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.
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.
The control of photons represents a pillar for our modern technological society. The emerging field of quantum photonics exploits quantum properties of light to dramatically improve the performance of protocols for metrology, communication and information processing. However, modern applications exploit very little of the enormous potential of the photon. Unfortunately, the challenges involved in the preparation and characterization of photonic states with multiple particles, impose practical limitations to realistic quantum technologies. In this talk, I will report on our recent results on the preparation, manipulation and characterization of quantum states with multiple photons. I will describe how the manipulation of the quantum electromagnetic fluctuations of a pair of vacuum states leads to a novel family of quantum-correlated multiphoton states with tunable mean photon numbers and degrees of correlations. Our technique relies on the use of conditional measurements to engineer the vacuum and consequently the excitation mode of the field through the simultaneous subtraction of photons from two-mode squeezed vacuum states. In addition, I will describe the potential of combing these states with photon number resolving measurements for quantum phase estimation. The last part of my talk will be devoted to discuss our recent technique that allowed us to utilize compressive sensing to demonstrate measurement of high-dimensional states, that describe telecom photon pairs in the spatial and spectral degrees of freedom, with 12 billions of elements using only a small fraction of measurements.
The use of quantum properties of light has paved new avenues in the field of imaging. Quantum illumination and ghost-imaging protocols have shown exciting promise in addressing the issues inherent in classical imaging, such as background noise and a high level of required illumination. Moreover, quantum metrological schemes analyzing the modal content of light would address the resolution limits of direct imaging, promising enhancement beyond the Rayleigh limit. Augmenting these novel techniques with machine learning, particularly deep learning architectures such as Convolutional Neural Networks (CNNs), one strives to see significant improvements in image reconstruction and object identification in quantum imaging protocols. In my talk, I present recent progress and development on reconstructing the image of different objects with quantum sources, employing a high degree of spatial correlation between photon pairs and autoencoder deep learning architecture.
In 2009, physicists at the National Institute of Standards and Technology in Colorado, Boulder developed what could arguable be called the first rudimentary quantum computer [1]. The past decade has seen unprecedented improvements in quantum information science culminating in the demonstration of quantum supremacy --- that quantum computers can solve problems that are impractical to be solved on the best supercomputers [2]. This remarkable progress necessitates the development of techniques to characterize the quantum devices that are being developed. In my thesis, I will focus on such devices that manipulate and detect light. In Chapter 1, I will introduce the reader to the historical underpinnings of the study of light. After surveying the history of light since time immemorial, I will delve into the developments in the study of light in the 19th and the early 20th century. I will then present a brief introduction to quantum mechanics. I end this chapter by demonstrating how light is quantized. In Chapter 2, I will introduce the various tools necessary to delve into this dissertation. After defining quadrature operators and Wigner functions, I will introduce various states of light used in this thesis. I will then discuss how the evolution, as well as detection of quantum optical states, are modelled. I will then present the formalism of Gaussian quantum information that simplifies the manipulation of certain states of light. Finally, I will briefly talk about quantum metrology and show its advantage in phase estimation. In Chapter 3, I will introduce a method to characterize linear and quadratically nonlinear optical systems. After motivating the need for this work, I will introduce the modifications necessary to the standard Mach-Zehnder interferometer in order to characterize optical systems with it. I will then show how to characterize linear optical systems with coherent probes. I will also show that this scheme is shot-noise limited. I will then show that by using single photons in addition, we can characterize quadratically nonlinear optical systems. Finally, I will show that no advantage is gained in sensitivity by using squeezed light along with coherent light as probes. In Chapter 4, I will introduce a method to characterize photodetectors. This is done by developing an experimental method to find the Wigner functions of the POVM set corresponding to a photodetector. After motivating the necessity of this work as well as describing the proposed experimental setup, I will show how this scheme can
Phase estimation has a wide range of applications. Over the years, several strategies have been studied to improve precision in phase estimation. These strategies include using exotic quantum states to quantum detection schemes. This dissertation summarizes my effort in improving the precision of phase estimation with a linear and nonlinear interferometer. Chapter 1 introduces quantum optics and quantum metrology. I introduce all relevant quantum states of light used. We also look into tools and terminologies of quantum metrology such as Fisher information, shot-noise limit, Heisenberg limit, etc., along with examples of phase estimation with a Mach-Zehnder interferometer. In Chapter 2, I discuss multiple phase estimation using a multimode interferometer. Building upon previous work, our scheme consists of a multimode interferometer with single-photon inputs. By using a quantum Fisher information analysis, we show that our scheme gives a constant improvement over other schemes. We also show that our scheme with photon-number-resolving detection approaches the quantum Cram\'er-Rao bound. Moreover, we also consider the probabilistic nature of photon emission at the input, and we study its effect on phase sensitivity. I discuss phase estimation with SU(1,1) interferometer in Chapter 3. We look at phase sensitivity in this interferometer with different input states. Namely, we consider two different phase estimation scheme, one using thermal and squeezed states, and others using coherent and displaced squeezed states with parity and on-off as a detection scheme. We also look into the effect of photon loss inside the interferometer. In Chapter 4, we revisit phase estimation in SU(1,1) interferometer from the perspective of quantum Fisher information. I discuss in detail a longstanding confusion regarding the use of quantum Fisher information in SU(1,1) interferometer. We show that phase averaging or quantum Fisher information matrix method is needed in general for calculating the phase sensitivity which resolves inconsistencies reported in previously published articles.
Today, quantum photonics is one of the leading platforms for the research and development of the quantum information sciences and technologies. It is also the most promising platform for quantum networking protocols. As such, the investigation and characterization of quantum light sources is vital to the future of quantum research. In this thesis document, titled “Multimode Statistical Photonics and Quantum State Tomography for Quantum Networks,” I present my research on the multi-mode statistical properties of classical light sources, with applications to quantum state tomography methods for use in quantum communications and networking protocols. During my time here at LSU, I have worked with my fellow researchers in the quantum photonics group to investigate the quantum dynamics which govern the classical statistical behaviors of stochastically-random light sources. By extracting the correlated multiphoton, multi-mode subsystems of such sources, we have discovered nontrivial, uniquely-quantum behaviors within sources of light which were previously thought to be only classical. I have also developed a robust theoretical framework for describing such sources, utilizing techniques from quantum field theory, which we have shown to be an excellent predictor of experimental measurements. I have then applied these innovations to projects concerning plasmonic nanostructures, quantum imaging, and quantum sensing. Additionally, in collaboration with the National Institute of Standards and Technology (NIST), I have performed an experiment utilizing weak-field interference to prove the correctness of a quantum state tomography method called weak-field homodyne detection, a low-noise procedure which is ideal for quantum communications and networking protocols. As a result, I was able to completely reconstruct a coherent quantum state within the interference mode, and also to obtain some limited information about the remaining modes of that state. Throughout all of this, my research has had a particular focus on multi-mode photonics and its applications to plasmonics and quantum networking, and I believe that the state-tomography protocols and the results concerning stochastically-random quantum light sources will be of use to the quantum information and photonics communities for years to come.
This thesis is divided into five parts, each with an accompanying publication. In Chapter 1, I motivate the broad scientific pursuit that underlies this thesis: the quest to build universal, fault-tolerant technology that operates on the principles of quantum mechanics and quantum information theory. I motivate the use of single photons as the quantum particles of choice for this task, and I describe the open challenges facing the field of researchers embarking on this quest. This motivation pervades each subsequent chapter of this thesis, which focus in turn on overcoming four distinct technological and scientific hurdles related to these open challenges. The first of these open challenges is to demonstrate experimentally a useful single-photon source. This source of single photons ought to release just one photon at a time, in an on-demand fashion, with high-rate, low-latency, and high quantum-state purity and indistinguishability, in a single spatial mode, at the right wavelengths for a given application, and ought to satisfy certain practical constraints on size, weight, power, and sensitivity to environmental noise and perturbation. This is a long list of performance metrics, some of which are orthogonal, some not, and non-trivial tradeoffs often exist between metrics. While in this thesis we do not present a solution to this general open problem, we modestly expand scientific knowledge of one of the fundamental mechanisms behind single-photon generation. In particular, we present a new formalism for describing the quantum properties of spontaneous Stokes scattering in the Raman interaction, and we probe its effects on the quantum state purity of resulting Stokes photons both experimentally and theoretically. This is the focus of Chapter 2. Another open challenge to universal, fault-tolerant photonic quantum processing is the experimental demonstration of a useful photonic quantum memory—a device that is capable of storing and releasing single photons in a quantum-information-conserving manner, and which possesses sufficiently high performance across, again, a large set of non-orthogonal metrics. On this challenge, we have made several substantial contributions. Chapter 3 describes a novel approach to optimizing the efficiency of photonic quantum memories in atomic ensembles possessing a three-level Lambda-type energy level structure, in an experimentally friendly fashion. Chapter 4 discusses the practical side of implementing robust quantum memory in these atomic systems, where we carefully consider the theoretical sensitivity of these systems to experimental noise and perturbation. These two Chapters lead up to the experimental work described in Chapter 5, where we experimentally demonstrate a state-of-the-art and best-in-class photonic quantum memory in neutral barium vapor that possesses simultaneously high efficiency, broad bandwidth, and low noise. Our experimental demonstration features >95% storage efficiency, at roughly 3 orders of magnitude larger bandwidth (higher speed) than the previous state of the art, as well as record-low noise for Lambda-type atomic memories. The noise is so low, and the bandwidth so large, that we are able to perform a novel characterization experiment to extract the temporal amplitude and phase of the photons retrieved from our memory, based on spectral interferometry with a known reference. This is the most demanding possible characterization of one of these memories, and has direct implications for using this type of memory in quantum processing tasks that require temporally indistinguishable photons. In Chapter 6 I do the requisite summing up of the thesis, and discuss ongoing and future work on the memory project. In the various and sundry appendices I include information that will chiefly be useful for my successors in the lab, but may be of passing interest to other readers.