Nanofiber control of ultracold quantum gases

While a great amount of attention is being given to the development of nanodevices, both through academic research and private industry, the field is still on the verge. Progress hinges upon the development of tools and components that can precisely control the interaction between light and matter, and that can be efficiently integrated into nano-devices. Nanofibers are one of the most promising candidates for such purposes. However, in order to fully exploit their potential, a more intimate knowledge of how nanofibers interact with single neutral atoms must be gained. As we learn more about the properties of nanofiber modes, and the way they interface with atoms, and as the technology develops that allows them to be prepared with more precisely known properties, they become more and more adaptable and effective. The work presented in this thesis touches on many topics, which is testament to the broad range of applications and high degree of promise that nanofibers hold. For immediate use, we need to fully grasp how they can be best implemented as sensors, filters, detectors, and switches in existing nano-technologies. Areas of interest also include how they might be best exploited for probing atom-surface interactions, single-atom detection and single photon generation. Nanofiber research is also motivated by their potential integration into fundamental cold atom quantum experiments, and the role they can play there. Combining nanofibers with existing optical and quantum technologies is a powerful strategy for advancing areas like quantum computation, quantum information processing, and quantum communication. In this thesis I present a variety of theoretical work, which explores a range of the applications listed above. The first work presented concerns the use of the evanescent fields around a nanofiber to manipulate an existing trapping geometry and therefore influence the centre-of-mass dynamics of the atom. The second work presented explores interesting trapping geometries that can be achieved in the vicinity of a fiber in which just four modes are allowed to propagate. In a third study I explore the use of a nanofiber as a detector of small numbers of photons by calculating the rate of emission into the fiber modes when the fiber is moved along next to a regularly separated array of atoms. Also included are some results from a work in progress, where I consider the scattered field that appears along the nanofiber axis when a small number of atoms trapped along that axis are illuminated orthogonally; some interesting preliminary results are outlined. Finally, in contrast with the rest of the thesis, I consider some interesting physics that can be done in one of the trapping geometries that can be created around the fiber, here I explore the ground states of a phase separated two-component superfluid Bose-Einstein condensate trapped in a toroidal potential.

Competition for Cooperation: variability, benefits and heritability of relational wealth in hunter-gatherers

Many defining human characteristics including theory of mind, culture and language relate to our sociality, and facilitate the formation and maintenance of cooperative relationships. Therefore, deciphering the context in which our sociality evolved is invaluable in understanding what makes us unique as a species. Much work has emphasised group-level competition, such as warfare, in moulding human cooperation and sociality. However, competition and cooperation also occur within groups; and inter-individual differences in sociality have reported fitness implications in numerous non-human taxa. Here we investigate whether differential access to cooperation (relational wealth) is likely to lead to variation in fitness at the individual level among BaYaka hunter-gatherers. Using economic gift games we find that relational wealth: a) displays individual-level variation; b) provides advantages in buffering food risk, and is positively associated with body mass index (BMI) and female fertility; c) is partially heritable. These results highlight that individual-level processes may have been fundamental in the extension of human cooperation beyond small units of related individuals, and in shaping our sociality. Additionally, the findings offer insight in to trends related to human sociality found from research in other fields such as psychology and epidemiology.

A disappearing act performed by magnesium: the nucleotide exchange mechanism of Ran GTPase by Quantum mechanics/Molecular mechanics studies

The Ran GTPase protein is a guanine nucleotide-binding protein (GNBP) with an acknowledged profile in cancer onset, progression and metastases. The complex mechanism adopted by GNBPs in exchanging GDP for GTP is an intriguing process and crucial for Ran viability. The successful completion of the process is a fundamental aspect of propagating downstream signalling events. QM/MM molecular dynamics simulations were employed in this study to provide a deeper mechanistic understanding of the initiation of nucleotide exchange in Ran. Results indicate significant disruption of the metal-binding site upon interaction with RCC1 (the Ran guanine nucleotide exchange factor), overall culminating in the prominent shift of the divalent magnesium ion. The observed ion drifting is reasoned to occur as a consequence of the complex formation between Ran and RCC1 and is postulated to be a critical factor in the exchange process adopted by Ran. This is the first report to observe and detail such intricate dynamics for a protein in Ras superfamily.

Quantum-limited estimation of continuous spontaneous localization

We apply the formalism of quantum estimation theory to extract information about potential collapse mechanisms of the continuous spontaneous localisation (CSL) form.
In order to estimate the strength with which the field responsible for the CSL mechanism couples to massive systems, we consider the optomechanical interaction
between a mechanical resonator and a cavity field. Our estimation strategy passes through the probing of either the state of the oscillator or that of the electromagnetic field that drives its motion. In particular, we concentrate on all-optical measurements, such as homodyne and heterodyne measurements.
We also compare the performances of such strategies with those of a spin-assisted optomechanical system, where the estimation of the CSL parameter is performed
through time-gated spin-like measurements.

(Quantum-) critical dynamics of magnetoelectric materials

In this thesis the critical dynamics of several magnetoelectric compounds at their phase transition were examined. Mostly measurements of the dielectric properties in the frequency range of below 1 Hz up to 5 GHz were employed to evaluate the critical exponents for both magnetic field and temperature-dependent measurements. Most of the materials that are part of this work show anomalous behavior, especially at very low temperatures where quantum fluctuations are of the order of or even dominate those induced thermally. This anomalous behavior manifests in different forms. In Dy2Ti2O7 we demonstrate the existence of electric dipoles on magnetic monopoles. Here the dynamics at the critical endpoint located at 0.36K and in a magnetic field of 1T parallel to the [111] direction are of special interest. At this critical endpoint the expected critical slowing down of the dynamics could not only not be observed but instead the opposite, critical speeding-up by several orders of magnitude, could be demonstrated. Furthermore, we show that the phase diagram of Dy2Ti2O7 in this field direction can be reproduced solely from the dynamical properties, for example the resonance frequency of the observed relaxation that is connected to the monopole movement. Away from this point of the phase diagram the dynamics are slowing-down with reduction of temperature as one would expect. Additional measurements on Y2Ti2O7, a structurally identical but non-magnetic material, show only slowing down with reduction of temperature and no additional features. A possible explanation for the observed critical speeding-up is a coherent movement of magnetic monopoles close to the critical field that increases the resonance frequency by reducing the damping of the process. LiCuVO4 on the other hand behaves normally at its phase transition as long as the temperature is higher than 0.4 K. In this temperature regime the dynamics show critical slowing-down analogous to classical ferroelectric materials. This analogy extends also towards higher frequencies where the permittivity displays a ‘dispersion’ minimum that is temperature-dependent but of the order of 2 GHz. Below 0.4K the observed behavior changes drastically. Here we found no longer relaxational behavior but instead an excitation with very low energy. This low energy excitation was predicted by theory and is caused by nearly gapless soliton excitations within the 1D Cu2+ chains of LiCuVO4. Finally, in TbMnO3 the dynamics of the phase transition into the multiferroic phase was observed at roughly 27 K, a much higher temperature compared to the other materials. Here the expected critical slowing-down was observed, even though in low-frequency measurements this transition into the ferroelectric phase is overshadowed by the so-called c-axis relaxation. Therefore, only frequencies above 1MHz could be used to determine the critical exponents for both temperatureand magnetic-field-dependent measurements. This was done for both the peak frequency as well as the relaxation strength. In TbMnO3 an electromagnetic soft-mode with small optical weight causes the observed fluctuations, similar to the case of multiferroic MnWO4.

Memory effects and geometrical considerations in open quantum systems

This thesis discusses memory effects in open quantum systems with an emphasis on the Breuer, Laine, Piilo (BLP) measure of non-Markovianity. It is shown how the calculation of the measure can be simplifed and how quantum information protocols can bene t from memory e ects. The superdense coding protocol is used as an example of this. The quantum Zeno effect will also be studied from the point of view of memory e ects. Finally the geometric ideas used in simplifying the calculation of the BLP measure are applied in studying the amount of resources needed for detecting bipartite quantum correlations. It is shown that to decide without prior information if an unknown quantum state is entangled or not, an informationally complete measurement is required. The first part of the thesis contains an introduction to the theoretical ideas such as quantum states, closed and open quantum systems and necessary mathematical tools. The theory is then applied in the second part of the thesis as the results obtained in the original publications I-VI are presented and discussed.

State sum models for quantum gravity

This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.

Geometrical measurements in three-dimensional quantum gravity

A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the distances between points, giving spectra and probabilities which have a geometrical interpretation. The observables are related to the evaluation of relativistic spin networks by a Fourier transform.

Multipartite entanglement in harmonic oscillators subjected to dissipative quantum dynamics

Una detallada descripción de la dinámica de bajas energías del entrelazamiento multipartito es proporcionada para sistemas armónicos en una gran variedad de escenarios disipativos. Sin hacer ninguna aproximación central, esta descripción yace principalmente sobre un conjunto razonable de hipótesis acerca del entorno e interacción entorno-sistema, ambas consistente con un análisis lineal de la dinámica disipativa. En la primera parte se deriva un criterio de inseparabilidad capaz de detectar el entrelazamiento k-partito de una extensa clase de estados gausianos y no-gausianos en sistemas de variable continua. Este criterio se emplea para monitorizar la dinámica transitiva del entrelazamiento, mostrando que los estados no-gausianos pueden ser tan robustos frente a los efectos disipativos como los gausianos. Especial atención se dedicada a la dinámica estacionaria del entrelazamiento entre tres osciladores interaccionando con el mismo entorno o diferentes entornos a distintas temperaturas. Este estudio contribuye a dilucidar el papel de las correlaciones cuánticas en el comportamiento de la corrientes energéticas.

Decoherence models for discrete-time quantum walks and their application to neutral atom experiments

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice. From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic-instead of diffusive-expansion in position space is not a good indicator of the range of coherent delocalization. We provide further physical insight by distinguishing the effects of short- and long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences. For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.

Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

We determine numerically the single-particle and the two-particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small momentum) S-matrix of the quasiparticles. The low energy part of the finite size spectrum can be understood in terms of a simple effective model introduced in a previous work, and is consistent with an asymptotic S-matrix of an exchange form below a momentum scale p*. This scale appears to vanish faster than the Compton scale, mc, as one approaches the critical point, suggesting that a dangerously irrelevant operator may be responsible for the behaviour observed on the lattice.

Optical properties of semiconductor quantum wires

This thesis presents theoretical investigations of the sub band structure and optical properties of semiconductor quantum wires. For the subband structure, we employ multiband effective-mass theory and the effective bond-orbital model both of which fully account for the band mixing and material anisotropy. We also treat the structure geometry in detail taking account of such effects as the compositional grading across material interfaces. Based on the subband structure, we calculate optical properties of quantum-wire structures. A recuring theme is the cross-over from one- to ~wo-dimensional behavior in these structures. This complicated behavior procludes the application of simple theoretical models to obtain the electronic structure. In particular, we calculate laser properties of quantum wires grown in V-grooves and find enhanced performance compared with quantum-well lasers. We also investigate optical anisotropy in quantum-wire arrays and propose an electro-optic device based on such structures.

SEEKING CULTURAL FAIRNESS IN A MEASURE OF RELATIONAL REASONING

Relational reasoning, or the ability to identify meaningful patterns within any stream of information, is a fundamental cognitive ability associated with academic success across a variety of domains of learning and levels of schooling. However, the measurement of this construct has been historically problematic. For example, while the construct is typically described as multidimensional—including the identification of multiple types of higher-order patterns—it is most often measured in terms of a single type of pattern: analogy. For that reason, the Test of Relational Reasoning (TORR) was conceived and developed to include three other types of patterns that appear to be meaningful in the educational context: anomaly, antinomy, and antithesis. Moreover, as a way to focus on fluid relational reasoning ability, the TORR was developed to include, except for the directions, entirely visuo-spatial stimuli, which were designed to be as novel as possible for the participant. By focusing on fluid intellectual processing, the TORR was also developed to be fairly administered to undergraduate students—regardless of the particular gender, language, and ethnic groups they belong to. However, although some psychometric investigations of the TORR have been conducted, its actual fairness across those demographic groups has yet to be empirically demonstrated. Therefore, a systematic investigation of differential-item-functioning (DIF) across demographic groups on TORR items was conducted. A large (N = 1,379) sample, representative of the University of Maryland on key demographic variables, was collected, and the resulting data was analyzed using a multi-group, multidimensional item-response theory model comparison procedure. Using this procedure, no significant DIF was found on any of the TORR items across any of the demographic groups of interest. This null finding is interpreted as evidence of the cultural-fairness of the TORR, and potential test-development choices that may have contributed to that cultural-fairness are discussed. For example, the choice to make the TORR an untimed measure, to use novel stimuli, and to avoid stereotype threat in test administration, may have contributed to its cultural-fairness. Future steps for psychometric research on the TORR, and substantive research utilizing the TORR, are also presented and discussed.

Efficient entanglement distillation without quantum memory

Entanglement distribution between distant parties is an essential component to most quantum communication protocols. Unfortunately, decoherence effects such as phase noise in optical fibres are known to demolish entanglement. Iterative (multistep) entanglement distillation protocols have long been proposed to overcome decoherence, but their probabilistic nature makes them inefficient since the success probability decays exponentially with the number of steps. Quantum memories have been contemplated to make entanglement distillation practical, but suitable quantum memories are not realised to date. Here, we present the theory for an efficient iterative entanglement distillation protocol without quantum memories and provide a proof-of-principle experimental demonstration. The scheme is applied to phase-diffused two-mode-squeezed states and proven to distil entanglement for up to three iteration steps. The data are indistinguishable from those that an efficient scheme using quantum memories would produce. Since our protocol includes the final measurement it is particularly promising for enhancing continuous-variable quantum key distribution.

Quantum Gate and Quantum State Preparation through Neighboring Optimal Control

Successful implementation of fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used to control the many-qubit state. It is known that an accuracy threshold Pa exists for any quantum gate that is to be used for such a computation to be able to continue for an unlimited number of steps. Specifically, the error probability Pe for such a gate must fall below the accuracy threshold: Pe < Pa. Estimates of Pa vary widely, though Pa ∼ 10−4 has emerged as a challenging target for hardware designers. I present a theoretical framework based on neighboring optimal control that takes as input a good quantum gate and returns a new gate with better performance. I illustrate this approach by applying it to a universal set of quantum gates produced using non-adiabatic rapid passage. Performance improvements are substantial comparing to the original (unimproved) gates, both for ideal and non-ideal controls. Under suitable conditions detailed below, all gate error probabilities fall by 1 to 4 orders of magnitude below the target threshold of 10−4. After applying the neighboring optimal control theory to improve the performance of quantum gates in a universal set, I further apply the general control theory in a two-step procedure for fault-tolerant logical state preparation, and I illustrate this procedure by preparing a logical Bell state fault-tolerantly. The two-step preparation procedure is as follow: Step 1 provides a one-shot procedure using neighboring optimal control theory to prepare a physical qubit state which is a high-fidelity approximation to the Bell state |β01⟩ = 1/√2(|01⟩ + |10⟩). I show that for ideal (non-ideal) control, an approximate |β01⟩ state could be prepared with error probability ϵ ∼ 10−6 (10−5) with one-shot local operations. Step 2 then takes a block of p pairs of physical qubits, each prepared in |β01⟩ state using Step 1, and fault-tolerantly prepares the logical Bell state for the C4 quantum error detection code.