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
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
This dissertation serves as a general introduction to Wigner functions, phase space, and quantum metrology but also strives to be useful as a how-to guide for those who wish to delve into the realm of using continuous variables, to describe quantum states of light and optical interferometry. We include many of the introductory elements one needs to appreciate the advantages of this treatment as well as show many examples in an effort to make this dissertation more friendly. In the initial segment of this dissertation, we focus on the advantages of Wigner functions and their use to describe many quantum states of light. We focus on coherent states and squeezed vacuum with a Mach Zehnder Interferometer for many of our examples, also used by experiments such as advanced LIGO. Later, we will also analyze this setup in more detail with a full example including the effects of many noise sources such as phase drift, photon loss, inefficient detectors, and thermal noise. In this setup, we also show the optimal measurement scheme, which is currently not employed in experiment. Throughout our metrology discussions, we will also discuss various quantum limits and use quantum Fisher information to show optimal bounds. When applicable, we also discuss the use of quantum Gaussian information and how it relates to our Wigner function treatment. The remainder of our discussion focuses on investigating the effects of photon addition and subtraction to various states of light and analyze the nondeterministic nature of this process. We use examples of m photon additions to a coherent state as well as discuss the properties of an m photon subtracted thermal state. We also provide an argument that this process must always be a nondeterministic one, or the ability to violate quantum limits becomes apparent. We show that using phase measurement as one's metric is much more restrictive, which limits the usefulness of photon addition and subtraction. When we consider SNR however, we show improved SNR statistics, at the cost of increased measurement time. In this case of SNR, we also quantify the efficiency of the photon addition and subtraction process.
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 optics has successfully been used to test fundamental principles in quantum physics and to demonstrate the potential of quantum-enhanced technologies. Linear quantum optics, in which large quantum states of light are produced by optical interference of smaller quantum states, has proved to be particularly fruitful. Further progress will rely both on developing improved experimental tools to manipulate and measure quantum light, and on expanding and refining the range of applications of these technologies. This thesis presents our contributions towards both of these endeavours. We first focus on some of the components necessary for linear quantum optics, starting with the requirement for reconfigurable interference between several optical modes. We propose a novel design for interferometers that satisfy this requirement, which is based on a new mathematical decomposition of unitary matrices used to describe optical interference. We show that our design is more efficient than previously known designs. We also experimentally demonstrate a modular approach to building these devices, which is based on the assembly of multiple UV-written integrated photonic chips. These chips are characterised, and three of them are assembled into a structure shown to enable a wide range of optical transformations. We then study methods of photon detection, showing how photon detectors can be calibrated and discussing the operation of superconducting photon number resolving transition edge sensors. Next, we study two applications of linear optics. We examine the applicability of a proposal for simulating molecular spectroscopy using quantum optics in the presence of experimental imperfections. Our findings are illustrated with a proof of principle experiment in which we simulate part of the vibronic spectrum of the tropolone molecule. Finally, we study a class of optical devices, known as optical Ising machines, that has been shown to find solutions to difficult combinatorial problems. Describing the optical pulses in these devices in phase space as Gaussian quasi-probability distributions that evolve stochastically, we analyse the computational mechanism of these machines and show in theory that they can be simplified without affecting their performance.
Measurements on states of light underpins the entire fields of classical and quantum optics. Without measurement we are unable to gain any information about the light we are studying or about the processes it has undergone. The property of the density matrix of light prior to measurement that we want to measure also relies heavily on the measurement technique we employ. We can use a single-photon detector to measure the particle nature of light--the photon--the discrete quanta of the electromagnetic field. We can conversely measure the wave nature of the light field by making phase-sensitive measurements. In this thesis, we shall explore some advanced implementations and applications of these measurement schemes. First, we shall focus on a specific type of single-photon detector: the Superconducting-Nanowire Single-Photon Detector. We will first consider the integration of these detectors on optical waveguides, and discuss their optical characterisation. Then we will consider a practical application of these detectors by investigating a method to perform broadband spectroscopy with a single detector. We shall then progress to phase-sensitive measurements, and consider the intermediate regime between measuring the wave-like and particle-like nature of light. First we will perform a fundamental investigation of the transition between both measurement regimes. We will see how varying the phase reference itself allows us to tune between both regimes. Following this we will discuss an application of this intermediate regime, by considering an experimental setup to perform state tomography with a weak phase reference. The final consideration of this thesis will be a theoretical benchmarking scheme for a practical application of quantum optics. The manipulation of certain quantum states of light followed by a photon-number measurement can have practical applications in a variety of fields, and therefore validating the results is of extreme importance. On this final topic, we will discuss an experimentally friendly technique to benchmark the output of such measurements by considering smaller subsystems, and the practical requirements of this technique.
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.
Quantum mechanics cements the intimate relationship between the nature of light and its detection. Historically, quantum theories of photodetection have generally fallen into two categories: the first tries to determine what quantum field observable is measured when photoelectrons are detected, laying the theoretical groundwork for photodetection being possible. The second type are phenomenological theories, which take great care to model the details of specific photodetectors. In this dissertation, we fill in the gap between these two models in the modern literature on photodetection by constructing a fully quantum-mechanical and sufficiently realistic model that includes all stages of the photodetection process. We accomplish this within the framework of quantum information theory using the language of positive operator valued measures (POVMs). \n\nA POVM provides the most general description of a quantum measurement. In the context of single-photon detection, the photodetector POVM provides a complete characterization of the single-photon detector (SPD) from which all figures of merit can be calculated. Each element of the POVM is comprised of a weighted sum over single-photon state projectors. To construct SPD POVMs, we identify the states projected onto by a measurement and the associated weights. We first accomplish this for a simple time-dependent system, laying out how to efficiently project onto arbitrary single-photon states. Then, we describe the three stages of a realistic SPD: transmission, amplification, and measurement.\n\nIn the transmission stage of photodetection a photon enters a network of discrete energy levels, its energy propagating through that network and finally exiting into another output continuum of modes, a process entirely described by a single complex function. In the amplification stage of photodetection, a single excitation is amplified into a macroscopic signal via a nonlinear amplification mechanism. In the final stage, an inefficient ``classical'' measurement is made on the macroscopic signal. By combining these three stages we form a chain of inference from the final ``click'' to the input photon and construct a POVM projecting onto the input Hilbert space. Lastly, we discuss limits and tradeoffs that arise at each stage and implications for photodetection applications.\n\nThis dissertation contains previously published and unpublished material.