Advances in Quantum Nonlinear Optics: a nonclassical journey from the optimization of silicon photomultipliers for Quantum Optics to quantum second-harmonic generation
In this thesis, we present our experimental and theoretical work on modern and old topics of Nonlinear Quantum Optics. The thesis is structured as follows. \nIn the first chapter, we provide a general introduction about the basis of this field, in particular about the main concepts and results that will be needed in the following.\nIn the second and third chapters, we explain our research on the role of silicon photomultipliers in Quantum Optics experiments. After a specific characterization of the sensors, we used them to detect nonclassical states of light. Different strategies for the estimation of experimental quantities are suggested.\nIn the fourth chapter, we propose our quantum description for the second-harmonic-generation process, based on well-known perturbative methods. After a general introduction on the state of the art, we immediately dive into the problem by explaining the employed methods and showing our analytical results.\nFinally, we resume the essence of our achievements and draw our conclusions.
In this thesis, we present our experimental and theoretical work on modern and old topics of Nonlinear Quantum Optics. The thesis is structured as follows. \nIn the first chapter, we provide a general introduction about the basis of this field, in particular about the main concepts and results that will be needed in the following.\nIn the second and third chapters, we explain our research on the role of silicon photomultipliers in Quantum Optics experiments. After a specific characterization of the sensors, we used them to detect nonclassical states of light. Different strategies for the estimation of experimental quantities are suggested.\nIn the fourth chapter, we propose our quantum description for the second-harmonic-generation process, based on well-known perturbative methods. After a general introduction on the state of the art, we immediately dive into the problem by explaining the employed methods and showing our analytical results.\nFinally, we resume the essence of our achievements and draw our conclusions.
This thesis presents a study of photon generation and conversion processes in nonlinear optics. Our results extend beyond the first order perturbative regime, in which only pairs of photons are generated in spontaneous parametric down-conversion or four wave mixing. They also allow us to identify the limiting factors for achieving unit efficiency frequency conversion, and to correctly account for the propagation of bright nonclassical photon states generated in the nonlinear material. This is done using the Magnus expansion, which allows us to incorporate corrections due to time-ordering effects in the time evolution of the state, while also respecting the quantum statistics associated with squeezed states (in photon generation) and single photons or coherent states (in photon conversion). We show more generally that this expansion should be the preferred strategy when dealing with any type of time-dependent Hamiltonian that is a quadratic form in the creation and annihilation operators of the fields involved. Using the Magnus expansion, simple figures of merit to estimate the relevance of these time-ordering corrections are obtained. These quantities depend on the group velocities of the modes involved in the nonlinear process and provide a very simple physical picture of the interactions between the photons at different times. These time-ordering effects are shown to be important only when the photons and pump beam overlap within the nonlinear material for a significant amount of time. We also discuss the possibility of preparing Fock states with many photons using parametric down-conversion sources and realistic photon-number-resolving detectors. After discussing photon generation processes, we study photon conversion processes in which a nonlinear material and a classical strong pump field are used modify the frequency of a second incoming low-intensity field. We show that time-ordering effects limit the efficiency of this conversion process, re-examine strategies to get around this problem, and show that it should be possible to have a clear observation of modified upconversion probabilities due to these effects, and thus have an experimental demonstration of time-ordering effects in nonlinear optics.
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
Nonlinear phenomena in quantum optics are reviewed, with particular emphasis on scientific activities in quantum optics at the Natural Science Faculty of Palacký University ln Olomouc (Czech Republic). The first section is devoted to quantum and classical methods to obtain photon statistics in higher-harmonics generation, including a method of classical trajectories. It is followed by a discussion of photon bunching and antibunching of nonstationary fields. The chapter continues with a discussion of methods for reconstruction of quantum states. Other topics covered include the process of frequency downconversion with pulses, Zeno and anti-Zeno effects based on optical parametric processes, Raman nonlinear couplers as switching elements and sources of nonclassical light for optoelectronics and photonics, and quantum cryptography. Finally, quantum spatial propagation of a two-mode squeezed light in a cubically behaved quadratic medium is treated as another feature of a two-field squeezed steady-state light, and this approach is compared with the conventional one.
One of the main issues in the domain of quantum information and communication is the generation, manipulation and detection of several qubits on a single chip. Several approaches are currently investigated for the implementation of qubits on different types of physical supports and a variety of quantum information technologies are under development: for quantum memories, spectacular advances have been done on trapped atoms and ions, while to transmit information, photons are the ideal support thanks to their high speed of propagation and their almost immunity against decoherence. My thesis work has been focused on the conception, fabrication and characterization of a miniaturized semiconductor source of entangled photons, working at room temperature and telecom wavelengths. First the theoretical concepts relevant to understand the work are described (chapter 1). Then the conception and fabrication procedures are given (chapter 2). Chapter 3 presents the optoelectronics characterization of the device under electrical pumping, and chapter 4 the results on the optical losses measurements and the nonlinear optical characterization (second harmonic generation, spontaneous parametric down conversion and joint spectral intensity reconstruction). Chapters 5 and 6 focus on the characterization of the quantum state generated by a passive sample (demonstration of indistinguishability and energy-time entanglement) and its utilization in a multi- user quantum key distribution protocol (polarization entanglement). Finally the work on the first electrically driven photon pairs source emitting in the telecom range and working at room temperature is presented (chapter 7).
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.
Optical generation of high-order harmonics is a prototypical example of nonlinear light–matter interactions in the high-field regime. Quantum optical effects have recently been demonstrated to have a significant influence on this phenomenon. These findings underline the importance of understanding the dynamics of the quantized electromagnetic field during high-order harmonic generation. In the following, we discuss the challenges that are related to the theoretical description of this process and summarize the results that were obtained using the high-field, multimode generalization of well-known quantum optical models that are based on the concept of the two-level atom.