The interaction of quantum light with matter is of great importance to a wide range of scientific disciplines, ranging from optomechanics to high-precision measurements. A central issue we discuss here, is how to make optimal use of both the spatial and the quantum degrees of freedom of light for characterizing and manipulating arbitrary observable parameters in a linear scattering system into which suitably engineered light fields are injected. Here, we discuss a comprehensive framework based on a quantum operator that can be assembled solely from the scattering matrix of a system and its dependence on the corresponding local parameter, making this operator experimentally measurable from the far field using only classical light. From this, the effect of quantum light in the near field, i.e., in the vicinity of the target object, can be inferred. Based on this framework, it is straightforward to formulate optimal protocols on how to jointly design both the spatial shape and the quantum characteristics of light for micromanipulation as well as for parameter estimation in arbitrarily complex media. Also, the forces of the quantum vacuum naturally emerge from this formalism. The aim of our tutorial is to bring different perspectives into alignment and thereby build a bridge between the different communities of wave control, quantum optics, micromanipulation, quantum metrology, and vacuum physics.
The interaction of quantum light with matter is of great importance to a wide range of scientific disciplines, ranging from optomechanics to high-precision measurements. A central issue we discuss here, is how to make optimal use of both the spatial and the quantum degrees of freedom of light for characterizing and manipulating arbitrary observable parameters in a linear scattering system into which suitably engineered light fields are injected. Here, we discuss a comprehensive framework based on a quantum operator that can be assembled solely from the scattering matrix of a system and its dependence on the corresponding local parameter, making this operator experimentally measurable from the far field using only classical light. From this, the effect of quantum light in the near field, i.e., in the vicinity of the target object, can be inferred. Based on this framework, it is straightforward to formulate optimal protocols on how to jointly design both the spatial shape and the quantum characteristics of light for micromanipulation as well as for parameter estimation in arbitrarily complex media. Also, the forces of the quantum vacuum naturally emerge from this formalism. The aim of our tutorial is to bring different perspectives into alignment and thereby build a bridge between the different communities of wave control, quantum optics, micromanipulation, quantum metrology, and vacuum physics.
The concepts of quantum detection and estimation theory can be of great help in the analysis of faint signals, which must be treated with extreme care due to the fragility and subtlety. But this is surely not the only domain, where the advanced concepts may be applied. Strong optical fields can be analyzed by similar techniques since by virtue of first quantization any optical wave plays role of a quantum state. More precisely, a classical mode of light can be given and alternative interpretation as a quantum state of the spatial degrees of freedom of a photon. Here the formulation of classical optics meets those of quantum information processing. The goal of the research is to optimize classical sensing schemes of strong signals in order to attain the best performance allowed by Nature. As examples of the approach, measurement of two point-like sources separation and full characterization of laser beams by a phase-space tomography will be discussed both theoretically and experimentally.
We show a general method to estimate with optimum precision, i.e., the best precision determined by the light-matter interaction process, a set of parameters that characterize a phase object. The method is derived from ideas presented by Pezze []. Our goal is to illuminate the main characteristics of this method as well as its applications to the physics community probably not familiar with the quantum language usually employed in works related to quantum estimation theory. First, we derive precision bounds for the estimation of the set of parameters characterizing the phase object. We compute the Crámer-Rao lower bound for two experimentally relevant types of illumination: a multimode coherent state with mean photon number N and N copies of a multimode single-photon quantum state. We show under which conditions these two models are equivalent. Second, we show that the optimum precision can be achieved by projecting the light reflected or transmitted from the object onto a set of modes with engineered spatial shape. We describe how to construct these modes and demonstrate explicitly that the precision of the estimation using these measurements is optimum. As an example, we apply these results to the estimation of the height and sidewall angle of a cliff-like nanostructure, an object relevant in the semiconductor industry for the evaluation of nanofabrication techniques. Published by the American Physical Society 2024
This book bridges the gap between introductory quantum mechanics and the research front of modern optics and scientific fields that make use of light. While suitable as a reference for the specialist in quantum optics, it also targets non-specialists from other disciplines who need to understand light and its uses in research. It introduces a single analytic tool, the density matrix, to analyze complex optical phenomena encountered in traditional as well as cross-disciplinary research. It moves swiftly in a tight sequence from elementary to sophisticated topics in quantum optics, including optical tweezers, laser cooling, coherent population transfer, optical magnetism, electromagnetically induced transparency, squeezed light, and cavity quantum electrodynamics. A systematic approach starts with the simplest systems—stationary two-level atoms—then introduces atomic motion, adds more energy levels, and moves on to discuss first-, second-, and third-order coherence effects that are the basis for analyzing new optical phenomena in incompletely characterized systems. Unconventional examples and original problems are used in exploring a mathematical methodology which can tackle virtually any new problem involving light. The steady progression from “simple” to “elaborate” makes the book accessible not only to students from traditional subject areas that make use of light, but also to researchers such as biophysicists using mechanical effects of light; photochemists developing coherent control for rare species detection; biomedical engineers imaging through scattering media; electromechanical engineers working on molecular design of materials for electronics and space; electrical and computer engineers developing schemes for quantum computation, cryptography, frequency references, and the like.
The insights offered by quantum mechanics to the field of optical metrology are many-fold, with non-classical states of light themselves used to make sensors that surpass the sensitivity of sensors using classical states of light. Unfortunately, this advantage, referred to often as "super-sensitivity" is notoriously fragile, and even the slightest experimental imperfections may greatly reduce the efficacy of the non-classical sensors, sometimes completely obviating their advantage. In my thesis I have shown that the performance of an otherwise ideal two-photon interferometer, which exploits entanglement between photons to make super-sensitive measurements of phase, is crippled by the slightest introduction of decoherence between modes of the interferometer. I have shown further that such drastic reduction in sensitivity can also appear in classical measurement problems, specifically that the recently developed methods of estimating the separation between a pair of point sources are rendered less effective when the ideal assumption of complete spatial incoherence is relaxed. Towards overcoming these and other issues, I have designed new configurations that use ancillary optical degrees of freedom, a tool-set that has recently garnered much interest in the field of quantum optics. In the context of two-photon interferometry, I have shown that by coupling polarization to the spatial-structure of the two photon state used to probe phase it is possible to obviate the need for a reference phase, even in the context of decoherence and imperfections in the interferometer. In the context of two-point resolution, I have developed an anisotropic imaging system that performs the function of an image-inversion interferometer and is inherently stable, offering an attractive implementation of recently developed methods of sub-Rayleigh imaging. I have further shown both theoretically and experimentally that the same anisotropic image-inversion interferometer is useful in measuring spatially encoded phases, both in the context of classical illumination as well as quantum-aided two-photon super-sensing. In both cases, the ability to perform interferometric measurements of the spatial structure of an electric field without splitting beam paths forms a bridge between conception and implementation of precision-sensing measurement strategies. Finally, I have shown that binary interferometric method based on the common-path anisotropic imaging system that I introduced, are able to measure both phase gradients and transverse beam tilts with a sensitivity beating conventional systems that are used both commercially and in research laboratories.
Abstract This book bridges the gap between introductory quantum mechanics and the research front of modern optics and scientific fields that make use of light. While suitable as a reference for the specialist in quantum optics, it also targets non-specialists from other disciplines who need to understand light and its uses in research. It introduces a single analytic tool, the density matrix, to analyze complex optical phenomena encountered in traditional as well as cross-disciplinary research. It moves swiftly in a tight sequence from elementary to sophisticated topics in quantum optics, including optical tweezers, laser cooling, coherent population transfer, optical magnetism, electromagnetically induced transparency, squeezed light, and cavity quantum electrodynamics. A systematic approach starts with the simplest systems—stationary two-level atoms—then introduces atomic motion, adds more energy levels, and moves on to discuss first-, second-, and third-order coherence effects that are the basis for analyzing new optical phenomena in incompletely characterized systems. Unconventional examples and original problems are used in exploring a mathematical methodology which can tackle virtually any new problem involving light. The steady progression from "simple" to "elaborate" makes the book accessible not only to students from traditional subject areas that make use of light, but also to researchers such as biophysicists using mechanical effects of light; photochemists developing coherent control for rare species detection; biomedical engineers imaging through scattering media; electromechanical engineers working on molecular design of materials for electronics and space; electrical and computer engineers developing schemes for quantum computation, cryptography, frequency references, and the like.
Recent progress in meta-optics, particularly the development of metasurfaces, has enabled compact, tunable, and integrable control over the amplitude, phase, polarization, and wavefront of light, thereby allowing a paradigm shift in traditional optical science and engineering. In parallel, the ability to generate and precisely manipulate nonclassical light is central to quantum optics, enabling key functionalities in secure quantum communication, precision measurement, and scalable quantum computation. This review aims to bridge these two rapidly advancing fields by presenting recent progress in the application of structured materials to the manipulation of quantum states of light. We begin by introducing the concept of singular optics, followed by a discussion of various families of spatially and temporally structured beams that form the foundation for many of the phenomena explored in quantum photonics. Next, we revisit the theoretical framework of quantum optics, including the formalism of photon quantization and the principles governing quantum frequency conversion. We then examine how metasurfaces can be engineered to enable highly efficient nonlinear quantum processes, including both up-conversion and down-conversion, thereby offering new approaches for generating and controlling complex quantum states. Furthermore, we discuss the crucial role of structured materials in shaping the properties of quantum light and in applications such as quantum ghost imaging. The review concludes by identifying emerging directions for integrating meta-optical platforms with quantum systems, highlighting their potential for scalable manipulation of nonclassical light at the nanoscale.