The classical or quantum nature of optical spectroscopy signals is a topic that has attracted great attention recently. Spectroscopic techniques have been classified as quantum or classical depending on the light-source used in their implementations. In this way, experiments performed with quantum light---such as entangled photon pairs---have been labeled as quantum spectroscopies, whereas those performed with coherent laser pulses are generally referred to as classical ones. In this work, we highlight the fact that typical laser-spectroscopy signals should sometimes be deemed quantum too, as they contain information about the quantum vacua of the modes that interact with the sample. Using a minimalistic model, namely frequency-integrated pump-probe spectroscopy, we demonstrate that vacuum contributions can be expressed as a correction term to the \emph{classical} pump-probe signals, which scales linearly with the intensity of the pump field. Remarkably, we show that these vacuum contributions may not be negligible and lead to the observation of superradiance in pump-probe experiments, provided that fields interacting with the medium are arranged in a collinear configuration.
The classical or quantum nature of optical spectroscopy signals is a topic that has attracted great attention recently. Spectroscopic techniques have been classified as quantum or classical depending on the light-source used in their implementations. In this way, experiments performed with quantum light---such as entangled photon pairs---have been labeled as quantum spectroscopies, whereas those performed with coherent laser pulses are generally referred to as classical ones. In this work, we highlight the fact that typical laser-spectroscopy signals should sometimes be deemed quantum too, as they contain information about the quantum vacua of the modes that interact with the sample. Using a minimalistic model, namely frequency-integrated pump-probe spectroscopy, we demonstrate that vacuum contributions can be expressed as a correction term to the \emph{classical} pump-probe signals, which scales linearly with the intensity of the pump field. Remarkably, we show that these vacuum contributions may not be negligible and lead to the observation of superradiance in pump-probe experiments, provided that fields interacting with the medium are arranged in a collinear configuration.
= 0, 1, 2, ··· classical light pulses and an entangled photon pair (a biphoton state) where one photon acts as a reference without interacting with the matter sample, identical signals can be obtained by replacing the biphotons with classical-like coherent states of light, where these are defined explicitly in terms of the parameters of the biphoton states. An input-output formulation of quantum nonlinear spectroscopy is used to prove this equivalence. We demonstrate the equivalence numerically by comparing a classical pump-quantum probe experiment with the corresponding classical pump-classical probe experiment. This analysis shows that understanding the equivalence between entangled biphoton probes and carefully designed classical-like coherent state probes leads to quantum-inspired classical experiments that yield equivalent signals and provides insights for the future design of QLS experiments that could provide a true quantum advantage.
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.
Studies on the nature of light have often played pivotal roles in the development of physics. The particle nature of light served as benchmark for the foundation of quantum physics and its derived branches, while its referential-independent speed in the vacuum, as seen through wave equations, led to the merge of space and time and culminated in the foundation of general relativity and cosmology. In spite of that, many light-based measurement techniques still rely heavily on a classical description of light, as has been for many years the case for electrooptic sampling. Luckily, this scenario has been changed in the course of the last few years, with both experimental and theoretical works highlighting the advantages and hidden properties that a quantum and/or relativistic description of light can unveil. Speci fically, the electrooptic sampling of a broadband section of the electric- field vacuum opened an entirely new window of possibilities, and the works presented here aim at filling a small portion of the gap opened by this simple, yet remarkable, technological leap. As a starting point, I study the spectral properties of quantum radiation of ultrashort duration. In particular, I introduce a continuous multimode squeezing operator for the description of subcycle pulses of entangled photons generated by a coherent-pulse driving in a thin nonlinear crystal with second-order susceptibility. The spectra of these ultrabroadband squeezed states can be found perturbatively in the strength of the driving electric-fi eld pulse. These can be related, for suitable choices of the driving pulses, to the spectra that one should hypothetically observe in an Unruh-Davies experiment, in which an observer (more precisely a particle detector) moving with constant proper acceleration in the Minkowski vacuum during a finite (life)time detects a thermal distribution of (virtual) particles. On the other hand, when describing the corresponding behavior of the normally ordered electric- field variance in the time domain, a connection to experiments in which such states have been generated and detected can be traced. This variance builds up as the electric fi eld (or correspondingly its state) evolves via propagation through the nonlinear crystal, and it can be shown that the world lines followed by the fi eld modes when propagating are indeed curved, as is usually the case for the Unruh-DeWitt detectors used to study the Unruh-Davies effect. Alongside the study of the states generated in a nonlinear crystal, I also investigate what influence these states have on the electrooptic measurements that rely on the same effective nonlinear interaction. When electrooptically sampling the electric- field vacuum, the evolution of the electric fi eld leads to a change in the initially sampled vacuum state. This change piles up backaction contributions that remain in superposition with the vacuum state after the measurement. When the superposition coefficients of the back-action contributions are small, the electrooptic-signal variance is dominated by the shot noise, with a small vacuum-related contribution on top. As the sampling regime shifts towards stronger probe-pulse intensities, the state superposition undergoes a change, which can be traced back to the signal variance and the clear change in its behavior, with a steep departure from the shot noise. This approach is then further extended to model another setup in which two probes, time-shifted relative to each other, are impinged on the nonlinear crystal to probe the vacuum. This approach allows for the evasion of shot noise and produces a way richer variety of back-action contributions that are then investigated.
Spectroscopy, the study of matter via its interactions with light, is a vast subject that includes many of humanity's principle means of probing the fundamental structure of matter. Though usually understood from the perspective of classical light, important effects arise due to the quantum nature of the electromagnetic field. Additionally, the quantum vacuum can serve as an effective couple between molecules in the system, generating many-body interactions and cooperative processes in the material. While many techniques are well-described classically, quantum-field corrections can dominate the desired signals in certain cases, such as cascading in higher-order n-wave mixing signals, and are key for experimental interpretation. Even spontaneous emission and light scattering are best understood from the perspective of quantum fields. In this thesis, we utilize a systematic procedure, based on the density matrix in Liouville space, to give a rigorous description of elementary quantum-field effects in nonlinear spectroscopy, with specific examples made to ultrafast x-ray and optical techniques.
In a recent paper [Phys. Rev. A 91, 053844 (2015)], Mukamel and Dorfman compare spectroscopies performed with classical vs quantum light and conclude that nonlinear quantum-spectroscopy signals cannot be obtained from averaging their classical-spectroscopy counterparts over the Glauber-Sudarshan quasiprobability distribution of the quantum field. In this Comment, we show that this interpretation is correct only when classical spectroscopy is perceived as a theoretical description which neglects quantum fluctuations of light altogether. While such an assumption can be a good approximation and useful for comparing theoretical results, it is never realized exactly in laser-spectroscopy experiments that typically use coherent states. Even though coherent states represent the most classical form of light, their quantumness must be considered to fully understand laser-spectroscopy experiments and their connection to quantum spectroscopy, performed with true quantum sources, such as Schr\"odinger's cat states. Thus, instead of using a classical approximation, the connection between coherent states and true quantum states of light must be considered. We rigorously show that quantum spectroscopy can always be projected from the experimentally realized coherent-state spectroscopy regardless how nonlinear the system response is.
Optical signals obtained by the material response to classical laser fields are given by nonlinear response functions which can be expressed by sums over various quantum pathways of matter. We show that some pathways can be selected by using nonclassical fields, through the entanglement of photon and material pathways, which results in a different-power law dependence on the incoming field intensity. Spectrally overlapping stimulated Raman scattering (SRS) and two-photon-absorption (TPA) pathways in a pump probe experiment are separated by controlling the degree of entanglement of pairs of incoming photons. Pathway-selectivity opens up new avenues for mapping photon into material entanglement. New material information, otherwise erased by interferences among pathways, is revealed.