Abstract We consider pulsed-pump spontaneous parametric downconversion (SPDC) as well as pulsed single- and dual-pump spontaneous four-wave mixing processes in waveguides within a unified Hamiltonian theoretical framework. Working with linear operator equations in k -space, our approach allows inclusion of linear losses, self- and cross-phase modulation, and dispersion to any order. We describe state evolution in terms of second-order moments, for which we develop explicit expressions. We use our approach to calculate the joint spectral amplitude of degenerate squeezing using SPDC analytically in the perturbative limit, benchmark our theory against well-known results in the limit of negligible group velocity dispersion, and study the suitability of recently proposed sources for quantum sampling experiments.
Abstract We consider pulsed-pump spontaneous parametric downconversion (SPDC) as well as pulsed single- and dual-pump spontaneous four-wave mixing processes in waveguides within a unified Hamiltonian theoretical framework. Working with linear operator equations in k -space, our approach allows inclusion of linear losses, self- and cross-phase modulation, and dispersion to any order. We describe state evolution in terms of second-order moments, for which we develop explicit expressions. We use our approach to calculate the joint spectral amplitude of degenerate squeezing using SPDC analytically in the perturbative limit, benchmark our theory against well-known results in the limit of negligible group velocity dispersion, and study the suitability of recently proposed sources for quantum sampling experiments.
We provide an efficient method for the calculation of high-gain, twin-beam generation in waveguides derived from a canonical treatment of Maxwell's equations. Equations of motion are derived that naturally accommodate photon generation via spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing and, also, include the effects both of self-phase modulation of the pump and of cross-phase modulation of the twin beams by the pump. The equations we solve involve fields that evolve in space and are labeled by a frequency. We provide a proof that these fields satisfy bona fide commutation relations and that in the distant past and future they reduce to standard time-evolving Heisenberg operators. Having solved for the input-output relations of these Heisenberg operators we also show how to construct the ket describing the quantum state of the twin beams. Finally, we consider the example of high-gain SPDC in a waveguide with a flat nonlinearity profile, for which our approach provides an explicit solution that requires only a single matrix exponentiation.
In this thesis we study three aspects of squeezed light. First, we investigate the generation of pulsed, near‑pure, degenerate, single‑temporal‑mode squeezed light produced by dual‑pump spontaneous four wave mixing in integrated silicon‑nitride coupled‑ring resonators. We show that parasitic spontaneous four wave mixing processes inherent to the dual‑pump configuration can substantially degrade the amount of generated squeezing and state purity. To mitigate these effects we explore pump detuning, engineered dispersion, and an auxiliary‑ring structure as suppression strategies. We then optimize the incident pump amplitude and phase, demonstrating that longer pump pulses can yield highly squeezed, temporally separable states and that an appropriate pre‑chirp tracks the effects of self‑ and cross‑phase modulation, increasing intracavity pump amplitudes and the amount of generated squeezing. Next, we analyze the spectral–temporal structure and photon statistics of strongly correlated squeezed light. We develop a general formalism based on the Whittaker–Shannon interpolation of the joint‑temporal amplitude that is particularly useful in the long‑pulse and continuous‑wave limits, where the instantaneous photon density is low but the total photon number may be large. This packet‑based description provides a local, physically transparent account of the state and its photon statistics that complements the Schmidt decomposition, and extends to nonclassical states for which a Schmidt decomposition is not available. Finally, we examine whether or not squeezed illumination can enhance two‑photon excitation relative to classical light, and whether any enhancement is experimentally detectable. We construct a model including radiative and nonradiative broadening to compute scattered and absorbed energy, and apply it to fluorescence from cesium atoms in a magneto‑optical trap driven by classical and squeezed light in both continuous‑wave and pulsed regimes. Under ideal conditions squeezed light can produce a measurable enhancement in both limits, but the gains are moderate and smaller than some recent molecular reports; additional broadening or loss would further reduce detectability.
Squeezed light is expected to enable new quantum metrology and quantum computation applications, but the very high degree of experimental control required in practice places severe demands on the physical devices used to generate it. As ultrafast squeezed light sources are reaching an unprecedented degree of brightness and modal control, there is a strong interest in developing methods for their experimental characterization and theoretical understanding. In this thesis, we demonstrate both a new application and a new characterization technique for pulsed squeezed light. In the first part of the thesis, we present a new metrological application of pulsed squeezed light: quantum-enhanced label-free nonlinear microscopy. Stimulated emission microscopy (SEM) is a state-of-the-art pump-probe microscopy technique whose sensitivity is ultimately limited by shot noise in the probe beam. We propose to overcome this fundamental limitation by using a sub-Poissonian probe generated via optical parametric amplification. We demonstrate an intensity-squeezed sub-picosecond pulsed probe, and a simple stimulated emission microscope. Using this squeezed probe, sub-Poissonian statistics are observed in the SEM signal. After this proof-of-principle experiment, we aim to provide an improved design for a source of intensity-squeezed light. First, we develop a theoretical framework to simulate the photon statistics of a general sub-Poissonian source, considering pulsed and focused pump and seed fields in a unified spatio-temporal description. Next, we use this framework to suggest possible improvements to our previous squeezed probe. In the second part of this thesis, we provide new theoretical and experimental tools to analyze the high gain regime of pulsed spontaneous parametric down-conversion (SPDC). We study a waveguided source capable of generating twin-beams with tens of photons in a single spatio-temporal mode. We develop a framework to efficiently simulate SPDC for an arbitrary nonlinear gain, including the effect of parasitic nonlinearities such as self-phase modulation (SPM) of the pump and cross-phase modulation (XPM) between pump and twin-beams. We experimentally characterize our source using a new technique based on stimulated difference-frequency generation (DFG). In a type-II down-conversion process, we measure the frequency generation produced not only in the orthogonal polarization to the seeding beam, but also in its same polarization, which we interpret as cascaded difference-frequency generation. We argue that the additional information obtained in this measurement allows for a self-referenced estimation of the squeezing gain. Using these measurements, we accurately fit our theoretical model, revealing that, in the high gain regime, parasitic nonlinearities strongly affect the spectral structure of the twin-beams. We propose a simple strategy to reduce the impact of these nonlinearities on the modal structure of SPDC.
We derive frequency correlation and exit probability expressions for photons generated via spontaneous parametric downconversion (SPDC) in nonlinear waveguides that exhibit linear scattering loss.Such loss is included within a general Hamiltonian formalism by connecting waveguide modes to reservoir modes with a phenomenological coupling Hamiltonian, the parameters of which are later related to the usual loss coefficients.In the limit of a low probability of SPDC pair production, the presence of loss requires that we write the usual lossless generated pair state as a reduced density operator, and we find that this density operator is naturally composed of two photon, one photon, and zero photon contributions.The biphoton probability density, or joint spectral intensity (JSI), associated with the two-photon contribution is determined not only by a phase matching term, but also by a loss matching term.The relative sizes of the loss coefficients within this term lead to three qualitatively different regimes of SPDC JSIs.If either the pump or generated photon loss is much higher than the other, the side lobes of the phase matching squared sinc function are washed out.On the other hand, if pump and generated photon loss are appropriately balanced, the lossy JSI is identical to the lossless JSI.Finally, if the generated photon loss is frequency dependent, the shape of the JSI can be altered more severely, potentially leading to generated photons that are less frequency correlated though also produced less efficiently when compared to photons generated in low-loss waveguides.
In this paper, we theoretically study the spectral and temporal properties of pulsed spontaneous parametric down-conversion (SPDC) generated in lossy waveguides. Our theoretical approach is based on the formalism of Gaussian states and the Langevin equation, which is elaborated for weak parametric down-conversion and photon-number-unresolved click detection. Using the example of frequency-degenerate type-II SPDC generated under the pump-idler group-velocity-matching condition, we show how the joint-spectral intensity, mode structure, normalized second-order correlation function, and Hong-Ou-Mandel interference pattern depend on internal losses of the SPDC process. We found that the joint-spectral intensity is almost insensitive to internal losses, while the second-order correlation function shows a strong dependence on them, being different for the signal and idler beams in the presence of internal losses. Based on the sensitivity of the normalized second-order correlation function, we show how its measurement can be used to experimentally determine internal losses.
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.