Philip C Stamp

In this thesis we discuss various aspects of low energy quantum gravity from a number of different angles. The ultimate goal we have in mind is to prepare ourselves for the upcoming wave of low-energy experiments which may test quantum gravity. In the first part of this thesis we remain within "conventional'' quantum theory. We start with a study of quantum decoherence via the emission of low energy gravitational radiation. We find that after sufficiently long times this radiation can completely decohere a matter system. In studying decoherence we needed a better understanding of gauge invariance and physical states in path-integrals with prescribed boundary data. We generalize the standard Faddeev-Popov procedure to fit this purpose, and in doing so we better understand the nature of electric fields around quantum charges. The analogous work is also done in linearized quantum gravity. This language is useful for analyzing the debate around a recently proposed gravitational-entanglement experiment. We do such an analysis, and ultimately agree that these experiments indeed test conventional quantum gravity. As a tangential project we study the interactions of quarks in a background gluon condensate, and show how this can cause confinement.In the second part of the thesis we study an "alternative'' quantum gravity theory, the Correlated WorldLine (CWL) theory. We study the theory perturbatively, and also make use of a large-N expansion to study it non-perturbatively. We apply our results to physical systems: verifying that two-path systems experience "path-bunching'' which suppresses superpositions of massive objects. We also predict a frequency band in the microhertz range where tests of CWL involving massive objects are expected to see a signature.

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The electromagnetic and gravitational fields transfer information between physical systems. This work is an attempt to better understand how matter systems communicate quantum information with one another using these fields, and also how quantum information about matter is broadcast into the fields themselves. We study the former process in Part I and the latter in Part II, by answering two distinct but related questions.Part I of this work studies experimental proposals to observe gravity-induced quantum entanglement between matter systems. If these are successful, it can be argued that they would be the first experimental witness of a quan- tum superposition of space-time geometries, although this interpretation of the proposals has been the subject of vigorous debate. To address this, we first utilize the “quantum action principle” to quantize the electromagnetic and (linearized) gravitational fields. We find that for the quantization to be self-consistent, physical quantum states in the theory must be gauge- and diffeomorphism-invariant. We then show that these constraints are the root cause of the confusion surrounding the proposed gravity-induced en- tanglement experiments. A deeper understanding, however, of how these constraints change when assigning quantum states to different hypersur- faces in space-time provides a satisfying resolution to the debate over the experimental proposals. We conclude that if gravity-induced entanglement is observed, it should be interpreted as experimental evidence in favor of the quantum nature of space-time.Part II then addresses the quantum information content of low energy “soft” radiation. We first show that whether matter particles emit such radiation depends entirely upon the past and future boundaries of the worldlines they follow. This observation explains all tree-level “soft theorems” in both electromagnetism and gravity. We then quantize the electromagnetic and gravitational fields asymptotically, at null infinity. Again, the quantization compels us to ensure physical states are invariant under gauge transforma- tions and diffeomorphisms which persist in the asymptotic limit. Invariance under these “large” transformations fully constrains the state of the leading- order soft radiation, meaning that this radiation cannot carry quantum in- formation. Finally, we illustrate how our construction also avoids infrared divergences when predicting decoherence rates in a model interferometry experiment.

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We present a theoretical discussion of various aspects of the dynamics of information in quantum systems of qubits. We begin by reviewing ideas about entanglement and information in systems of qubits, different models for realistic qubits coupled to an external environment, how this causes the loss of information stored in qubits, and some practical designs for qubits that have been created. Then we study how the state of many-body systems can be decomposed in terms of its different subsystems and derived a hierarchy of equations describing the motion of these different parts. We show that in a qubit system, the central objects in this hierarchy are correlators between different components of different qubits. Systems where the environment coupled to a central qubit is a "spin bath'' of environmental qubits are then considered in detail and we find that information lost by the central qubit is transferred via a cascade to higher and higher order correlations with the environment. We discuses this process in the realistic example of an "Fe₈'' magnetic molecule qubit. Finally we discuss simple models of the dynamics of many entangled qubits.

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I investigate the dynamics of multi-state central systems coupled bilinearly to an externaloscillator bath within the noninteracting-blip approximation. I focus on both a 3-siteconfiguration, as well as a 2-site model for the central systems of interest. The 2-sitemodel, dubbed the dual-coupling spin-boson (DCSB) model, includes both diagonal andnon-diagonal system-bath couplings, whereas the 3-site model considers only diagonalcouplings. The bath spectral densities considered in this work include both Ohmic andsuper-Ohmic forms, as well as single optical phonon peaks. This work is motivated by therecent observance of long-lived quantum coherence effects in the photosynthetic organismknown as the Fenna-Matthews-Olson (FMO) complex. The models investigated in thisthesis are applied to this system in an attempt to explain its remarkably efficient excitontransfer mechanism, as well as to shed light on the functionality of coherence. The DCSBmodel is shown to reproduce the rapid exciton transfer times as well as the relatively longcoherence times observed in the FMO complex. The non-diagonal system-bath couplingis shown to play a crucial role in this process. This can be attributed to the inelasticphonon-assisted tunnelling (IPAT) mechanism arising from the presence of significantnon-diagonal system-bath interactions. Conversely, the 3-site model predicts rapid butincoherent exciton transfer. This can be attributed to the presence of a resonant state inthe 3-site architecture, resulting in a relatively slow exciton transfer mode in the system.Therefore efficient exciton transfer requires a careful configuration of the chromophoreenergy landscape to avoid a resonant 3-site-V configuration. Furthermore, I concludethat coherence effects arising from excitons delocalised across multiple chromophores,promotes IPAT processes arising from non-diagonal system-bath couplings, producingrapid exciton transfer between chromophores. This offers a potential explanation as to thefunctional role that coherence plays in the energy transfer mechanism of photosynthesis.

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There are two kinds of environmental modes in open quantum systems: the delocalized modeswhich can typically be modeled by "oscillator bath" models and the localized modes which can be mapped to "spin bath" modes. To understand the quantum phenomena in photosynthetic energy transfer, we at first conduct thorough studies of the proper modeling of light harvesting molecules as well as their interactions with the central system. These modes can couple to the system by either modulating the on-site energy (Holstein coupling) or modulating the hopping amplitude (Peierls coupling). Only the Holstein couplings of delocalized modes have been extensively studied. The importance of other types of couplings is rarely discussed in the literature. For the spin bath, we study a particle hopping around a general lattice, coupled to a spin bath. Analytical results are found for the dynamics of the influence functional and for the reduced density matrix of the particle in various parameter regimes. Spin baths behave qualitatively differently from oscillator baths and dissipation and decoherence happen independently in different parameter regimes. For the Peierls couplings, we start with a dimer model for light harvesting molecules, which contains a reaction center and both types of phonon couplings. We find that the effect of Peierls type coupling on the transfer rate can be significant even when it is not noticeable in the spectrum. Our study suggests that Peierls couplings cannot be easily neglected in light harvesting molecules in which the energy difference between the sites is usually much larger than the hopping amplitude. We apply our method to a real light harvesting model. Although we do not have much detailed information of the Peierls couplings in vivo, we find that vibrational phonons can affect the path-selecting of the central particles as well as increasing the transfer rate.

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The quantum Ising model is perhaps the simplest possible model of a quantum magnetic material. Despite its simplicity, its versatility and wide range of applications, from quantum computation, to combinatorial optimization, to biophysics, make it one of the most important models of modern physics. In this thesis, we develop a general framework for studying quantum Ising systems with an arbitrary single ion Hamiltonian, with emphasis on the effects of quantum fluctuations, and the quantum phase transition between paramagnetic and ferromagnetic states that occurs when a magnetic field is applied transverse to the easy axis of the system. The magnetic insulating crystal LiHoF₄ is a physical realization of the quantum Ising model, with the additional features that the dominant coupling between spins is the long range dipolar interaction, and each electronic spin is strongly coupled to a nuclear degree of freedom. These nuclear degrees of freedom constitute a spin bath environment acting on the system. In this thesis, we present an effective low temperature Hamiltonian for LiHoF₄ that incorporates both these features, and we analyze the effects of the nuclear spin bath on the system. We find the lowest energy crystal field excitation in the system is gapped at the quantum critical point by the presence of the nuclear spins, with spectral weight being transferred down to a lower energy electronuclear mode that fully softens to zero at the quantum critical point. Furthermore, we present a toy model, the spin half spin half model, that illustrates the effects of an anisotropic hyperfine interaction on a quantum Ising system. We find the critical transverse field is increased when the longitudinal hyperfine coupling is dominant, as well as an enhancement of both the longitudinal electronic susceptibility and an applied longitudinal field. In addition, we present a field theoretic formalism for incorporating the effects of fluctuations beyond the random phase approximation in general quantum Ising systems. We find that any regular on site interaction, such as a nuclear spin bath, does not fundamentally alter the critical properties of a quantum Ising system. This formalism is used to calculate corrections to the magnetization of LiHoF₄.

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Quantum vortices are an important excitation in a wide variety of systems. They are a basic ingredient in our understanding of superfluids and superconductors --- indeed, the very definition of these phases relies heavily on the existence of quantum vortices. Despite this,the equation of motion of a quantum vortex remains controversial. In this thesis, we derive the two dimensional equation of motion of a vortex in superfluid helium, and also discuss adapting our derivation for a vortex in a ferromagnet dot.In addition to the undisputed superfluid Magnus force and vortex inertia, we derive the controversial Iordanskii force, a pair of memory forces, and the associated fluctuating force. The memory forces include a generalization of the usual longitudinal damping force, a frequency dependent inertial force, and a higher order, frequency dependent correction to the Iordanskii force. We quantify the slow limit in which these forces become local or frequency independent. In a superfluid, the motion is frequency dependent, manifest primarily through a suppression of the damping rate of the vortex motion. Magnetic vortex motion is typically at much lower frequencies and the memory effects can so far be ignored. Our analysis involves a careful separation of vortex and quasiparticle degrees of freedom. We prove definitively that there are no interactions that are first order in quasiparticle variables: therefore, all resulting forces on the vortex resulting from interactions with the quasiparticles are temperature-dependent. We calculate the vortex influence functional resulting from a velocity-dependent quadratic coupling with perturbed quasiparticles that have already been perturbed by the presence of the static vortex. From the vortex influence functional and the bare vortex action, we derive the full quantum equation of motion of a vortex.We relate our arguments and results to the wealth of ideas presented in the superfluid and magnetic literature. We discuss extensions of this work: on including normal fluid viscosity, dynamics of a multiple vortex configuration, to a finite system, and to a three-dimensional system.

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Many condensed matter problems involve a particle coupled to its environment. The polaron, originally introduced to describe electrons in a polarizable medium, describes a particle coupled to a bosonic field. The Holstein polaron model, although simple, including only optical Einstein phonons and an interaction that couples them to the electron density, captures almost all of the standard polaronic properties. We herein investigate polarons that differ significantly from this behaviour. We study a model with phonon-modulated hopping, and find a radically different behaviour at strong couplings. We report a sharp transition, not a crossover, with a diverging effective mass at the critical coupling. We also look at a model with acoustic phonons, away from the perturbative limit, and again discover unusual polaron properties. Our work relies on the Bold Diagrammatic Monte Carlo (BDMC) method, which samples Feynman diagrammatic expansions efficiently, even those with weak sign problems. Proposed by Prokof'ev and Svistunov, it is extended to lattice polarons for the first time here. We also use the Momentum Average (MA) approximation, an analytical method proposed by Berciu, and find an excellent agreement with the BDMC results. A novel MA approximation able to treat dispersive phonons is also presented, along with a new exact solution for finite systems, inspired by the same formalism.

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