Fluctuations in and out of equilibrium: Thermalization, quantum measurements and Coulomb disorder

This purely theoretical thesis covers aspects of two contemporary research fields: the non-equilibrium dynamics in quantum systems and the electronic properties of three-dimensional topological insulators. In the first part we investigate the non-equilibrium dynamics in closed quantum systems. Thanks to recent technologies, especially from the field of ultracold quantum gases, it is possible to realize such systems in the laboratory. The focus is on the influence of hydrodynamic slow modes on the thermalization process. Generic systems in equilibrium, either classical or quantum, in equilibrium are described by thermodynamics. This is characterized by an ensemble of maximal entropy, but constrained by macroscopically conserved quantities. We will show that these conservation laws slow down thermalization and the final equilibrium state can be approached only algebraically in time. When the conservation laws are violated thermalization takes place exponential in time. In a different study we calculate probability distributions of projective quantum measurements. Newly developed quantum microscopes provide the opportunity to realize new measurement protocols which go far beyond the conventional measurements of correlation functions. The second part of this thesis is dedicated to a new class of materials known as three-dimensional topological insulators. Also here new experimental techniques have made it possible to fabricate these materials to a high enough quality that their topological nature is revealed. However, their transport properties are not fully understood yet. Motivated by unusual experimental results in the optical conductivity we have investigated the formation and thermal destruction of spatially localized electron- and hole-doped regions. These are caused by charged impurities which are introduced into the material in order to make the bulk insulating. Our theoretical results are in agreement with the experiment and can explain the results semi-quantitatively. Furthermore, we study emergent lengthscales in the bulk as well as close to the conducting surface.

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.

Centre-of-mass motion in multi-particle Schrodinger-Newton dynamics

We investigate the implication of the nonlinear and non-local multi-particle Schrodinger-Newton equation for the motion of the mass centre of an extended multi-particle object, giving self-contained and comprehensible derivations. In particular, we discuss two opposite limiting cases. In the first case, the width of the centre-of-mass wave packet is assumed much larger than the actual extent of the object, in the second case it is assumed much smaller. Both cases result in nonlinear deviations from ordinary free Schrodinger evolution for the centre of mass. On a general conceptual level we include some discussion in order to clarify the physical basis and intention for studying the Schrodinger-Newton equation.

Classical and quantum approaches to the interaction of light and matter at the nanoscale

168 p.

Radio Frequency Superconducting Quantum Interference Device Meta-atoms and Metamaterials: Experiment, Theory, and Analysis

Metamamterials are 1D, 2D or 3D arrays of articial atoms. The articial atoms, called "meta-atoms", can be any component with tailorable electromagnetic properties, such as resonators, LC circuits, nano particles, and so on. By designing the properties of individual meta-atoms and the interaction created by putting them in a lattice, one can create a metamaterial with intriguing properties not found in nature. My Ph. D. work examines the meta-atoms based on radio frequency superconducting quantum interference devices (rf-SQUIDs); their tunability with dc magnetic field, rf magnetic field, and temperature are studied. The rf-SQUIDs are superconducting split ring resonators in which the usual capacitance is supplemented with a Josephson junction, which introduces strong nonlinearity in the rf properties. At relatively low rf magnetic field, a magnetic field tunability of the resonant frequency of up to 80 THz/Gauss by dc magnetic field is observed, and a total frequency tunability of 100% is achieved. The macroscopic quantum superconducting metamaterial also shows manipulative self-induced broadband transparency due to a qualitatively novel nonlinear mechanism that is different from conventional electromagnetically induced transparency (EIT) or its classical analogs. A near complete disappearance of resonant absorption under a range of applied rf flux is observed experimentally and explained theoretically. The transparency comes from the intrinsic bi-stability and can be tuned on/ off easily by altering rf and dc magnetic fields, temperature and history. Hysteretic in situ 100% tunability of transparency paves the way for auto-cloaking metamaterials, intensity dependent filters, and fast-tunable power limiters. An rf-SQUID metamaterial is shown to have qualitatively the same behavior as a single rf-SQUID with regards to dc flux, rf flux and temperature tuning. The two-tone response of self-resonant rf-SQUID meta-atoms and metamaterials is then studied here via intermodulation (IM) measurement over a broad range of tone frequencies and tone powers. A sharp onset followed by a surprising strongly suppressed IM region near the resonance is observed. This behavior can be understood employing methods in nonlinear dynamics; the sharp onset, and the gap of IM, are due to sudden state jumps during a beat of the two-tone sum input signal. The theory predicts that the IM can be manipulated with tone power, center frequency, frequency difference between the two tones, and temperature. This quantitative understanding potentially allows for the design of rf-SQUID metamaterials with either very low or very high IM response.

The case for quantum key distribution

Quantum key distribution (QKD) promises secure key agreement by using quantum mechanical systems. We argue that QKD will be an important part of future cryptographic infrastructures. It can provide long-term confidentiality for encrypted information without reliance on computational assumptions. Although QKD still requires authentication to prevent man-in-the-middle attacks, it can make use of either information-theoretically secure symmetric key authentication or computationally secure public key authentication: even when using public key authentication, we argue that QKD still offers stronger security than classical key agreement.

Generalising unitary time evolution

In this third Quantum Interaction (QI) meeting it is time to examine our failures. One of the weakest elements of QI as a field, arises in its continuing lack of models displaying proper evolutionary dynamics. This paper presents an overview of the modern generalised approach to the derivation of time evolution equations in physics, showing how the notion of symmetry is essential to the extraction of operators in quantum theory. The form that symmetry might take in non-physical models is explored, with a number of viable avenues identified.

The role of non-factorizability in determining "pseudo-classical" non-separability

This article introduces a “pseudo classical” notion of modelling non-separability. This form of non-separability can be viewed as lying between separability and quantum-like non-separability. Non-separability is formalized in terms of the non-factorizabilty of the underlying joint probability distribution. A decision criterium for determining the non-factorizability of the joint distribution is related to determining the rank of a matrix as well as another approach based on the chi-square-goodness-of-fit test. This pseudo-classical notion of non-separability is discussed in terms of quantum games and concept combinations in human cognition.

A quantum probability perspective on borderline vagueness

The term “vagueness” describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno’s sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib’s and Pelletier’s (2011) theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substan- tial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon.

Quantum one-time programs

A one-time program is a hypothetical device by which a user may evaluate a circuit on exactly one input of his choice, before the device self-destructs. One-time programs cannot be achieved by software alone, as any software can be copied and re-run. However, it is known that every circuit can be compiled into a one-time program using a very basic hypothetical hardware device called a one-time memory. At first glance it may seem that quantum information, which cannot be copied, might also allow for one-time programs. But it is not hard to see that this intuition is false: one-time programs for classical or quantum circuits based solely on quantum information do not exist, even with computational assumptions. This observation raises the question, "what assumptions are required to achieve one-time programs for quantum circuits?" Our main result is that any quantum circuit can be compiled into a one-time program assuming only the same basic one-time memory devices used for classical circuits. Moreover, these quantum one-time programs achieve statistical universal composability (UC-security) against any malicious user. Our construction employs methods for computation on authenticated quantum data, and we present a new quantum authentication scheme called the trap scheme for this purpose. As a corollary, we establish UC-security of a recent protocol for delegated quantum computation.

Quantum direct secret sharing with efficient eavesdropping-check and authentication based on distributed fountain codes

We propose to use a simple and effective way to achieve secure quantum direct secret sharing. The proposed scheme uses the properties of fountain codes to allow a realization of the physical conditions necessary for the implementation of no-cloning principle for eavesdropping-check and authentication. In our scheme, to achieve a variety of security purposes, nonorthogonal state particles are inserted in the transmitted sequence carrying the secret shares to disorder it. However, the positions of the inserted nonorthogonal state particles are not announced directly, but are obtained by sending degrees and positions of a sequence that are pre-shared between Alice and each Bob. Moreover, they can confirm that whether there exists an eavesdropper without exchanging classical messages. Most importantly, without knowing the positions of the inserted nonorthogonal state particles and the sequence constituted by the first particles from every EPR pair, the proposed scheme is shown to be secure.

A formalization of logical imaging for information retrieval using quantum theory

In this paper we introduce a formalization of Logical Imaging applied to IR in terms of Quantum Theory through the use of an analogy between states of a quantum system and terms in text documents. Our formalization relies upon the Schrodinger Picture, creating an analogy between the dynamics of a physical system and the kinematics of probabilities generated by Logical Imaging. By using Quantum Theory, it is possible to model more precisely contextual information in a seamless and principled fashion within the Logical Imaging process. While further work is needed to empirically validate this, the foundations for doing so are provided.

Ge/Si quantum dot formation from non-uniform cluster fluxes

The controlled growth of ultra-small Ge/Si quantum dot (QD) nuclei (≈1 nm) suitable for the synthesis of uniform nanopatterns with high surface coverage, is simulated using atom-only and size non-uniform cluster fluxes. It is found that seed nuclei of more uniform sizes are formed when clusters of non-uniform size are deposited. This counter-intuitive result is explained via adatom-nanocluster interactions on Si(100) surfaces. Our results are supported by experimental data on the geometric characteristics of QD patterns synthesized by nanocluster deposition. This is followed by a description of the role of plasmas as non-uniform cluster sources and the impact on surface dynamics. The technique challenges conventional growth modes and is promising for deterministic synthesis of nanodot arrays.

Explanation of relevance judgement discrepancy with quantum interference

A key concept in many Information Retrieval (IR) tasks, e.g. document indexing, query language modelling, aspect and diversity retrieval, is the relevance measurement of topics, i.e. to what extent an information object (e.g. a document or a query) is about the topics. This paper investigates the interference of relevance measurement of a topic caused by another topic. For example, consider that two user groups are required to judge whether a topic q is relevant to a document d, and q is presented together with another topic (referred to as a companion topic). If different companion topics are used for different groups, interestingly different relevance probabilities of q given d can be reached. In this paper, we present empirical results showing that the relevance of a topic to a document is greatly affected by the companion topic’s relevance to the same document, and the extent of the impact differs with respect to different companion topics. We further analyse the phenomenon from classical and quantum-like interference perspectives, and connect the phenomenon to nonreality and contextuality in quantum mechanics. We demonstrate that quantum like model fits in the empirical data, could be potentially used for predicting the relevance when interference exists.