Nonlinear spectroscopy is a powerful method for measuring complex systems with significant inter-state correlations. Even methods such as these are, however, still vulnerable to spectral congestion. One of the proposed methods to enhance the resolution of this already powerful technique is to harness the strong correlations of photon-frequency entanglement. This is easier said than done of course, but this doctoral thesis presents work in nonlinear spectroscopy and towards practical implementations of entangled-photon spectroscopy.Initially, we present some theoretical analysis of problems which may arise in nonlinear spectroscopy when pulse overlap is an issue. This is carried out in Paper I, which also numerically quantifies a fundamental theoretical limitation that pulse overlap presents, especially for short-lived signals.We then go on to experimental data analysis of the origins of coherent beatings and the size-dependence of primarily biexciton binding energies in CdSe quantum dots. These are covered in Papers II and III respectively.Finally, we perform an investigation of the possible upper bounds of an entangled-two photon absorption cross-section. Claims of strong quantum advantages in low-flux regimes have warranted further observation, and in examining them we are taking the first steps towards nonlinear entangled spectroscopy. This is done through use of a Franson interferometer, used here in a novel way by performing delay-dependent coincidence measurements for the purpose of obtaining an upper bound on entangled two-photon absorption cross-sections. This work is covered in Paper IV. We then discuss possible future directions for entangled-photon spectroscopy and the forms it can take.
Nonlinear spectroscopy is a powerful method for measuring complex systems with significant inter-state correlations. Even methods such as these are, however, still vulnerable to spectral congestion. One of the proposed methods to enhance the resolution of this already powerful technique is to harness the strong correlations of photon-frequency entanglement. This is easier said than done of course, but this doctoral thesis presents work in nonlinear spectroscopy and towards practical implementations of entangled-photon spectroscopy.Initially, we present some theoretical analysis of problems which may arise in nonlinear spectroscopy when pulse overlap is an issue. This is carried out in Paper I, which also numerically quantifies a fundamental theoretical limitation that pulse overlap presents, especially for short-lived signals.We then go on to experimental data analysis of the origins of coherent beatings and the size-dependence of primarily biexciton binding energies in CdSe quantum dots. These are covered in Papers II and III respectively.Finally, we perform an investigation of the possible upper bounds of an entangled-two photon absorption cross-section. Claims of strong quantum advantages in low-flux regimes have warranted further observation, and in examining them we are taking the first steps towards nonlinear entangled spectroscopy. This is done through use of a Franson interferometer, used here in a novel way by performing delay-dependent coincidence measurements for the purpose of obtaining an upper bound on entangled two-photon absorption cross-sections. This work is covered in Paper IV. We then discuss possible future directions for entangled-photon spectroscopy and the forms it can take.
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.
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.
Conspectus 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 10 7 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.
Optical quantum metrology uses specially-prepared states of light to probe sensitive samples. Choosing a suitable probe state allows one to extract more information per probe photon about an unknown parameter than is possible using any classical technique. In effect, these techniques improve the sensitivity of the measurement whenever the number of probe photons is constrained in some way. This thesis presents experimental and theoretical results on the use of pairs of time-frequency entangled photons in precision measurements. It begins with an overview of necessary background knowledge about quantum optics and quantum information. This is followed by a theoretical discussion on the estimation of a single delay using two-photon interference. We show that constraints on the probe photon's bandwidth complicate the measurement problem, requiring suitable optimization of the two-photon quantum state to avoid losing precision. We then consider the use of two-photon interference for linear spectroscopic measurements. Linear spectroscopy relates the absorption and phase spectrum of a sample to unknown electronic parameters. We describe a proof-of-principle experiment demonstrating that two-photon interferometric spectroscopy can be used for simultaneously measurement of both absorption and phase. This is followed by an information-theoretic discussion of the precision of this technique. For low losses, we show that the method provides phase sensitivity similar to classical interferometry while approaching the optimal absorption precision of any possible measurement. If the absorption and phase values are both related to a single unknown parameter, then our technique provides improved sensitivity to this parameter compared to both classical measurements and other quantum techniques in the presence of realistic levels of loss. We conclude with a discussion of quantum-optical coherence tomography, which is a two-photon interferometric method for determining the material structure of a sample. We present an ongoing experiment which aims to apply the method to tissue-like samples, where the quantum measurement is limited by a poor signal-to-noise ratio. Preliminary results demonstrate that this noise can be largely reduced by suitable frequency-domain filtering. This allows us to precisely determine the position of a scattering center using a few hundred detected photon pairs despite the presence of large amounts of noise. We follow this with a theoretical discussion of signal artifacts which are known to complicate the measured interferogram. We show these artifacts are due to a distinct interferometric effect, which can be distinguished from the signal of interest using the relative time delay between detected photons. We conclude with a brief discussion on possible techniques for artifact removal.
Nonlinear spectroscopy and microscopy techniques are ubiquitous in a wide range of applications across physics and biology. However, these usually rely on high-powered pulsed laser systems. A promising alternative is to exploit entangled two-photon absorption (ETPA), which can lead to tens of orders of magnitude lower incident fluxes than in conventional two-photon absorption schemes. However, the role of different entangled degrees of freedom in ETPA was unclear following recent experimental studies, when compared to earlier theoretical works. Here, we first demonstrate a linear dependence of the ETPA rate with the photon-pair rate, a clear signature of ETPA, and estimate the values for the concentration-dependent ETPA cross section for Rhodamine 6G. We then investigate the signature of energy-time entanglement and polarization dependence in the ETPA fluorescence rate and demonstrate a strong dependence of the signal on the interphoton delay that reflects the coherence time of the entangled two-photon wave packet.
Entangled photons offer quantum correlations with no classical analogue. In entangled pair two-photon absorption (ETPA), absorption rate is predicted to scale linearly rather than quadratically with photon flux, promising molecular excitation at fluxes far below the classical threshold. Reported ETPA cross sections nevertheless vary widely across experiments, largely since the observable, the differential of the transmitted flux or weak fluorescence, is difficult to separate from scattering and linear losses. We present a method which uses Franson interference to study entangled two-photon absorption through delay-dependent coincidence measurements on dye molecules. Applying the method to Rhodamine 6G, we observe a small asymmetry in the Franson interference envelope and obtain a model-derived effective cross section of approximately 2.1 E(-21) centimeter squared for Rhodamine 6G. However, the estimated systematic uncertainty does not allow a definitive ETPA assignment. Instead, the experiment establishes a quantitative bound on the ETPA response and provides a background-free benchmark for future measurements.