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.
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.
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.
With the rapid advancement of science and technology, phase measurement plays a crucial role in various fields such as optics, communication, and radar. Traditional phase measurement methods, relying on classical light sources, produce results following the central limit theorem, limiting measurement precision to the standard quantum limit. However, recent in-depth studies of quantum theory and quantum enhanced experimental techniques are breaking this barrier. The use of specially designed non-classical light sources for phase measurement not only provides the possibility of breaking through the limits of measurement precision but also meets the growing demand for high-precision measurements.This paper started from a statistical perspective, introduced key indicators for evaluating measurement precision, including the Cramér-Rao Boundary (CRB) and Fisher Information, and extends to experimental approaches beyond the standard quantum limit. Subsequently, by introducing quantum light sources such as squeezed states, entangled states, and methods like harmonic amplification to achieve amplifier the phase and optical detection, the paper provides a comprehensive review of recent research achievements in super-resolution phase measurement techniques. Finally, we select several technological categories with a promising engineering outlook, analyze the technical challenges limiting their maturity, and provide a prospective outlook.
Quantum-enhanced interferometers utilize non-classical states of light in order to surpass the limitations imposed by classical physics on phase measurement sensitivity and resolution. We review key scientific developments in this growing field of research and derive fundamental metrology concepts, namely the Cram\'{e}r-Rao bound and the Fisher information, which are used to analyze the metrological performance of quantum states of light. We propose a supersensitive quantum interferometry protocol that can be amplified to the macroscopic realm (i.e. the mean number of photons of the probe state can reach approximately 100,000 photons) using contemporary techniques of spontaneous parametric down conversion. The parity measurement on the output field asymptotically saturates the quantum Cram\'{e}r-Rao bound, which scales like the Heisenberg limit. We uncover the role of photon statistics on phase sensitivity and rule out the necessity of mode entanglement for quantum-enhanced interferometry. Based on these insights we outline a practical metrology technique (independent of mode entanglement) that measures a phase delay of a single-mode anti-squeezing operation. This scheme can also be scaled macroscopically using contemporary techniques and is shown to significantly surpass the shot-noise limit (SNL) in the presence of realistic losses. Finally, the physical resources that enable quantum-enhanced interferometry is studied by analyzing the quantum Fisher information (QFI) using the first quantization and the second quantization formalisms of quantum mechanics. It is shown that increasing the intra-mode correlations of an interferometer (as quantified by the second order Glauber coherence function) can be conducive to attaining a quantum advantage in phase estimation; whereas, introducing mode entanglement can reduce phase sensitivity. Using the first quantization description, we derive a formula for the QFI that shows explicitly how the Heisenberg scaling term depends on particle entanglement.
A great deal of research in optics concentrates on developing quantum methods ranging from precision measurement to optical telecommunication, and from quantum information processing to fundamental tests of nature. To this aim, engineering and characterization of quantum states of light becomes extremally important. Nonclassical sources are based on various underlying physical phenomena, from parametric downconversion and four-wave mixing to solid state and atomic single emitters to ensembles of atoms or ions. I will discuss recent efforts in engineering and characterization of nonclassical light states applicable to a broad range of sources, predominantly based on tunable narrow-band filtering.
The technologies utilizing quantum states of light have been in the spotlight for the last two decades. In this regard, quantum metrology, quantum imaging, quantum-optical communication are some of the important applications that exploit fascinating quantum properties like quantum superposition, quantum correlations, and nonclassical photon statistics. However, the state-of-art technologies operating at the single-photon level are not robust enough to truly realize a reliable quantum-photonic technology. In Chapter 1, I present a historical account of photon-based technologies. Furthermore, I discuss recent efforts and encouraging developments in the field of quantum-photonic technologies, and major challenges for the experimental realization of reliable quantum technologies utilizing photons, setting up a stage for unveiling our smart methodologies to cope with them. Similarly, in Chapter 2, I review the fundamental concepts such as states of light, spatial modes of light, and machine learning. In Chapter 3 of this dissertation, I present a theoretical work on a nonlinear quantum metrology scheme, showing a sub-shot-noise limited phase estimation using the displaced-squeezed light and on/off detection. Furthermore, I discuss a camera-based squeezed-light detection technique that can be a smart and time-efficient alternative to conventional balanced-homodyne detection. In Chapter 4, I discuss our efforts to incorporate artificial intelligence in a quest to improve the efficiency of discriminating thermal light sources from coherent light sources. The conventional identification technique requires a large number of measurements. We utilize artificial neural networks to dramatically reduce the number of measurements required to distinguish thermal light and coherent light. In Chapter 5, I present a communication protocol that utilizes the spatial modes of light. Despite being valuable resources for a wide variety of quantum technologies, spatial modes of light are extremely vulnerable to random phase fluctuations. The conventional techniques to cope with these challenges are relatively inefficient. We utilize convolutional neural networks to perform the spatial mode correction of single photons, resulting in a near-unity fidelity of correction. I wrap up my dissertation in Chapter 6 by summarizing the historical context of quantum technologies, challenging problems facing state-of-art quantum technologies, and the importance of our efforts to introduce artificial intelligence in photonic technologies.
Quantum metrology is an auspicious discipline of quantum information which is currently witnessing a surge of experimental breakthroughs and theoretical developments. The main goal of quantum metrology is to estimate unknown parameters as accurately as possible. By using quantum resources as probes, it is possible to attain a measurement precision that would be otherwise impossible using the best classical strategies. For example, with respect to the task of phase estimation, the maximum precision (the Heisenberg limit) is a quadratic gain in precision with respect to the best classical strategies. Of course, quantum metrology is not the sole quantum technology currently undergoing advances. The theme of this thesis is exploring how quantum metrology can be enhanced with other quantum techniques when appropriate, namely: graph states, error correction and cryptography.