as in renewable energy, healthcare and information science. In the latter case, the intrinsic quantum nature of the electronic, nuclear and spin degrees of freedom in molecules offers intriguing new possibilities to advance the emerging field of quantum information science. In this Perspective, which resulted from discussions by the co-authors at a US Department of Energy workshop held in November 2018, we discuss how chemical systems and reactions can impact quantum computing, communication and sensing. Hierarchical molecular design and synthesis, from small molecules to supramolecular assemblies, combined with new spectroscopic probes of quantum coherence and theoretical modelling of complex systems, offer a broad range of possibilities to realize practical quantum information science applications.

Fluorescence-detected Fourier transform electronic spectroscopy by phase-tagged photon counting

Fluorescence-detected Fourier transform (FT) spectroscopy is a technique in which the relative paths of an optical interferometer are controlled to excite a material sample, and the ensuing fluorescence is detected as a function of the interferometer path delay and relative phase. A common approach to enhance the signal-to-noise ratio in these experiments is to apply a continuous phase sweep to the relative optical path, and to detect the resulting modulated fluorescence using a phase-sensitive lock-in amplifier. In many important situations, the fluorescence signal is too weak to be measured using a lock-in amplifier, so that photon counting techniques are preferred. Here we introduce an approach to low-signal fluorescence-detected FT spectroscopy, in which individual photon counts are assigned to a modulated interferometer phase ('phase-tagged photon counting,' or PTPC), and the resulting data are processed to construct optical spectra. We studied the fluorescence signals of a molecular sample excited resonantly by a pulsed coherent laser over a range of photon flux and visibility levels. We compare the performance of PTPC to standard lock-in detection methods and establish the range of signal parameters over which meaningful measurements can be carried out. We find that PTPC generally outperforms the lock-in detection method, with the dominant source of measurement uncertainty being associated with the statistics of the finite number of samples of the photon detection rate.

Towards a spectroscopic protocol for unambiguous detection of quantum coherence in excitonic energy transport

We propose a witness for quantum coherence in EET that can be extracted directly from two-pulse pump–probe spectroscopy experimental data.

Temperature-Controlled Entangled-Photon Absorption Spectroscopy

Entangled two-photon absorption spectroscopy (TPA) has been widely recognized as a powerful tool for revealing relevant information about the structure of complex molecular systems. However, to date, the experimental implementation of this technique has remained elusive, mainly because of two major difficulties: first, the need to perform multiple experiments with two-photon states bearing different temporal correlations, which translates into the necessity to have at the experimenter's disposal tens, if not hundreds, of sources of entangled photons; second, the need to have a priori knowledge of the absorbing medium's lowest-lying intermediate energy level. In this work, we put forward a simple experimental scheme that successfully overcomes these two limitations. By making use of a temperature-controlled entangled-photon source, which allows the tuning of the central frequencies of the absorbed photons, we show that the TPA signal, measured as a function of the temperature of the nonlinear crystal that generates the paired photons, and a controllable delay between them, carries all information about the electronic level structure of the absorbing medium, which can be revealed by a simple Fourier transformation.

Wave-Particle Duality in Complex Quantum Systems

Stunning progress in the experimental resolution and control of natural or man-made complex systems at the level of their quantum mechanical constituents raises the question, across diverse subdisciplines of physics, chemistry, and biology, whether the fundamental quantum nature may condition the dynamical and functional system properties on mesoscopic if not macroscopic scales. However, which are the distinctive signatures of quantum properties in complex systems, notably when modulated by environmental stochasticity and dynamical instabilities? It appears that, to settle this question across the above communities, a shared understanding is needed of the central feature of quantum mechanics: wave-particle duality. In this Perspective, we elaborate how randomness induced by this very quantum property can be discerned from the stochasticity ubiquitous in complex systems already on the classical level. We argue that in the study of increasingly complex systems, such distinction requires the analysis of single incidents of quantum dynamical processes.

Delocalized excitons and interaction effects in extremely dilute thermal ensembles

Long-range interparticle interactions are revealed in extremely dilute thermal atomic ensembles using highly sensitive nonlinear femtosecond spectroscopy. Delocalized excitons are detected in the atomic systems at particle densities where the mean interatomic distance (>10 μm) is much greater than the laser wavelength and multi-particle coherences should destructively interfere over the ensemble average. With a combined experimental and theoretical analysis, we identify an effective interaction mechanism, presumably of dipolar nature, as the origin of the excitonic signals. Our study implies that even in highly-dilute thermal atom ensembles, significant transition dipole-dipole interaction networks may form that require advanced modeling beyond the nearest neighbor approximation to quantitatively capture the details of their many-body properties.

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.

Multiphoton Effects Enhanced due to Ultrafast Photon-Number Fluctuations

The rate of an n-photon effect generally scales as the nth order autocorrelation function of the incident light, which is high for light with strong photon-number fluctuations. Therefore, "noisy" light sources are much more efficient for multiphoton effects than coherent sources with the same mean power, pulse duration, and repetition rate. Here we generate optical harmonics of the order of 2-4 from a bright squeezed vacuum, a state of light consisting of only quantum noise with no coherent component. We observe up to 2 orders of magnitude enhancement in the generation of optical harmonics due to ultrafast photon-number fluctuations. This feature is especially important for the nonlinear optics of fragile structures, where the use of a noisy pump can considerably increase the effect without overcoming the damage threshold.

Generation of broadband ultraviolet frequency-entangled photons using cavity quantum plasmonics

Application of quantum entangled photons is now extending to various fields in physics, chemistry and biology. In particular, in terms of application to molecular science, broadband ultraviolet frequency-entangled photons are desired because molecules inducing photochemical reactions of interest often have electronic transition energies in the ultraviolet region. Recent standard method for generating such entangled photons is a chirped quasi-phase-matching method, however this method is not suitable for the generation of ultraviolet frequency-entangled photons because it requires down-conversion of a photon with a wavelength shorter than ultraviolet into an entangled photon pair. Here we propose a simple method for generating broadband ultraviolet frequency-entangled photons using cavity quantum plasmonics, in which conventional cavity quantum electrodynamics theory is applied to quantum plasmonics. We introduce a cavity-plasmon system in which localised surface plasmon (LSP) is coupled to the cavity fields of a state-of-the-art microcavity. Using this system, we theoretically show that broadband ultraviolet frequency-entangled photons can be generated simply by utilising the absorption saturation effect of LSP.

Advances in multi-dimensional coherent spectroscopy of semiconductor nanostructures

Multi-dimensional coherent spectroscopy (MDCS) has become an extremely versatile and sensitive technique for elucidating the structure, composition, and dynamics of condensed matter, atomic, and molecular systems. The appeal of MDCS lies in its ability to resolve both individual-emitter and ensemble-averaged dynamics of optically created excitations in disordered systems. When applied to semiconductors, MDCS enables unambiguous separation of homogeneous and inhomogeneous contributions to the optical linewidth, pinpoints the nature of coupling between resonances, and reveals signatures of many-body interactions. In this review, we discuss the implementation of MDCS to measure the nonlinear optical response of excitonic transitions in semiconductor nanostructures. Capabilities of the technique are illustrated with recent experimental studies that advance our understanding of optical decoherence and dissipation, energy transfer, and many-body phenomena in quantum dots and quantum wells, semiconductor microcavities, layered semiconductors, and photovoltaic materials.

Efficient photon triplet generation in integrated nanophotonic waveguides

Generation of entangled photons in nonlinear media constitutes a basic building block of modern photonic quantum technology. Current optical materials are severely limited in their ability to produce three or more entangled photons in a single event due to weak nonlinearities and challenges achieving phase-matching. We use integrated nanophotonics to enhance nonlinear interactions and develop protocols to design multimode waveguides that enable sustained phase-matching for third-order spontaneous parametric down-conversion (TOSPDC). We predict a generation efficiency of 0.13 triplets/s/mW of pump power in TiO₂-based integrated waveguides, an order of magnitude higher than previous theoretical and experimental demonstrations. We experimentally verify our device design methods in TiO₂ waveguides using third-harmonic generation (THG), the reverse process of TOSPDC that is subject to the same phase-matching constraints. We finally discuss the effect of finite detector bandwidth and photon losses on the energy-time coherence properties of the expected TOSPDC source.

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.

Multidimensional spectroscopy with entangled light: loop vs ladder delay scanning protocols

Multidimensional optical signals are commonly recorded by varying the delays between time ordered pulses. These control the evolution of the density matrix and are described by ladder diagrams. We propose a new non-time-ordered protocol based on following the time evolution of the wavefunction and described by loop diagrams. The time variables in this protocol allow to observe different types of resonances and reveal information about intraband dephasing not readily available by time ordered techniques. The time variables involved in this protocol become coupled when using entangled light, which provides high selectivity and background free measurement of the various resonances. Entangled light can resolve certain states even when strong background due to fast dephasing suppresses the resonant features when probed by classical light.