This thesis summarizes investigations on quantum correlations in the fluorescence light of single trapped atoms. The results found have applications in the broad field of quantum information science: it is shown how to overcome classical imaging boundaries using a new developed scheme of quantum imaging, how to project and engineer correlated quantum states in the ground states of multi-level atoms by detecting their fluorescence light and how to prove the quantum nature of these correlations using fundamental tests of quantum information science. Without the need of further introduction to these topics it is interesting to note at this early point that all correlations observed are indeed of quantum nature and show in particular entanglement features, while initially the system under consideration is entirely uncorrelated and the only intervention comes along with the measurement process itself. Therefore, this thesis is embedded into a current field of research activities in the area of quantum information science which is commonly referred to as measurement-induced entanglement. In the first part of this thesis, the correlated photon signal as measured in the fluorescence light of single-photon emitters is at the focus of investigations. It is shown that this correlated signal can be used to overcome classical signals in terms of resolution when applied to image processing. In the second part, the fluorescence signal of a system of multi-level atoms is used to project correlated quantum states into the long-lived ground levels of the atoms. Hereby, a broad variety of entangled quantum states can be generated, ranging from symmetric states like the W-states and GHZ-states to arbitrary total angular momentum eigenstates. Finally, the last part of this thesis takes a closer look at the fundamental physical processes inherent in all schemes and applications investigated throughout the thesis. There, amongst others we investigate Bell-type inequalities that are able to prove the quantum nature of the correlations.
This thesis summarizes investigations on quantum correlations in the fluorescence light of single trapped atoms. The results found have applications in the broad field of quantum information science: it is shown how to overcome classical imaging boundaries using a new developed scheme of quantum imaging, how to project and engineer correlated quantum states in the ground states of multi-level atoms by detecting their fluorescence light and how to prove the quantum nature of these correlations using fundamental tests of quantum information science. Without the need of further introduction to these topics it is interesting to note at this early point that all correlations observed are indeed of quantum nature and show in particular entanglement features, while initially the system under consideration is entirely uncorrelated and the only intervention comes along with the measurement process itself. Therefore, this thesis is embedded into a current field of research activities in the area of quantum information science which is commonly referred to as measurement-induced entanglement. In the first part of this thesis, the correlated photon signal as measured in the fluorescence light of single-photon emitters is at the focus of investigations. It is shown that this correlated signal can be used to overcome classical signals in terms of resolution when applied to image processing. In the second part, the fluorescence signal of a system of multi-level atoms is used to project correlated quantum states into the long-lived ground levels of the atoms. Hereby, a broad variety of entangled quantum states can be generated, ranging from symmetric states like the W-states and GHZ-states to arbitrary total angular momentum eigenstates. Finally, the last part of this thesis takes a closer look at the fundamental physical processes inherent in all schemes and applications investigated throughout the thesis. There, amongst others we investigate Bell-type inequalities that are able to prove the quantum nature of the correlations.
This thesis fathoms the possibilities and limitations of measurements in quantum optics. After a short introduction to the general aspects of measurements in quantum mechanics, it presents three examples of a measurement process in concrete applications to quantum optics. For one, while operators describing quantities of interest might have a simple theoretical form, it is often hard to actually implement a measurement of their expectation values experimentally. This situation is encountered in the first part which is devoted to the measurement of quantum statistical properties of a light beam. In contrast to classical optics, these statistics are not fully determined by first- and second-order correlations. Instead, higher-order correlations, usually described by non-Hermitian operators, are necessary to characterize the quantum state completely. A particular example is the N-photon Fock state, for which only a measurement of the Nth-order correlations allows for a full characterization. Here, we present a new method how to measure an important class of Nth-order correlations for arbitrary N in a single spatial mode with two polarizations with limited experimental resources. The second part is again centered around the realization of specific measurement operators for photon correlation measurements. However, in contrast to the previous chapter, these measurements are not an end in their own, but are designed to create specific quantum states as a consequence of the measurement process: A suitable measurement of photons emitted by a number of atoms allows to transfer the atoms into long-lived entangled states. We find that with this method it is possible to entangle two remote atomic qubits to an arbitrary and well-defined degree. Furthermore, we show how to generate two families of quantum states in an arbitrary number of remote atomic qubits: one family consists of all -- symmetric and non-symmetric -- total angular momentum eigenstates in N remote qubits, the other is a family of cluster states. It is also systematically investigated whether the technique of quantum state engineering by projective measurements allows for the creation of any arbitrary state. We find explicit solutions for the case of two and three qubits, while it is shown that no solution exist for N > 6. We conclude the section by proving that with some changes in the setup, this measurement-based quantum state engineering technique allows to create the same states among the scattered photons themselves rather than among the emitting atoms. The last part is devoted to the amount of information one is able to gain about a given system when performing a measurement. The corresponding limits of information are investigated at the example of the duality that arises in a two-way interferometer between the visibility of the interference pattern and the knowledge about the path of the interfering object. We show that there exist correlations between the phase difference the interfering object acquires on its way through the interferometer and the amount of which-way information retrievable from certain observables of the which-way detector. In this way, the which-way information becomes a phase-dependent quantity. In particular, we find that for certain values of the phase shift, the amount of extractable which-way information can be larger than allowed by phase-independent measurement. This property is put to use to find the optimal observable for the which-way detector readout in dependence on the phase of the interfering object. Following this strategy, we are able to gain more which-way information than previously thought possible.
In the present thesis we investigate spatial and temporal intensity correlations which are created by statistically independent or by entangled light sources. Even though this classification may appear quite technical, the diverseness of the statistical properties of the considered photon sources naturally brings into our focus two different lines of research. In the first part of this thesis we will quantitatively study the non-classical and potentially entangled character of light fields which originate from a variety of different statistically independent light sources. To this end quantum correlations between light fields are analyzed which either stem from non-classical single-photon emitters (like ensembles of uncorrelated atoms) or from a mixture of non-classical and classical photon sources (like lasers with uncorrelated fluctuating initial phase). In the second part of this thesis we study correlations between initially entangled lightsources, namely localized atoms which share an entangled state. In the course of the investigations we physically reinterpret in particular the so called superradiance effect in a quantum-path formalism: superradiance denotes an enhanced mean radiated intensity in a particular direction, i.e., a focussing of the photons scattered by an atomic gas. This effect is commonly explained by a successive synchronization of the dipole moments of all participating atoms leading to a photon emission predominantly in one direction. For more than 60 years this focussing has been physically interpreted as a cooperative effect depending on the dipole-dipole interaction between the atoms. In contrast, we will show that it is rather a quantum-interference effect which is caused by non-synchronized and potentially widely separated entangled atoms.
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.
This thesis is a dissemination of the experimental work I have carried out in the last three and a half years, under supervision of Prof. Miles Padgett and Dr. Sonja Franke-Arnold. Presented within are seven unique experiments investigating the orbital angular momentum (OAM) states of light, and the associated spatial modes. Six of these experiments relate to measurements on quantum-entangled photon pairs produced in down-conversion. The first chapter of my thesis is a brief review of the some of the contributions made to the field of research of OAM, both involving classical and quantum states of light. This chapter introduces some of the hallmark experiments within the subject, from which my experimental work reported in this thesis is inspired. The second chapter details the set up of the down conversion experiment, and the experimental techniques used to design a fully functioning quantum measurement system. Most importantly, this includes the holographic techniques used to measure the spatial states of the photon pairs. In addition to holographic measurements, a system to holographically auto-align the down-conversion experiment was developed. Due to the sensitive nature of the experiments presented, this automated system has been crucial to the success of all of the single photon experiments presented within this document. The experimental results are split into three separate categories. The first (Chapter 3) describes measurements investigating the Fourier relationship between OAM and angular position states, both at the classical and quantum levels. The following chapter (Chapter 4) consists of four experiments designed to quantify the degree of entanglement of states of OAM and angular position. This includes the first demonstration of the historic EPR (Einstein-Podolsky-Rosen) paradox for OAM and angle states, violation of a Bell-type inequality for arbitrary OAM states, and characterisation of the density matrices for a range of OAM state-spaces. The final chapter (Chapter 5) reports a new type of ghost imaging using down-converted photon pairs. In this experiment, we violate a Bell inequality within a ghost image, demonstrating the entangled nature of our system and contributing a new element to the long standing contention over quantum vs. classical features within ghost imaging. These experiments have seen a wide range of collaboration. The experimental work on the Fourier relation on single photons was carried out in collaboration with Dr. Anand Kumar Jha (University of Rochester). The work on ghost imaging was performed with collaboration with Prof. Monika Ritsch-Marte (Innsbruck Medical University), and the angular EPR paradox work was carried out in collaboration with Prof. Robert Boyd (Univ. of Rochester) and Prof. David Ireland (Univ. of Glasgow). The work I present here is experimental, however any theoretical developments are in a large part due to the support of Dr. Sonja Franke-Arnold and Prof. Steve Barnett (Univ. of Strathclyde).
This dissertation deals with theoretical and experimental research on nonclassical, or entangled, states of atoms and photons. In the first part, I describe two approaches to the preparation of entangled states of a large number of atoms. The first approach is based on the transfer of quantum correlations from non-classical light to the atomic spins. I consider three different situations: (a) the atoms are placed in a loss-free cavity and no relaxation of any kind is present; (b) the atoms are placed in a cavity with input and output for the electromagnetic field and the atoms spontaneously decay from the upper state; (c) there is no cavity around the atoms and spontaneous emission is present. I show that in all three situations with judicious choice of parameters, entangled samples of atoms can be produced. The second approach is based on quantum-nondemolition (QND) measurements of collective atomic operators. I describe experiments with pulsed and cw light as the probe, that result in squeezed spin states of atoms. When a rf magnetic field is applied to the atomic sample, sub- shot noise performance of an atomic spin interferometer is demonstrated. In the second part of the thesis I describe investigations of phase properties of two-photon and single-photon states. These experiments make use of spontaneous type-II down-conversion in a nonlinear crystal. First, interferometric measurement of a phase shift at the Heisenberg limit for a two-photon state is described. Next, a violation of Bell-type inequalities in phase space is demonstrated for the quantum optical version of the Einstein-Podolsky-Rosen state. Finally, some recent work directed toward homodyning a single photon against a strong local oscillator field is described.
Quantum optics offers a huge variety of exciting phenomena. Many of them are still in their infancy and especially when it comes to implementing devices using these effects for more than a proof of principle demonstration still many things have to be investigated and understood. In this thesis I discuss the role of correlations in some areas of quantum optics and in some cases compare it to classical optics. Four papers form the core of the thesis. In the first paper, I propose a new measure for entanglement. This measure is based on correlations between two states. I show, how this measure relates to another measure, the concurrence. It turns out that the measure is a bijective map of the concurrence for a pure state of two qubits. I motivate why the new measure is useful if one wants to implement it experimentally. I discuss its behaviour for the case of two qubits and show its properties when dealing with pure and with mixed states. The second paper extends the result of the first one to the case where one has higher-dimensional states than qubits. In the third paper I look at phase super-resolution. I show that it can be interpreted as a purely classical effect and I analyse what is needed and what is not needed to achieve it. Specifically, I show that quantum correlations in terms of entanglement is not needed to demonstrate phase super-resolution. By doing so I propose how one could achieve arbitrarily high phase super-resolution. Finally, the last paper looks at the efficiency of quantum lithography and quantum imaging. It shows, that some basic assumptions in the original proposals of quantum lithography seems unfounded and that, as a consequence, the efficiency is poor. I give formulæ for the explicit scaling behaviour when changing the number of photons in a mode or when changing the number of pixels. The effect of the results on the future of quantum lithography is discussed as well.