This thesis describes a linear-optical device for performing generalized quantum measurements on quantum bits (qubits) encoded in photon polarization, the implementation of said device, and its use in two diff erent but related experiments. The device works by coupling the polarization degree of freedom of a single photon to a `mode' or `path' degree of freedom, and performing a projective measurement in this enlarged state space in order to implement a tunable four-outcome positive operator-valued measure (POVM) on the initial quantum bit. In both experiments, this POVM is performed on one photon from a two-photon entangled state created through spontaneous parametric down-conversion. In the fi rst experiment, this entangled state is viewed as a two-qubit photonic cluster state, and the POVM as a means of increasing the computational power of a given resource state in the cluster-state model of quantum computing. This model traditionally achieves deterministic outputs to quantum computations via successive projective measurements, along with classical feedforward to choose measurement bases, on qubits in a highly entangled resource called a cluster state; we show that `virtual qubits' can be appended to a given cluster by replacing some projective measurements with POVMs. Our experimental demonstration fully realizes an arbitrary three-qubit cluster computation by implementing the POVM, as well as fast active feed-forward, on our two-qubit photonic cluster state. Over 206 diff erent computations, the average output delity is 0.9832 +/- 0.0002; furthermore the error contribution from our POVM device and feedforward is only of order 10^-3, less than some recent thresholds for fault-tolerant cluster computing. In the second experiment, the POVM device is used to implement a deterministic protocol for remote state preparation (RSP) of arbitrary photon polarization qubits. RSP is the act of preparing a quantum state at a remote location without actually transmitting the state itself. We are able to remotely prepare 178 diff erent pure and mixed qubit states with an average delity of 0.995. Furthermore, we study the the fidelity achievable by RSP protocols permitting only classical communication, without shared entanglement, and compare the resulting benchmarks for average fidelity against our experimental results. Our experimentally-achieved average fi delities surpass the classical thresholds whenever classical communication alone does not trivially allow for perfect RSP.

Quantum key-distribution (QKD) is a scheme for establishing shared secret key between remote parties. In such a scheme, quantum preparation and measurement devices (sources and detectors) are used. In existing theoretical treatments of QKD, the device models used do not capture all the imperfections which might occur in realistic devices. This creates a gap between the practical implementations and theoretical descriptions of QKD. In the present work, we contribute in bridging this gap by three methods: 1) Advancing the study of squashing models of measurement devices, 2) Devising an alternative to squashing models using statistical estimation in optical QKD, and 3) Modifying the security proof formalism of QKD to account for imperfect devices.

In this thesis, we develop a number of operational tests and tools for benchmarking the quantum nature of optical quantum communication devices. Using the laws of quantum physics, ideal quantum devices can fundamentally outperform their classical counterparts, or even achieve objectives which are classically impossible. Actual devices will not be ideal, but they may still be capable of facilitating quantum communication. Benchmarking tests, based on the presence of entanglement, can be used to verify whether or not imperfect quantum devices offer any advantage over their classical analogs. The general goal in this thesis is to provide strong benchmarking tools which simultaneously require minimal experimental resources but also offer a wide range of applicability. Another major component is the extension of existing qualitative benchmarks (`Is it quantum or classical?') to more quantitative forms (`How quantum is it?'). We provide a number of benchmarking results applicable to two main situations, namely discrete remote state preparation protocols and continuous-variable quantum device testing. The theoretical tools derived throughout this thesis are also applied to the tasks of certifying a remote state preparation experiment and a continuous-variable quantum memory.

In the present quantum optics and laser physics study, the non-linear interaction of electromagnetic fields with atomic, molecular and biomolecular media is analyzed. Particular emphasis is given to coherent phenomena, while propagation and dispersion effects are also extensively investigated. The fields involved vary from ultra short pulses to continuous waves; while their energies range from the very strong that are addressed classically, to the very weak which are described quantum mechanically. Applications and problems addressed span a wide range. A scheme for a real time detector of chemical and biological hazards, like anthrax spores, is presented; in it, a strong spectroscopic signature is obtained from complex molecules by using ultrashort, femtosecond, laser pulses and inducing vibrational coherence on them. Furthermore, a way of reversing the phase matching condition in coherent spectroscopy, based on dispersion, is developed; which allows for the use of such spectroscopic methods in remote detection. More fundamental questions addressed include a resolution of the centennial old paradox of Maxwell's demon via quantum thermodynamics, and the role of atomic coherence in enhancing the efficiency of a heat engine as well as in obtaining lasing without population inversion. Additionally, a quantum storage scheme is presented, in which the information contained in an optical pulse is stored and restored via photon echoes.

Semiconductor quantum dots tightly confine excited electron-hole pairs, called excitons, resulting in discrete energy levels similar to those of single atoms. Transition energies in the visible or near-infrared make quantum dots suitable for many applications in quantum optics and quantum information science, but to take advantage of all the properties of quantum dot emission, it is necessary to excite them coherently which has been a great challenge due to background scattering of the excitation laser. This dissertation presents the first coherent control of a single quantum dot with observation of its resonance fluorescence and decoherence phenomena. Strong continuous-wave excitation causes the dot to undergo several Rabi oscillations before emitting. These are visible as oscillations in the first- and second-order correlation functions of the emission, and the quantum dot states are "dressed", resulting in a Mollow triplet in the emission spectrum. Some resonantly excited dots, in addition to resonance fluorescence, also emit light from excited states several meV higher in energy. Such up-conversion fits existing theories of decoherence but has never been directly observed before. The up-conversion intensity is shown to be described well by a fairly simple three-level model with single-phonon absorption. The coherent phenomena of resonance fluorescence and the decoherence due to up-conversion paint a dual picture of single quantum dots wherein they can sometimes be treated as an ideal two-level system, but their interactions with the host crystal can lead to many complex behaviors. / text

Modern communications technology has encouraged an intimate connection between Semiconductor Physics and Optics, and this connection shows best in the combination of electron-confining structures with light-confining structures. Semiconductor quantum dots are systems engineered to trap electrons in a mesoscopic scale (the are composed of [approximately] 10000 atoms), resulting in a behavior resembling that of atoms, but much richer. Optical microrseonators are engineered to confine light, increasing its intensity and enabling a much stronger interaction with matter. Their combination opens a myriad of new directions, both in fundamental Physics and in possible applications. This dissertation explores both semiconductor quantum dots and microresonators, through experimental work done with semiconductor quantum dots and microsphere resonators spanning the fields of Quantum Optics, Quantum Information and Photonics; from quantum algorithms to polarization converters. Quantum Optics leads the way, allowing us to understand how to manipulate and measure quantum dots with light and to elucidate the interactions between them and microresonators. In the Quantum Information area, we present a detailed study of the feasibility of excitons in quantum dots to perform quantum computations, including an experimental demonstration of the single-qubit Deutsch-Jozsa algorithm performed in a single semiconductor quantum dot. Our studies in Photonics involve applications of microsphere resonators, which we have learned to fabricate and characterize. We present an elaborate description of the experimental techniques needed to study microspheres, including studies and proof of concept experiments on both ultra-sensitive microsphere sensors and whispering gallery mode polarization converters. / text

Nonlinear magneto-optical effects, originated from atomic coherence, are studied both theoretically and experimentally in thermal Rb vapor. The analytical description of the fundamental properties of coherent media are based on the simplified three- and four-level systems, and then verified using numerical simulations and experimental measurements. In particular, we analyze the modification of the long-lived atomic coherence due to various physical effects, such as reabsorption of spontaneous radiation, collisions with a buffer gas atoms, etc. We also discuss the importance of the high-order nonlinearities in the description of the polarization rotation for the elliptically polarized light. The effect of self-rotation of the elliptical polarization is also analyzed. Practical applications of nonlinear magneto-optical effects are considered in precision metrology and magnetometery, and for the generation of non-classical states of electromagnetic field.

Quantum mechanics allows us to use nonclassical states of light to make measurements with a greater precision than comparable classical states. Here an experiment is presented that squeezes the polarization state of three photons. We demonstrate the deep connection that exists between squeezing and entanglement, unifying the squeezed state and multi-photon entangled state approaches to quantum metrology. For the first time we observe the phenomenon of over-squeezing where a system is squeezed to the point that further squeezing leads to a counter-intuitive increase in measurement uncertainty. Quasi-probability distributions on the surface of a Poincaré sphere are the most natural way to represent the topology of our polarization states. Using this representation it is easy to observe the squeezing and over-squeezing behaviour of our photon states. Work is also presented on two different technologies for generating nonclassical states of light. The first is based on the nonlinear process of spontaneous parametric downconversion to produce pairs of photons. With this source up to 200,000 pairs of photons/s have been collected into single-mode fibre, and over 100 double pairs/s have been detected. This downconversion source is suitable for use in a wide variety of multi-qubit quantum information applications. The second source presented is a single-photon source based on semiconductor quantum dots. The single-photon character of the source is verified using a Hanbury Brown-Twiss interferometer.

Quantum mechanics allows us to use nonclassical states of light to make measurements with a greater precision than comparable classical states. Here an experiment is presented that squeezes the polarization state of three photons. We demonstrate the deep connection that exists between squeezing and entanglement, unifying the squeezed state and multi-photon entangled state approaches to quantum metrology. For the first time we observe the phenomenon of over-squeezing where a system is squeezed to the point that further squeezing leads to a counter-intuitive increase in measurement uncertainty. Quasi-probability distributions on the surface of a Poincaré sphere are the most natural way to represent the topology of our polarization states. Using this representation it is easy to observe the squeezing and over-squeezing behaviour of our photon states. Work is also presented on two different technologies for generating nonclassical states of light. The first is based on the nonlinear process of spontaneous parametric downconversion to produce pairs of photons. With this source up to 200,000 pairs of photons/s have been collected into single-mode fibre, and over 100 double pairs/s have been detected. This downconversion source is suitable for use in a wide variety of multi-qubit quantum information applications. The second source presented is a single-photon source based on semiconductor quantum dots. The single-photon character of the source is verified using a Hanbury Brown-Twiss interferometer.

A major field of research at the current time is that of implementing Quantum Key Distribution over large distances using satellites. If this protocol works with this technology, it will have huge implications on future information security. In order for a satellite to implement this idea, there are many aspects that must be taken into account. One of the big issues that comes up for this type of system is that of propagating light through the turbulent atmosphere and its effects on the acquisition, pointing and tracking system. The projects studied in this thesis study some of the effects of the atmosphere on certain detectors, try to develop pointing schemes for better accuracy as well as develop knowledge in free space propagation of other single photon experiments. In the first experiment, I study the spatial correlations of the daughter photons created in spontaneous parametric down conversion. I look at the effect of altering the pump beam on the positions of the down converted photons and see if the pump can be manipulated in a way to control the directions of the daughter photons. I begin to utilize a deformable mirror and Shack-Hartmann wavefront sensor which are generally used in adaptive optics, but we plan to use them to alter the pump beam in the spontaneous parametric down conversion process to analyze the correlations between the pump and down converted photons. The second experiment investigates the effects of laser scintillation on the performance of a possible tracking device that could be implemented on a satellite. This quad sensor tracks the position of a beam and a system will be developed to move the sensor to keep the beam in the center where there is a hole for the quantum single photons to stream through. In order to create the effects of scintillation, a turbulence simulator box was built and characterized. This box combines wind turbulence with a heat gradient to mimic atmospheric turbulence on a small scale. Finally, my contributions to a large scale, long distance free space quantum optics experiment are explained and the overall goal of the experiment is discussed. This experiment exposed me to actual free space transmission issues as well as many fundamental techniques for performing long distance optics experiments. In this experiment there was no correction for atmospheric turbulence, but in the future, techniques could be implemented which might increase the efficiencies of the free space links.