In optical quantum information processing, two of the most basic elements are the sources of quantum mechanical states of light, and the devices that can detect these states. In this chapter, we narrow this down to photon sources and photodetectors. We will describe first how detectors work, starting from abstract ideal detectors, via a complete description of realistic detectors in terms of POVMS, to a brief overview of current photodetectors. Subsequently, we will define what is a single-photon source, and how we can determine experimentally whether a source produces single photons or something else. Having laid down the ground rules, we will survey some of the most popular ways photons are produced in the laboratory. Finally, we take a look at the production of entangled photon sources and quantum non-demolition measurements of photons. A mathematical model of photodetectors Photodetectors are devices that produce a macroscopic signal when triggered by one or more photons. In the ideal situation, every photon that hits the detector contributes to the macroscopic signal, and there are no ‘ghost’ signals, or so-called dark counts. In this situation we can define two types of detector, namely the ‘photon-number detector’, and ‘detectors without number resolution’. First, the photon number detector is a (largely hypothetical) device that tells us how many photons there are in a given optical mode that is properly localized in space and time. This property is called ‘photon-number resolution’.
In optical quantum information processing, two of the most basic elements are the sources of quantum mechanical states of light, and the devices that can detect these states. In this chapter, we narrow this down to photon sources and photodetectors. We will describe first how detectors work, starting from abstract ideal detectors, via a complete description of realistic detectors in terms of POVMS, to a brief overview of current photodetectors. Subsequently, we will define what is a single-photon source, and how we can determine experimentally whether a source produces single photons or something else. Having laid down the ground rules, we will survey some of the most popular ways photons are produced in the laboratory. Finally, we take a look at the production of entangled photon sources and quantum non-demolition measurements of photons. A mathematical model of photodetectors Photodetectors are devices that produce a macroscopic signal when triggered by one or more photons. In the ideal situation, every photon that hits the detector contributes to the macroscopic signal, and there are no ‘ghost’ signals, or so-called dark counts. In this situation we can define two types of detector, namely the ‘photon-number detector’, and ‘detectors without number resolution’. First, the photon number detector is a (largely hypothetical) device that tells us how many photons there are in a given optical mode that is properly localized in space and time. This property is called ‘photon-number resolution’.
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.
Over the last sixty years, classical information theory has revolutionized the understanding of the nature of information, and how it can be quantified and manipulated. Quantum information processing extends these lessons to quantum systems, where the properties of intrinsic uncertainty and entanglement fundamentally defy classical explanation. This growing field has many potential applications, including computing, cryptography, communication, and metrology. As inherently mobile quantum particles, photons are likely to play an important role in any mature large-scale quantum information processing system. However, the available methods for producing and detecting complex multi-photon states place practical limits on the feasibility of sophisticated optical quantum information processing experiments. In a typical quantum information protocol, a source first produces an interesting or useful quantum state (or set of states), perhaps involving superposition or entanglement. Then, some manipulations are performed on this state, perhaps involving quantum logic gates which further manipulate or entangle the intial state. Finally, the state must be detected, obtaining some desired measurement result, e.g., for secure communication or computationally efficient factoring. The work presented here concerns the first and last stages of this process as they relate to photons: sources and detectors. Our work on sources is based on the need for optimized non-classical states of light delivered at high rates, particularly of single photons in a pure quantum state. We seek to better understand the properties of spontaneous parameteric downconversion (SPDC) sources of photon pairs, and in doing so, produce such an optimized source. We report an SPDC source which produces pure heralded single photons with little or no spectral filtering, allowing a significant rate enhancement. Our work on detectors is based on the need to reliably measure single-photon states. We have focused on optimizing the detection efficiency of visible light photon counters (VLPCs), a single-photon detection technology that is also capable of resolving photon number states. We report a record-breaking quantum efficiency of 91 +/- 3% observed with our detection system. Both sources and detectors are independently interesting physical systems worthy of study, but together they promise to enable entire new classes and applications of information based on quantum mechanics.
Although light quanta were known since the works by Planck and Einstein, for several decades after these works, there was no need to treat light quantum mechanically, and all experiments could be well explained using the quantum description of matter and classical description of light (the semiclassical approach). The situation changed with the development of sources of so-called nonclassical light, i.e., light whose properties cannot be understood in the framework of the semiclassical approach. Two simple examples can be given here. The first one is the suppression of shot noise in optical detectors. Shot noise, i.e., fluctuations of photocurrent scaling as the square root of the photocurrent mean value, can be, in principle, attributed to the discrete nature of the charge generated by the detector. At the same time, the effect of shot-noise suppression, which is observed with certain light sources (squeezed light) is clearly related to the statistics of light, and quantum mechanics is completely necessary for its description. Another example, which brings us closer to the subject of the present paper, is two-photon light. This type of light contains only pairs of photons (often called biphotons), and hence, a pair of properly aligned photon-counting detectors registering two-photon light, in an ideal case, will produce only simultaneous photocounts. This behavior, again, can only be explained in terms of a quantum-mechanical description for the light.
The statistical properties of photon sequences originating from single-molecule emitters differ from those produced by generic light sources. Let us start with the latter. A typical light source (such as a lightbulb) is composed of numerous independent lightemitting atoms or molecules. A sufficiently sensitive photodetector may be used to record the arrival time of each individual photon. The simplest assumption one could adopt to describe this kind of measurement is that the arrival times for different photons are completely uncorrelated (see, however, the discussion at the end of this section). If the properties of the light source (such as, e.g., its brightness) do not depend on time then we should expect that the probability of detecting a photon during an infinitesimal time interval dt is proportional to dt , with the proportionality constant being independent of time or the arrival times of other photons. Let us call this probability λdt , where λ is the probability of detecting a photon per unit time (which will be referred to as the photon count rate). To estimate λ we could measure the number of photons n detected over a certain period of time t and divide it by t : λ ≈ n/t. (7.1) But, since photon arrival times are random, the exact number of photons found during any finite time interval t will fluctuate around its mean value λt , as illustrated in Fig.7.1. A complete description of this process thus requires the probability wn(t) that a specified number of photons, n, is observed during the time interval t . To obtain this probability, it is helpful to think of the number of detected photons, n, as the “state” of the system at time t . At t = 0 we have n = 0. Each time a new photon is detected, the system undergoes a first-order irreversible “reaction” n → n + 1. The overall process thus can be described by the kinetic scheme: 0 λ→ 1 λ→ 2 λ→ 3 λ→ 4 → · · · . Accordingly, wn(t) is described by a system of differential equations of the form dwn(t)/dt = λwn−1(t) − λwn(t), n > 0 (7.2) and dw0(t)/dt = −λw0(t), (7.3) with the initial conditions wn(0) = 0, n > 0 and w0(0) = 1. The solution to Eq. 7.3 is w0(t) = e−λt . (7.4) Substituting this into the differential equation for w1 (Eq. 7.2) we can find the time dependence of w1(t), then substitute the result into the equation for w2(t) and so on. Suppose we have found wn−1(t) and now wish to solve for wn(t). It is convenient to use the ansatz wn(t) = ρn(t)e−λt .
Characterizing the input-output photon-number distribution of an unknown optical quantum channel is a worthwhile task for many applications in quantum information processing. Ideally, this would require deterministic photon-number sources and photon-number-resolving detectors, but these technologies are still work in progress. In this work, we propose a general method to rigorously bound the input-output photon-number distribution of an unknown optical channel using standard optical devices such as coherent light sources and non-photon-number-resolving detectors and homodyne detectors. To demonstrate the broad utility of our method, we consider the security analysis of practical quantum key distribution systems based on calibrated single-photon detectors and an experimental proposal to implement time-correlated single-photon counting technology using homodyne detectors instead of single-photon detectors.
Ultrafast quantum light pulses with durations of 1ps and below show great promise as information carriers in quantum communication and computation. In future they may also be used to probe physical processes at ultrashort timescales with a resolution beyond the limits of Heisenberg uncertainty. This thesis focuses on the creation and manipulation of quantum light pulses with second order nonlinear optical processes in optical waveguides. In chapter 1. Introduction, we lead the reader towards this work's topic by giving a brief qualitative overview over the EPR paradox, quantum entanglement, three-wave-mixing and quantum light pulses. Chapter 2. Basic concepts familiarizes the reader with the physical concepts and mathematical tools underlying this thesis. In chapter 3. Spectral engineering, we discuss the requirements to produce separable photon pair states with group velocity matching and examine several nonlinear materials widely used for optical waveguide inscription for their suitability to group velocity matching in the telecom wavelength regime. In chapter 4. A PP-KTP waveguide as parametric downconversion source, we give the basic spontaneous parametric downconversion source setup, as well as some initial measurements to characterize the single photon detectors, to demonstrate the production of correlated photons, and to determine the phasematching properties of the PP-KTP source. In the following chapter, 5. Fiber spectrometer, we present the single-photon fiber spectrometer. We discuss the experimental setup and calibration of the device, and measure the joint spectrum of photon pairs from our PP-KTP source. Finally, we investigate the behavior of a joint spectrum measurement of a high mean photon number source with binary detectors. In 6. Two-mode squeezed vacuum source, we characterize spectral correlations of an ultrafast SPDC source with the second order correlation function g². We present the g² measurement results and show that we can control the spectral correlations to produce a two-mode squeezed vacuum state of light. We then determine the mean photon number and gain of the source. 7. Quantum pulse gate: While the previous chapters focus on the creation and characterization of ultrafast quantum pulses of light, we now propose a way to manipulate the mode structure of a given quantum light state. We discuss the concept of an active optical filter sensitive to spectral/temporal pulse shape: The quantum pulse gate. In the final chapter 8. Conclusion and outlook, we recapitulate the main results of this thesis and provide a few pointers towards possibilities for future research building on it.