Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite-size spin chains with a chiral spin ground state observed on biatomic Fe chains deposited on iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the noncollinear nature of the classical ground state, there is a significant zero-point reduction of the ground-state magnetization of the spin spiral. Second, there is a critical external field from which the ground state changes from chiral spin ground state to collinear ferromagnetic order. The character of the two lowest-energy spin waves changes from edge modes to confined bulk modes over this critical field. Third, in the spin-spiral state, the spin-wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.

Theory of many-particle correlations and optical properties of semiconductor quantum dots : photons and quantum dots

Otto-von-Guericke-Universität Magdeburg, Fakultät für Naturwissenschaften, Dissertation, 2016

Modern quantum theory.

Includes bibliography.

Quantum theory of scattering

Includes bibliography.

The quantum theory.

Mode of access: Internet.

Quantum theory, with applications to chemistry.

Reproduced from typewritten copy.

On the quantum theory of line-spectra,

Issued in three parts.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

Synapses, quantum theory and panpsychism

The introduction situates the ‘hard problem’ in its historical context and argues that the problem has two sides: the output side (the Kant-Eccles problem of the freedom of the Will) and the input side (the problem of qualia). The output side ultimately reduces to whether quantum mechanics can affect the operation of synapses. A discussion of the detailed molecular biology of synaptic transmission as presently understood suggests that such affects are unlikely. Instead an evolutionary argument is presented which suggests that our conviction of free agency is an evolutionarily induced illusion and hence that the Kant-Eccles problem is itself illusory. This conclusion is supported by well-known neurophysiology. The input side, the problem of qualia, of subjectivity, is not so easily outflanked. After a brief review of the neurophysiological correlates of consciousness (NCC) and of the Penrose-Hameroff microtubular neuroquantology it is again concluded that the molecular neurobiology makes quantum wave-mechanics an unlikely explanation. Instead recourse is made to an evolutionarily- and neurobiologically-informed panpsychism. The notion of an ‘emergent’ property is carefully distinguished from that of the more usual ‘system’ property used by most dual-aspect theorists (and the majority of neuroscientists) and used to support Llinas’ concept of an ‘oneiric’ consciousness continuously modified by sensory input. I conclude that a panpsychist theory, such as this, coupled with the non-classical understanding of matter flowing from quantum physics (both epistemological and scientific) may be the default and only solution to the problem posed by the presence of mind in a world of things.

Projected equations of motion approach to hybrid quantum/classical dynamics in dielectric-metal composites

We introduce a hybrid method for dielectric-metal composites that describes the dynamics of the metallic system classically whilst retaining a quantum description of the dielectric. The time-dependent dipole moment of the classical system is mimicked by the introduction of projected equations of motion (PEOM) and the coupling between the two systems is achieved through an effective dipole-dipole interaction. To benchmark this method, we model a test system (semiconducting quantum dot-metal nanoparticle hybrid). We begin by examining the energy absorption rate, showing agreement between the PEOM method and the analytical rotating wave approximation (RWA) solution. We then investigate population inversion and show that the PEOM method provides an accurate model for the interaction under ultrashort pulse excitation where the traditional RWA breaks down.

(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.

Spectral graph theory with applications to quantum adiabatic optimization

In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.

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.