The creation of optical states of light that are quantum mechanical in nature in optical fibers is discussed and demonstrated experimentally. Specifically, two- photon states created by spontaneous four-wave-mixing in commercially available single-mode, birefringent fibers are studied. When creating photon states of light, it is important to verify the created states are of the proper photon number distribution and free of noise. We detail a method for combining thresholding, non-number resolving detectors to characterize the photon number distribution created via SFWM and a procedure to quantify the noise sources present in the process. Frequency translation in optical fibers with two-photon states is discussed and experimental considerations are presented.
The creation of optical states of light that are quantum mechanical in nature in optical fibers is discussed and demonstrated experimentally. Specifically, two- photon states created by spontaneous four-wave-mixing in commercially available single-mode, birefringent fibers are studied. When creating photon states of light, it is important to verify the created states are of the proper photon number distribution and free of noise. We detail a method for combining thresholding, non-number resolving detectors to characterize the photon number distribution created via SFWM and a procedure to quantify the noise sources present in the process. Frequency translation in optical fibers with two-photon states is discussed and experimental considerations are presented.
The field of quantum optics offers the intriguing possibility of developing new, potentially ground-breaking technologies based on the laws of quantum physics. Single quanta of light, called photons, are at the heart of many such quantum optical technologies. They can serve, for example, as information carriers in quantum cryptography and in quantum-information processing. If such applications are to fulfill their enormous potential, it is essential to have sources available that provide photons in the required quantum states. An established way of generating states of single photons is based on photon-pair sources. In this approach, the detection of one photon of a pair heralds the presence of the partner photon, which can then be further processed. However, to generate heralded photons in pure quantum states, specific conditions have to be met, making the design and implementation of such sources challenging. This thesis presents two new photon-pair sources that allow the heralded generation of single photons with high purity. Both sources are based on optical fiber, which allows high collection efficiencies for the generated states and opens the possibility of easy integration into modern-day fiber networks. Chapter 1 provides an introduction to quantum optical technologies and gives a short overview of current approaches to generate pure single photons. Chapter 2 presents the basic theory on which the experimental work presented in Chapters 3 and 4 is based. It explains the concept of a spectrally broad single photon and how photon purity can be tested using Hong-Ou-Mandel (HOM) interference. Subsequently, the properties of photon-pair states and the heralded generation of single photons from such states are discussed. It is shown that for a heralded photon to be pure, the original photon pair has to be in a factorable state, that is, free of any correlations. The introduced theory is then applied to spontaneous four-wave mixing (SFWM) in optical fibers, a nonlinear process that allows the generation of photon pairs. It is shown how the factorability of the created pairs depends on the fiber's dispersion properties, and the necessary conditions for the generation of factorable states are derived. The chapter concludes with an analysis of the photon statistics of the four-wave mixing process, explaining how statistics and the g(2) correlation function can be used to evaluate the factorability of the SFWM output state. Chapters 3 and 4 contain the main results of this thesis. Chapter 3 presents the first spectrally decorrelated photon-pair source bridging the visible and telecommunication wavelength ranges. The photon pairs are generated by SFWM in a photonic crystal fiber (PCF). The chapter documents the procedure of how the PCF source was designed and fabricated, as well as its characterization based on spectral measurements and photon statistics. One photon of the pair state is generated in the visible at 513.5 nm, where it can be efficiently detected with silicon-based single-photon detectors. It serves as a herald for its broadband partner photon, which is emitted in the telecom wavelength range at 1547 nm. A spectral coincidence measurement shows that the heralded photon exhibits a purity of up to 0.82. At increased pump powers, even the heralded generation of higher photon-number states in the telecom band becomes feasible. In Chapter 4, we use commercial birefringent fiber to herald high-purity photons of picosecond duration at 848 nm. The presented two-source HOM interference experiment shows that the heralded unfiltered state has a purity of at least 0.73. This value is increased to 0.84 with the application of wavelength filters suppressing low-intensity side peaks in the spectrum. The heralded photons are coupled into a single-mode fiber with an efficiency of 85%, the highest reported value to date for factorable sources. It is also shown that a commercial polarization controller can be used to fine-tune the generated wavelengths. This facilitates matching photons from multiple sources, as required for optical quantum computing schemes. Chapter 5 summarizes all results and provides an outlook toward potential future projects.
We study both experimentally and theoretically the generation of photon pairs by spontaneous four-wave mixing (SFWM) in standard birefringent optical fibers. The ability to produce a range of two-photon spectral states, from highly correlated (entangled) to completely factorable, by means of cross-polarized birefringent phase matching, is explored. A simple model is developed to predict the spectral state of the photon pair which shows how this can be adjusted by choosing the appropriate pump bandwidth, fiber length and birefringence. Spontaneous Raman scattering is modeled to determine the tradeoff between SFWM and background Raman noise, and the predicted results are shown to agree with experimental data.
The purpose of this tutorial paper is to present a broad overview of photon-pair generation through the spontaneous four wave mixing (SFWM) process in optical fibers. Progress in optical fiber technology means that today we have at our disposal a wide variety of types of fiber, which, together with the fact that SFWM uses two pump fields, implies a truly remarkable versatility in the resulting possible photon-pair properties. We discuss how the interplay of frequency, transverse mode, and polarization degrees of freedom—the first linked to the latter two through fiber dispersion—leads to interesting entanglement properties both in individual degrees of freedom and also permitting hybrid and hyper entanglement in combinations of degrees of freedom. This tutorial covers methods for photon-pair factorability, frequency tunability, and SFWM bandwidth control, the effect of frequency non-degenerate and counterpropagating pumps, as well as methods for characterizing photon pairs generated in optical fibers.
We present a theoretical and experimental study of the generation of photon pairs through the process of spontaneous four-wave mixing (SFWM) in a few-mode, birefringent fiber. Under these conditions, multiple SFWM processes are in fact possible, each associated with a different combination of transverse modes for the four waves involved. We show that in the weakly guiding regime, for which the propagation modes may be well approximated by linearly polarized modes, the departure from circular symmetry due to the fiber birefringence translates into conservation rules, which retain elements from azimuthal and rectangular symmetries: both OAM and parity must be conserved for a process to be viable. We have implemented a SFWM source based on a bowtie birefringent fiber, and have measured for a collection of pump wavelengths the SFWM spectra of each of the signal and idler photons in coincidence with its partner photon. We have used this information, together with knowledge of the transverse modes into which the signal and idler photons are emitted, as input for a genetic algorithm, which accomplishes two tasks: (i) the identification of the particular SFWM processes that are present in the source, and (ii) the characterization of the fiber used.
We explore the frequency translation of single-photon states of light and the creation of photon pairs by four-wave mixing in optical fiber. Frequency translation refers to changing the central frequency of a field, while photon pair creation refers to the creation of two individual photons at the same time. We demonstrate these effects in third-order nonlinear optical fiber. While both phenomena have previously been shown by three-wave mixing in second-order nonlinear media, there are compelling reasons to develop these tasks in third-order media. Most importantly, frequency translation in third-order material allows for the practical implementation of both small and large frequency shifts, while second-order material only practically allows for large shifts. Photon creation in third-order media often permits more flexible phase-matching conditions, allowing for the creation of a wider variety of quantum states than is often possible in second-order media. In our theoretical study of photon pair creation, we focus on the spectral correlations of the photon pairs. We pay particular attention to the creation of quantum states of high purity, where the photons are not spectrally correlated with one another. High purity photons are a requisite resource for several different quantum information processing applications, such as linear-optical quantum computing. We find that states with high purity can be realized with a minimal amount of spectral filtering. Experimentally, we study photon frequency translation in photonic crystal fiber. The central wavelength of the input photons was translated from 683 nm to 659 nm. We perform second-order intensity correlation measurements on both channels to demonstrate their quantum nature. This resulted in values of 0.21 ± 0.02 and 0.19 ± 0.05 for the 683-nm and 659-nm channels, respectively, demonstrating that those fields were dominated by their single-photon component. The efficiency at which the process occurred was 29 percent. Theoretically, we develop a Green function formalism to describe the translation process and develop a computational model to calculate the solution to the governing equations. Also, in a related experiment, we demonstrate classical frequency translation from 851 nm to 641 nm, a record translation in both wavelength and frequency, at an efficiency of 0.2 percent in a birefringent fiber.
In quantum optics experiments, heralding, a form of conditional state preparation, is a useful tool for creating photon-number states from nonlinear optical sources for quantum-information science experiments. Heralding occurs when one photon from a correlated pair is detected to herald the presence of the other photon, labeled the signal photon. However, as heralding is extended to two or more photon pairs, the presence of noise photons in the herald channel quickly degrades the photon statistics of the signal photons. We create two-photon number states from a non-degenerate, third-order nonlinear optical fiber source with double heralding and present a method for verifying these photon-number states. The consequences of noisy heralding on the statistics of states created via third-order nonlinear processes are analyzed. We present a method for estimating the effects of noise photons on the signal photon statistics. Additionally, we prove the equivalence between noise in the herald channel and a loss in the signal channel. We utilize this equivalence to infer the photon statistics of the photon-number states in the signal channel that would be present in the absence of noise in the herald channel. By measuring the statistics of the signal channels with noise in the herald channel and comparing to the inferred, noise-free distribution, we can estimate the potential benefits of additional noise-reducing procedures on the experiment.