We investigate properties of quantum mechanical systems in the light of quantum information theory. We put an emphasize on systems with infinite-dimensional Hilbert spaces, so-called continuous-variable systems'', which are needed to describe quantum optics beyond the single photon regime and other Bosonic quantum systems. We present methods to obtain a description of such systems from a series of measurements in an efficient manner and demonstrate the performance in realistic situations by means of numerical simulations. We consider both unconditional quantum state tomography, which is applicable to arbitrary systems, and tomography of matrix product states. The latter allows for the tomography of many-body systems because the necessary number of measurements scales merely polynomially with the particle number, compared to an exponential scaling in the generic case. We also present a method to realize such a tomography scheme for a system of ultra-cold atoms in optical lattices. Furthermore, we discuss in detail the possibilities and limitations of using continuous-variable systems for measurement-based quantum computing. We will see that the distinction between Gaussian and non-Gaussian quantum states and measurements plays an crucial role. We also provide an algorithm to solve the large and interesting class of naturally occurring Hamiltonians, namely frustration free ones, efficiently and use this insight to obtain a simple approximation method for slightly frustrated systems. To achieve this goals, we make use of, among various other techniques, the well developed theory of matrix product states, tensor networks, semi-definite programming, and matrix analysis. / Die stürmische Entwicklung der Quanteninformationstheorie in den letzten Jahren brachte einen neuen Blickwinkel auf quantenmechanische Probleme. Insbesondere die fundamentale Eigenschaft der Verschränkung von Quantenzuständen spielt hierbei eine Schlüsselrolle. Einstein, Podolsky und Rosen haben 1935 versucht die Unvollständigkeit der Quantenmechanik zu demonstrieren, indem sie zeigten, dass sie keine lokale, realistische Therie ist und der Ausgang einer Messung an einem Ort von Messungen abhängen kann, die an beliebig weit entfernten Orten gemacht wurden. John Bell stellte 1964 eine, später nach ihm benannte, Ungleichung auf, die eine Grenze an mögliche Korrelationen von Messergebnissen in lokalen, realistischen Theorien gibt. Die Vorhersagen der Quatenmechanik verletzen diese Ungleichung, eine Tatsache, die 1981 von Alain Aspect und anderen auch experimentell bestätigt wurde. Solche nicht-lokalen Quantenzustände werden verschränkt'' genannt. In neuerer Zeit wurde Verschränkung nicht mehr nur als mysteriöse Eigenschaft der Quantenmechanik sondern auch als Resource für Aufgaben der Informationsverarbeitung gesehen. Ein Computer, der sich diese Eigenschaften der Quantenmechanik zu nutze macht, ein sogenannter Quantencomputer, würde es erlauben gewisse Aufgaben schnell zu lösen für die normale'' Computer zu lange brauchen. Das wichtigste Beispiel hierfür ist die Zerlegung von großen Zahlen in ihre Primfaktoren, für die Shor 1993 einen Quantenalgorithmus präsentierte. In dieser Arbeit haben wir uns mit den Eigenschaften von Quantensystemen, die durch sogenannte kontinuierliche Variablen beschrieben werden, beschäftigt. Diese sind nicht nur theoretisch sonder auch experimentell von besonderem Interesse, da sie quantenoptische Systeme beschreiben, die sich verhältnismäßig leicht im Labor präparieren, manipulieren und messen lassen. Wenn man eine vollständige Beschreibung eines Quantenzustandes erhalten will, braucht man, auf Grund der Heisenberg'schen Unschärferelation, mehrere Kopien von ihm an denen man dann Messungen durchführt. Wir haben eine Methode, compressed-sensing genannt, eingeführt um die Anzahl der nötigen Messungen substantiell zu reduzieren. Wir haben die theoretische Effizienz dieser Methode bewiesen und durch numerische Simulationen auch ihre Praktikabilität demonstriert. Desweiteren haben wir beschrieben, wie man compressed-sensing für die schon erwähnten optischen Systemen sowie für ultrakalte Atome experimentell realisieren kann. Ein zweites Hauptthema dieser Arbeit war messbasiertes Quantenrechnen. Das Standardmodell des Quantenrechnens basiert auf sogenannten Gattern, die eine genaue Kontrolle der Wechselwirkung zwischen den Bestandteilen des Quantencomputers erfordern. Messbasiertes Quantenrechnen hingegen kommt mit der Präparation eines geeigneten Quantenzustands, Resource genannt, gefolgt von einfachen Messungen auf diesem Zustand aus. Wir haben gezeigt, dass Systeme mit kontinuierlichen Variablen eine vorteilhafte Realisierung eines Quantencomputers in diesem Paradigma erlauben, es jedoch auch wichtige Beschränkungen gibt, die kompliziertere Zustandspräparationen und Messungen nötig machen.

Ultracold neutral atoms confined in optical dipole traps have important applications in quantum computation and information processing, quantum simulators of interacting-many-body systems and atomic frequency metrology. While optical dipole traps are powerful tools for cold atom experiments, the energy level structures of the trapped atoms are shifted by the trapping field, and it is important to characterize these shifts in order to accurately manipulate and control the quantum state of the system. In order to measure the light shifts, we have designed a system that allows us to reliably trap individual 87Rb atoms. A non-destructive detection technique is employed so that the trapped atoms can be continuously observed for over 100 seconds. Single atom spectroscopy, trap frequency measurements, and temperature measurements are performed on single atoms in a single focus trap and small number of atoms in a 1D optical lattice in order to characterize the trapping environment, the perturbed energy level structures, and the probe-induced heating. In the second part of the thesis, we demonstrate deterministic delivery of an array of individual atoms to an optical cavity and selective addressability of individual atoms in a 1D optical conveyor, which serves as a potential candidate for scalable quantum information processing. The experiment is extended to a dual lattice system coupled to a single cavity with the capability of independent lattice control and addressability. The mutual interactions of atoms in different lattices mediated by a common cavity field are demonstrated. A semi-classical model in the many-atom regime based on the Jaynes-Cummings model is developed to describe the system that is in good qualitative agreement with the data. This work provides a foundation for developing multi-qubit quantum information experiments with a dual lattice cavity system.

This thesis describes the design, development, and implementation of a pulsed source of polarization-entangled photons using spontaneous parametric down-conversion in a Sagnac interferometer. A tangle of 0.9286 ± 0.0015, fidelity to the state (|10〉 + |01〉)/√2 of 0.9798 ± 0.0004 and a brightness of 597 pairs/s/mW were demonstrated. Spontaneous parametric down-conversion is a nonlinear optical process in which one photon is split into two lower-frequency photons while conserving momentum and energy, in this experiment nearly degenerate photons are produced. These photons are then interfered at the output beamsplitter of the interferometer, exchanging path entanglement for polarization entanglement and generating the desired polarization-entangled photon pairs.

This thesis describes the design, development, and implementation of a pulsed source of polarization-entangled photons using spontaneous parametric down-conversion in a Sagnac interferometer. A tangle of 0.9286 ± 0.0015, fidelity to the state (|10〉 + |01〉)/√2 of 0.9798 ± 0.0004 and a brightness of 597 pairs/s/mW were demonstrated. Spontaneous parametric down-conversion is a nonlinear optical process in which one photon is split into two lower-frequency photons while conserving momentum and energy, in this experiment nearly degenerate photons are produced. These photons are then interfered at the output beamsplitter of the interferometer, exchanging path entanglement for polarization entanglement and generating the desired polarization-entangled photon pairs.

NV centers in a diamond are proving themselves to be good building blocks for quantum information, electron spin resonance (ESR) imaging, and sensor applications. The key feature of the NV is that it has an electron spin that can be polarized and read out at room temperature. The readout is optical, thus the magnetic field imaging can also be done easily. Magnetic field variation with feature sizes below 0.3 microns cannot be directly resolved, and so in this region magnetic resonance imaging must be employed. To realize the full sensitivity of NV diamond, the spin transition linewidth must be as narrow as possible. Additionally, in the case of NV ensembles for micron-sized magnetometers, there must be a high concentration of NV. To this end three techniques are explored: (1) Electron paramagnetic resonance (EPR) imaging with microwave field gradients, (2) Magic angle rotation of magnetic field, and (3) TEM irradiation to optimize the yield of NV in a diamond. For the EPR imaging demonstration a resonant microwave field gradient is used in place of the usual DC magnetic gradient to obtain enough spatial resolution to resolve two very close "double NV" centers in a type Ib bulk diamond. Microfabrication technology enabled the micron-size wire structure to sit directly on the surface of millimeter-scale diamond plate. In contrast to conventional magnetic resonance imaging pulsed ESR was used to measure the Rabi oscillations. From the beating of Rabi oscillations from a "double NV," the pair was resolved using the one-dimension EPR imaging (EPRI) and the spatial distance was obtained. To achieve high sensitivity in nitrogen-doped diamond, the dipole-dipole coupling between the electron spin of the NV center and the substitutional nitrogen (14N) electron must be suppressed because it causes linewidth broadening. Magic angle spinning is an accepted technique to push T2 and T2 * down toward the T1 limit. An experiment was performed using the HPHT diamond with a high concentration of nitrogen, and a rotating field was applied with a microfabricated wire structure to reduce line broadening. In this experiment, ~50% suppression of the linewidth was observed and the effective time constant T2* improved from 114 ns to 227 ns. To achieve the highest possible sensitivity for micro-scale magnetic sensors the concentration of NV should be large. Since the unconverted N are magnetic impurities they shorten T2 and T2*, giving a tradeoff between NV (and therefore N) concentration and sensitivity. To construct a damage monitor, a type Ib HPHT sample was irradiated with electrons from a transmission electron microscope (TEM) and the effects on the ESR transition were seen well before physical damage appeared on the diamond and thus this proved to be a sensitive metric for irradiation damage.

Optical imaging of soft biological tissue is highly desirable since it is nonionizing and provides sensitive contrast information which enables the detection of physiological functions and abnormalities, including potentially early cancer detection. However, due to the diffusive nature of light in soft biological tissue, it is difficult to achieve simultaneously good spatial resolution and good imaging depth with pure optical imaging modalities. This work focuses on the ultrasound-modulated optical tomography (UOT): a hybrid technique which combines the advantages of ultrasonic resolution and optical contrast. In this technique, focused ultrasound and optical radiation of high temporal coherence are simultaneously applied to soft biological tissue. The intensity of the sideband, or ultrasound ‗tagged‘ photons depends on the optical absorption in the region of interest where the ultrasound is focused. Demodulation of the optical speckle pattern yields the intensity of tagged photons for each location of the ultrasonic focal spot. Thus UOT yields an image with spatial resolution of the focused ultrasound — typically submillimeter — whose contrast is related to local optical absorption and the diffusive properties of light in the organ. Thus it extends all the advantages of optical imaging deep into highly scattering tissue. However lack of efficient tagged light detection techniques has so far prevented ultrasound-modulated optical tomography from achieving maturity. The signal-to-noise ratio (SNR) and imaging speed are two of the most important figures of merit and need further improvement for UOT to become widely applicable. In the first part of this work, nonlinear optics detection methods have been implemented to demodulate the ―tagged‖ photons. The most common of these is photorefractive (PR) two wave mixing (TWM) interferometry, which is a time-domain filtering technique. When used for UOT, it is found that this approach extracts not only optical properties but also mechanical properties for the area of interest. To improve on TWM, PR four wave mixing (FWM) experiments were performed to read out only the modulated light and at the same time strongly suppressing the ‗untagged‘ light. Spectral-hole burning (SHB) in a rare-earth-ion-doped crystal has been developed for UOT more recently. Experiments in Tm3 :Y3Al5O12 (Tm:YAG) show the outstanding features of SHB: large angle acceptance (etendue), light speckle processing in parallel (insensitive to the diffusive light nature) and real-time signal collection (immune to light speckle decorrelation). With the help of advanced laser stabilization techniques, two orders of magnitude improvement of SNR have been achieved in a persistent SHB material (Pr^3 :Y2SiO5) compared to Tm:YAG. Also slow light with PSHB further reduces noise in Pr:YSO UOT that is caused by polarization leakage by performing time-domain filtering.

Although mathematical cryptography has been widely used, its security has only been proven under certain assumptions such as the computational power of opponents. As an alternative, quantum communication, in particular quantum key distribution (QKD) can get around unproven assumptions and achieve unconditional security. However, the key generation rate of practical QKD systems is limited by device imperfections, excess noise from the quantum channel, limited rate of true random-number generation, quantum entanglement preparation, and/or post-processing efficiency. This dissertation contributes to improving the performance of quantum communication systems. First, it proposes a new continuous-variable QKD (CVQKD) protocol that loosens the efficiency requirement on post-processing, a bottleneck for long-distance CVQKD systems. It also demonstrates an experimental implementation of the proposed protocol. To achieve high rates, the CVQKD experiment uses a continuous-wave local oscillator (CWLO). The excess noise caused by guided acoustic-wave Brillioun scattering (GAWBS) is avoided by a frequency-shift scheme, resulting in a 32 dB noise reduction. The statistical distribution of the GAWBS noise is characterized by quantum tomography. Measurements show Gaussian statistics upto 55 dB of dynamical range, which validates the security calculations in the proposed CVQKD protocol. True random numbers are required in quantum and classical cryptography. A second contribution of this thesis is that it experimentally demonstrates an ultrafast quantum random-number generator (QRNG) based on amplified spontaneous emission (ASE). Random numbers are produced by a multi-mode photon counting measurement on ASE light. The performance of the QRNG is analyzed with quantum information theory and verified with NIST standard random-number test. The QRNG experiment demonstrates a random-number generation rate at 20 Gbits/s. Theoretical studies show fundamental limits for such QRNGs. Quantum entanglement produced in nonlinear optical processes can help to increase quantum communication distance. A third contribution is the research on nonlinear optics of graphene, a novel 2D material with unconventional physical properties. Based on a quantum-dynamical model, optical responses of graphene are derived, showing for the first time a link between the complex linear optical conductivity and the quantum decoherence. Nonlinear optical responses, in particular four-wave mixing, is studied for the first time. The theory predicts saturation effects in graphene and relates the saturation threshold to the ultrafast quantum decoherence and carrier relaxation in graphene. For the experimental part, four-wave mixing in graphene is demonstrated. Twin-photon production in graphene is under investigation.

Recently, developments in novel and high-purity materials allow for the presence of a single, solitary crystalline defect to define the electronic, magnetic, and optical functionality of a device. The discrete nature of the active dopant, whose properties are defined by a quantum mechanical description of its structure, enables radically new quantum investigations and applications in these arenas. Finally,there has been significant development in large-scale device engineering due to mature semiconductor manufacturing techniques. The diverse set of photonic device architectures offering light confinement, guiding, and extraction is a prime example. These three paradigms – solitary dopant photonics and optoelectronics (solotronics), quantum science and technology, and device engineering – merge in the development of novel quantum photonic devices for the next generation of information processing systems. We present in this thesis a series of investigations of optical nanostructures for single optically active spins in single crystal diamond. Chapter 1 introduces the Nitrogen-Vacancy (NV) color center, summarizes its applications, and motivates the need for their integration into photonic structures. Chapter 2 describes two prototype nanobeam photonic crystal cavities for generating strong light-matter interactions with NV centers. The first device consists of a silicon nitride photonic crystal nanobeam cavity with high quality factor \(Q \sim 10^5\) and small mode volume \(V \sim 0.5*(\lambda/n)^3\). The second device consists of a monolithic diamond nanobeam cavity fabricated with the focused ion beam (FIB) directly in a single crystal diamond sample. Chapter 3 presents a high-efficiency source of single photons consisting of a single NV center in a photonic diamond nanowire. Early FIB prototypes are described, as is the first successful realization of the device achieved via reactive ion etching nanowires in a single crystal diamond containing NV centers, and finally a variation of this approach based on incorporation of NV centers in pure diamond via ion implantation. In chapter 4 we consider the optimal design of photonic devices offering both collection efficiency and cavity-enhancements and extend the model of the NV center to include photonic effects. In chapter 5 we briefly introduce a novel optically active spin discovered in a diamond nanowire. Finally, in chapter 6 we conclude with several proposals to extend this research program. / Engineering and Applied Sciences

Metallic nanostructures that employ localized surface plasmon resonances to capture or radiate electromagnetic waves at optical frequencies are termed "plasmonic optical antennas". These structures enhance light-matter interactions in an efficient manner, enabling unique linear and nonlinear optical applications. One such application is surface-enhanced Raman scattering (SERS), which employs plasmonic antennas to enhance Raman cross-section of molecules by orders of magnitude. SERS has attracted a significant amount of research attention since it enables molecules to be identified through their characteristic vibrational spectra, even at the single molecule level. / Engineering and Applied Sciences

I present a series of experimental and theoretical advances in the field of quantum state estimation. Techniques for measuring the quantum state of light that were originally developed for distinguishable photons fail when the particles are indistinguishable. I develop new methods for handling indistinguishability in quantum state estimation. The technique I present provides the first complete description of states of experimentally indistinguishable photons. It allows me to derive the number of parameters needed to describe an arbitrary state and to quantify distinguishability. I demonstrate its use by applying it to the measurement of the quantum polarization state of two and three-photon systems. State characterization is optimal when no redundant information is collected about the state of the system. I present the results of the first optimal characterization of the polarization state of a two-photon system. I show an improved estimation power over the previous state of the art. I also show how the optimal measurements lead to a new description of the quantum state in terms of a discrete Wigner function. It is often desirable to describe the quantum state of a system in terms of properties that are not themselves quantum-mechanical observables. This usually requires a full characterization of the state followed by a calculation of the properties from the parameters characterizing the state. I apply a technique that allows such properties to be determined directly, without a full characterization of the state. This allows one such property, the purity, to be determined in a single measurement, regardless of the size of the system, while the conventional method of determining purity requires a number of measurements that scales exponentially with the system size.