<p>When light exhibits particle properties, and when matter exhibits wave properties quantum mechanics is needed to describe physical phenomena. </p><p>A two-photon source produces nonmaximally entangled photon pairs when the source is small enough to diffract light. It is shown that diffraction degrades the entanglement. Quantum states produced in this way are used to probe the complementarity between path information and interference in Young's double slit experiment.</p><p>When two photons have a nonmaximally entangled polarization it is shown that the Pancharatnam phase is dependent on the entanglement in a nontrivial way. This could be used for implementing simple quantum logical circuits. </p><p>Magnetic traps are capable of holding cold neutral atoms. It is shown that magnetic traps and guides can be generated by thin wires etched on a surface using standard nanofabrication technology. These <i>atom chips</i> can hold and manipulate atoms located a few microns above the surface with very high accuracy. The potentials are very versatile and allows for highly complex designs, one such design implemented here is a beam splitter for neutral atoms. Interferometry with these confined de Broglie is also considered. These atom chips could be used for implementing quantum logical circuits.</p>

When light exhibits particle properties, and when matter exhibits wave properties quantum mechanics is needed to describe physical phenomena. A two-photon source produces nonmaximally entangled photon pairs when the source is small enough to diffract light. It is shown that diffraction degrades the entanglement. Quantum states produced in this way are used to probe the complementarity between path information and interference in Young's double slit experiment. When two photons have a nonmaximally entangled polarization it is shown that the Pancharatnam phase is dependent on the entanglement in a nontrivial way. This could be used for implementing simple quantum logical circuits. Magnetic traps are capable of holding cold neutral atoms. It is shown that magnetic traps and guides can be generated by thin wires etched on a surface using standard nanofabrication technology. These atom chips can hold and manipulate atoms located a few microns above the surface with very high accuracy. The potentials are very versatile and allows for highly complex designs, one such design implemented here is a beam splitter for neutral atoms. Interferometry with these confined de Broglie is also considered. These atom chips could be used for implementing quantum logical circuits.

Entanglement is a key resource in many quantum information schemes and in the last years the research on multi-qubit entanglement has drawn lots of attention. In this thesis the experimental generation and characterisation of multi-qubit entanglement is presented. Specifically we have prepared entangled states of up to six qubits. The qubits were implemented in the polarisation degree of freedom of single photons. We emphasise that one type of states that we produce are rotationally invariant states, remaining unchanged under simultaneous identical unitary transformations of all their individual constituents. Such states can be applied to e.g. decoherence-free encoding, quantum communication without sharing a common reference frame, quantum telecloning, secret sharing and remote state preparation schemes. They also have properties which are interesting in studies of foundations of quantum mechanics. In the experimental implementation we use a single source of entangled photon pairs, based on parametric down-conversion, and extract the first, second and third order events. Our experimental setup is completely free from interferometric overlaps, making it robust and contributing to a high fidelity of the generated states. To our knowledge, the achieved fidelity is the highest that has been observed for six-qubit entangled states and our measurement results are in very good agreement with predictions of quantum theory. We have also performed another novel test of the foundations of quantum mechanics. It is based on an inequality that is fulfilled by any non-contextual hidden variable theory, but can be violated by quantum mechanics. This test is similar to Bell inequality tests, which rule out local hidden variable theories as possible completions of quantum mechanics. Here, however, we show that non-contextual hidden variable theories cannot explain certain experimental results, which are consistent with quantum mechanics. Hence, neither of these theories can be used to make quantum mechanics complete.

Laser-cooled atoms offer an excellent platform for testing new ideas of quantum control and measurement. I will discuss experiments where we use light and magnetic fields to drive and monitor non-trivial quantum dynamics of a large spin-angular momentum associated with an atomic hyperfine ground state. We can design Hamiltonians to generate arbitrary spin states and perform a full quantum state reconstruction of the results. We have implemented and verified time optimal controls to generate a broad variety of spin states, including spin-squeezed states useful for metrology. Yields achieved are of the range 0.8-0.9.We present a first experimental demonstration of the quantum kicked top, a popular paradigm for quantum and classical chaos. We make `movies' of the evolving quantum state which provides a direct observation of phase space dynamics of this system. The spin dynamics seen in the experiment includes dynamical tunneling between regular islands, rapid spreading of states throughout the chaotic sea, and surprisingly robust signatures of classical phase space structures. Our data show differences between regular and chaotic dynamics in the sensitivity to perturbations of the quantum kicked top Hamiltonian and in the average electron-nuclear spin entanglement during the first 40 kicks. The difference, while clear, is modest due to the small size of the spin.

We pursue topics in optics that follow three major themes; time averaged dynamics with the associated Effective Hamiltonian theory, quantification and transformation of polarization, and periodicity within quantum circuits. Within the first theme, we develop a technique for finding the dynamical evolution in time of a time averaged density matrix. The result is an equation of evolution that includes an Effective Hamiltonian, as well as decoherence terms that sometimes manifest in a Lindblad-like form. We also apply the theory to examples of the AC Stark Shift and Three-Level Raman Transitions. In the theme of polarization, the most general physical transformation on the polarization state has been represented as an ensemble of Jones matrix transformations, equivalent to a completely positive map on the polarization matrix. This has been directly assumed without proof by most authors. We follow a novel approach to derive this expression from simple physical principles, basic coherence optics and the matrix theory of positive maps. Addressing polarization measurement, we first establish the equivalence of classical polarization and quantum purity, which leads to the identical structure of the Poincar\' and Bloch spheres. We analyze and compare various measures of polarization / purity for general dimensionality proposed in the literature, with a focus on the three dimensional case. % entanglement? In pursuit of the final theme of periodic quantum circuits, we introduce a procedure that synthesizes the circuit for the simplest periodic function that is one-to-one within a single period, of a given period p. Applying this procedure, we synthesize these circuits for p up to five bits. We conjecture that such a circuit will need at most n Toffoli gates, where p is an n-bit number. Moreover, we apply our circuit synthesis to compiled versions of Shor's algorithm, showing that it can create more efficient circuits than ones previously proposed. We provide some new compiled circuits for experimentalists to use in the near future. A layer of "classical compilation" is pointed out as a method to further simplify circuits. Periodic and compiled circuits should be helpful for creating experimental milestones, and for the purposes of validation.

We pursue topics in optics that follow three major themes; time averaged dynamics with the associated Effective Hamiltonian theory, quantification and transformation of polarization, and periodicity within quantum circuits. Within the first theme, we develop a technique for finding the dynamical evolution in time of a time averaged density matrix. The result is an equation of evolution that includes an Effective Hamiltonian, as well as decoherence terms that sometimes manifest in a Lindblad-like form. We also apply the theory to examples of the AC Stark Shift and Three-Level Raman Transitions. In the theme of polarization, the most general physical transformation on the polarization state has been represented as an ensemble of Jones matrix transformations, equivalent to a completely positive map on the polarization matrix. This has been directly assumed without proof by most authors. We follow a novel approach to derive this expression from simple physical principles, basic coherence optics and the matrix theory of positive maps. Addressing polarization measurement, we first establish the equivalence of classical polarization and quantum purity, which leads to the identical structure of the Poincar\' and Bloch spheres. We analyze and compare various measures of polarization / purity for general dimensionality proposed in the literature, with a focus on the three dimensional case. % entanglement? In pursuit of the final theme of periodic quantum circuits, we introduce a procedure that synthesizes the circuit for the simplest periodic function that is one-to-one within a single period, of a given period p. Applying this procedure, we synthesize these circuits for p up to five bits. We conjecture that such a circuit will need at most n Toffoli gates, where p is an n-bit number. Moreover, we apply our circuit synthesis to compiled versions of Shor's algorithm, showing that it can create more efficient circuits than ones previously proposed. We provide some new compiled circuits for experimentalists to use in the near future. A layer of "classical compilation" is pointed out as a method to further simplify circuits. Periodic and compiled circuits should be helpful for creating experimental milestones, and for the purposes of validation.

The rapidly developing interdisciplinary field of quantum information, which merges quantum and information science, studies non-classical aspects of quantum systems. These studies are motivated by the promise that the non-classicality can be used to solve tasks more efficiently than classical methods would allow. In many quantum informational studies, non-classical behaviour is attributed to the notion of entanglement. In this thesis we use photons to experimentally investigate fundamental questions such as: What happens to the entanglement in a system when it is affected by noise? In our study of noisy entanglement we pursue the challenging task of creating bound entanglement. Bound entangled states are created through an irreversible process that requires entanglement. Once in the bound regime, entanglement cannot be distilled out through local operations assisted by classical communication. We show that it is possible to experimentally produce four-photon bound entangled states and that a violation of a Bell inequality can be achieved. Moreover, we demonstrate an entanglement-unlocking protocol by relaxing the condition of local operations. We also explore the non-classical nature of quantum mechanics in several single-photon experiments. In these experiments, we show the violation of various inequalities that were derived under the assumption of non-contextuality. Using qutrits we construct and demonstrate the simplest possible test that offers a discrepancy between classical and quantum theory. Furthermore, we perform an experiment in the spirit of the Kochen-Specker theorem to illustrate the state-independence of this theorem. Here, we investigate whether or not measurement outcomes exhibit fully contextual correlations. That is, no part of the correlations can be attributed to the non-contextual theory. Our results show that only a small part of the experimental generated correlations are amenable to a non-contextual interpretation. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Submitted. Paper 5: Submitted. Paper 6: Submitted.</p>

Spontaneous parametric down conversion (SPDC) – incoherent light scattering – is one of the main entangled photons source applied in quantum optics experiments. The tradition to pump SPDC by laser radiation was established from the very first SPDC experiments in 1968. The aim of this thesis was experimentally to investigate the ability to generate an SPDC pumping by both temporal and spatially incoherent radiation - a high-power blue LED. Weak SPDC signals were registered with high sensitivity CCD cameras, photons coincidences were detected with photon counters. The theoretical simulations were performed in parallel with experiments. Therefore, mathematical simulation code was written in order to estimate the SPDC power distribution and simulate photon coincidence experiment changing the properties of pump beam and detection system. Experimental results reveal that incoherent light sources can be good alternative for the laser systems in order to generate average quality biphoton fields especially in those experiments in which low biphoton field coherency would be advantage. The main advantages of the incoherent sources over laser systems are low cost, simple production technology and the huge commercial variety of different wavelength sources. / Parametrinė fluorescencija (PF) – nekoherentinė šviesos sklaida – yra vienas pagrindinių susietųjų fotonų šaltinių taikomų kvantinės optikos eksperimentuose. Nuo pat pirmųjų PF eksperimentinių tyrimų 1968 metais įsigalėjo tradicija šį reiškinį žadinti išimtinai lazerine spinduliuote. Šios disertacijos tikslas – eksperimentiškai ištirti galimybę generuoti PF tiek laikiškai, tiek ir erdviškai nekoherentine spinduliuote – didelės galios šviesos diodu. Atliekant tyrimus didelio jautrio CCD kamera buvo registruojami silpni PF signalai, pavienių fotonų skaitliukais buvo registruojami fotonų sutapimai,. Lygiagrečiai eksperimentiniams tyrimams buvo atliekami teoriniai skaičiavimai. Šiuo tikslu buvo parašytas matematinio modeliavimo programinis kodas, skirtas įvertinti PF erdvinį galios pasiskirstymą bei modeliuoti fotonų sutapimų eksperimentą, keičiant kaupinimo pluošto ir detekcijos sistemos savybes. Šio darbo rezultatai atskleidžia, kad nekoherentiniai šaltiniai gali būti puiki alternatyva lazerinėms sistemoms siekiant žadinti vidutinės kokybės dvyninius laukus, ypatingai tokiose tyrimų srityse, kuriose mažas dvyninio lauko koherentiškumas būtų didžiulis privalumas. Pagrindiniai nekoherentinių šaltinių pranašumai prieš lazerines sistemas: maža kaina, paprasta gamybos technologija ir didžiulė komercinė skirtingo bangos ilgio šaltinių įvairovė.

Parametrinė fluorescencija (PF) – nekoherentinė šviesos sklaida – yra vienas pagrindinių susietųjų fotonų šaltinių taikomų kvantinės optikos eksperimentuose. Nuo pat pirmųjų PF eksperimentinių tyrimų 1968 metais įsigalėjo tradicija šį reiškinį žadinti išimtinai lazerine spinduliuote. Šios disertacijos tikslas – eksperimentiškai ištirti galimybę generuoti PF tiek laikiškai, tiek ir erdviškai nekoherentine spinduliuote – didelės galios šviesos diodu. Atliekant tyrimus didelio jautrio CCD kamera buvo registruojami silpni PF signalai, pavienių fotonų skaitliukais buvo registruojami fotonų sutapimai,. Lygiagrečiai eksperimentiniams tyrimams buvo atliekami teoriniai skaičiavimai. Šiuo tikslu buvo parašytas matematinio modeliavimo programinis kodas, skirtas įvertinti PF erdvinį galios pasiskirstymą bei modeliuoti fotonų sutapimų eksperimentą, keičiant kaupinimo pluošto ir detekcijos sistemos savybes. Šio darbo rezultatai atskleidžia, kad nekoherentiniai šaltiniai gali būti puiki alternatyva lazerinėms sistemoms siekiant žadinti vidutinės kokybės dvyninius laukus, ypatingai tokiose tyrimų srityse, kuriose mažas dvyninio lauko koherentiškumas būtų didžiulis privalumas. Pagrindiniai nekoherentinių šaltinių pranašumai prieš lazerines sistemas: maža kaina, paprasta gamybos technologija ir didžiulė komercinė skirtingo bangos ilgio šaltinių įvairovė. / Spontaneous parametric down conversion (SPDC) – incoherent light scattering – is one of the main entangled photons source applied in quantum optics experiments. The tradition to pump SPDC by laser radiation was established from the very first SPDC experiments in 1968. The aim of this thesis was experimentally to investigate the ability to generate an SPDC pumping by both temporal and spatially incoherent radiation - a high-power blue LED. Weak SPDC signals were registered with high sensitivity CCD cameras, photons coincidences were detected with photon counters. The theoretical simulations were performed in parallel with experiments. Therefore, mathematical simulation code was written in order to estimate the SPDC power distribution and simulate photon coincidence experiment changing the properties of pump beam and detection system. Experimental results reveal that incoherent light sources can be good alternative for the laser systems in order to generate average quality biphoton fields especially in those experiments in which low biphoton field coherency would be advantage. The main advantages of the incoherent sources over laser systems are low cost, simple production technology and the huge commercial variety of different wavelength sources.

One of the current hot topics in physics is quantum information, which, broadly speaking, is concerned with exploring the information-processing and storing tasks that can be performed in quantum mechanical systems. Besides driving forward our experimental control and understanding of quantum systems, the field is also in the early stages of developing revolutionary new technology of far reaching implication. As part of these endeavors, this thesis presents some results in experimental quantum information. Specifically, we develop several new tools for performing quantum information processing in optical quantum systems, and use them to explore a number of applications and novel physical phenomena. A central theme, and one of the most sought after applications of quantum information, is the pursuit of a programmable quantum computer. This thesis is divided into 3 parts. In Part I we develop some new optical quantum logic gates, which are tools for manipulating quantum information and the fundamental building blocks of a quantum computer. We also develop a new technique for simplifying the construction of quantum logic circuits, by exploiting multi-level quantum systems, that has the potential for application in any physical encoding of quantum information. In Part II we use these tools to perform some of the first demonstrations of quantum algorithms. Each of these could, in principle, efficiently solve an important problem that is thought to be fundamentally intractable using conventional `classical' techniques. Firstly we implement a simplified version of the quantum algorithm for factoring numbers, and demonstrate the core processes, coherent control, and resultant entangled states required for a full-scale implementation. Secondly we implement an algorithm for calculating the energy of many-body quantum systems. Specifically, we calculate the energy spectrum of the Hydrogen molecule, in a minimal basis. Finally we demonstrate an algorithm for a novel model of quantum computing that uses mixed states. Here we perform the first characterisation of intrinsically non-classical correlations between fully separable quantum systems, captured by the 'discord'---a measure of quantum correlations in mixed states that goes beyond entanglement. Part III presents a technique that extends experimental control over biphotons---the novel quantum information carriers formed by the polarisation of two photons in the same spatial and temporal mode. We also generate and explore new forms of entanglement: producing the first instance of qubit-qutrit entanglement, by entangling the polarisation of a photon and a biphoton, and developing a technique that enables full control over the level of `W-class' of multi-partite entanglement between the polarisation of three photons.