I investigate some algebras and calculi naturally associated with the symplectic and metric Clifford algebras. In particular, I reformulate the well known Lepage decomposition for the symplectic exterior algebra in geometrical form and present some new results relating to the simple subspaces of the decomposition. I then present an analogous decomposition for the symmetric exterior algebra with a metric. Finally, I extend this symmetric exterior algebra into a new calculus for the symmetric differential forms on a pseudo-Riemannian manifold. The importance of this calculus lies in its potential for the description of bosonic systems in Quantum Theory.

The advent of quantum computing has challenged classical conceptions of which problems are efficiently solvable in our physical world. This raises the general question of what broad relationships exist between physical principles and computation. The current thesis explores this question within the operationally-defined framework of generalised probabilistic theories. In particular, we investigate the limits on computational power imposed by simple physical principles. At present, the best known upper bound on the power of quantum computers is that <b>BQP</b> is contained in <b>AWPP</b>, where <b>AWPP</b> is a classical complexity class contained in PP. We define a circuit-based model of computation in the above mentioned operational framework and show that in theories where local measurements suffice for tomography, efficient computations are also contained in <b>AWPP</b>. Moreover, we explicitly construct a theory in which the class of efficiently solvable problems exactly equals <b>AWPP</b>, showing this containment to be tight. We also investigate how simple physical principles bound the power of computational paradigms which combine computation and communication in a non-trivial fashion, such as interactive proof systems. Additionally, we show how some of the essential components of computational algorithms arise from certain natural physical principles. We use these results to investigate the relationship between interference behaviour and computational power, demonstrating that non-trivial interference behaviour is a general resource for post-classical computation. We then investigate whether post-quantum interference is a resource for post-quantum computation. Sorkin has defined a hierarchy of possible post-quantum interference behaviours where, informally, the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. In quantum theory, at most pairs of paths can ever interact in a fundamental way. We consider how Grover's speed-up depends on the order of interference in a theory, and show that, surprisingly, the quadratic lower bound holds regardless of the order of interference.

In this thesis I address two different topics in quantum theory. The first one is the long discussed Schrodinger's cat problem, and the issues related to having a macroscopic superposition state. I show that the quantum theory provides full explanation to the problem. In the second part, I discuss the time measurement related issues in quantum mechanics. Since there does not exist any time operator in quantum mechanics generally, time is not directly measurable. Therefore we should devise other methods to register time. We study different time-energy relations and will find that accurate clocks have high energy uncertainties. If we use accurate clocks in quantum systems to observe their time evolutions, their high energy uncertainties interfere with system's normal evolution and slows it down. I also provide a formal proof to a previously suggested limiting accuracy relation on the measurements of the time-of-arrival experiments. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

No description available.

Thesis: M.S., Massachusetts Institute of Technology, Department of Physics, 1978 / Includes bibiliographical references. / M.S. / M.S. Massachusetts Institute of Technology, Department of Physics

The phenomenon of dynamically induced anomalous diffusion is both the classical and quantum kicked rotor is investigated in this dissertation. We discuss the capability of the quantum mechanical version of the system to reproduce for extended periods the corresponding classical chaotic behavior.

In this thesis we investigate different phases of matter in systems driven out of equilibrium. In particular, we focus on current driven metal insulator transitions and on the physics of negative conductivity in photoexcited metals. We present a new mechanism by which a modest applied electric field can destabilize a correlated insulating phase at finite temperature, without directly exciting carriers across the gap. We investigate the consequences of a metal insulator phase interface, and show that the large difference in Seebeck coefficients leads to a substantial heat generation or removal at the interface depending on the direction of the applied electric current; our findings explain the key features of recent interesting experiments in Calcium Ruthenate. We also analyze a model of a metal coupled to a strongly photoexcited phonon mode and show that under general conditions the system exhibits a negative conductivity, even long after the removal of the pump; we study the phenomenological consequences of such state and find that it leads to a novel and purely non-equilibrium collective mode coupling charge and entropy. The resonance of this mode with probe radiation induces an enhancement of the optical reflectivity and can explain the experimental reports of the non-equilibrium state in photoexcited fullerides.

Photons are robust carriers of quantum information as they can propagate long distances without losing quantum entanglement and coherence. Compared to quantum information in matter-based carriers, such as superconducting oscillators, trapped ions and atoms, quantum dots, and vacancy centers in crystals, the photonic quantum states are robust against perturbations from the environment, such as parasitic electromagnetic fields and thermal fluctuations (phonons), making it an ideal candidate for room-temperature-based quantum metrology and information processing applications. Such robustness is due to photon-photon scattering in the vacuum being extremely improbable and photon-atom interactions being in the linear regime for most materials. Nevertheless, photon-photon or photon-atom nonlinear interactions are also critical for all quantum photonic applications as nonlinearity is required for generating non-classical states of light. Furthermore, nonlinear interactions greatly expand the variety of Hamiltonian that can be engineered for a given system or subsystem, which is a direct measure of the system's functionality. Thus, the ability to engineer nonlinear interactions has been one of the primary research focuses in quantum photonics. This thesis presents research on using nonlinear photonic chips to harness the unique properties offered by quantum mechanics, with applications in precision metrology and information procession. Atoms possess a rich set of quantum properties that have no counterparts in the classical world. Even in warm vapor form, atomic gases maintain sufficient coherence for tasks, including time keeping, electric field sensing and quantum memories. We develop chip-based light sources that can interact with narrow-band atomic transitions in order to miniaturize these applications. Typical Alkali atoms have transition around the visible light regime, where photonic materials exhibit strong normal group-velocity dispersion (GVD) which inhibits light generation via nonlinear interactions. We offer a systematic solution by re-examining the dispersion engineer techniques, which revealed that higher-order waveguide modes can have stronger anomalous GVD. With this technique, we demonstrate on-chip mode-locked pulses (Kerr combs) at a record-low wavelength, which can be used for high-precision atomic clocks. We also develop chip-based narrow-band high-brightness photon sources at the visible regime using nonlinear interactions. Such photons can interact with atom-based quantum memories and gates, which can find applications in both quantum communication and computation. Squeezed state is also an important class of non-classical states with key applications in quantum metrology, quantum simulation, and continuous-variable quantum information processing. Typically, squeezed states are generated using χ² processes, which are not readily available on most photonic platforms. For the first time, we demonstrate squeezed state generation using a dual-pumped four-wave-mixing process, which we implement on a silicon-nitride chip. To perform quantum simulation or computation with squeezed states, we need programmable interferometer arrays and photon-number resolving (PNR) detectors. Current PNR detectors rely on superconducting effects which require Kelvin level temperatures. We propose a room-temperature PNR scheme based on optical nonlinearity. We show that using cascaded χ² interactions, a single photon can impart an observable phase on a probe beam, which can be implemented within the current fabrication capabilities. Our squeezed-state-generation and PNR-detection devices lay a practical path towards room-temperature quantum simulation and computing.

In this thesis I present contributions to the development, analysis and application of tensor network state methods for numerically exact quantum dynamics in one and two-dimensional lattice systems. The setting of numerically exact quantum dynamics is introduced in Chapter 2. This includes a discussion of exact diagonalization approaches and massively parallel implementations thereof as well as a brief introduction of tensor network states. In Chapter 3, I perform a detailed analysis of the performance of n-ary tree tensor network states for simulating the dynamics of two-dimensional lattices. This constitutes the first application of this class of tensor network to dynamics in two spatial dimensions, a long-standing challenge, and the method is found to perform on par with existing state-of-the-art approaches. Chapter 4 showcases the efficacy of a novel tensor network format I developed, tailored to electron-phonon coupled problems in their single-electron sector, through an application to the Holstein model. The applicability of the approach to a broad range of parameters of the model allows to reveal the strong influence of the spread of the electron distribution on the initial state of the phonons at the site where the electron is introduced, for which a simple physical picture is offered. I depart from method development in Chapter 5 and analyse the prospects of using tensor network states evolved using the time-dependent variational principle as an approximate approach to determine asymptotic transport properties with a finite, moderate computational effort. The method is shown to not yield the correct asymptotics in a clean, non-integrable system and can thus not be expected to work in generic systems, outside of finely tuned parameter regimes of certain models. Chapters 6 and 7 are concerned with studies of spin transport in long-range interacting systems using tensor network state methods. For the clean case, discussed in Chapter 6, we find that for sufficiently short-ranged interactions, the spreading of the bulk of the excitation is diffusive and thus dominated by the local part of the interaction, while the tail of the excitation decays with a powerlaw that is twice as large as the powerlaw of the interaction. Similarly, in the disordered case, analysed in Chapter 7, we find subdiffusive transport of spin and sub-linear growth of entanglement entropy. This behaviour is in agreement with the behaviour of systems with local interactions at intermediate disorder strength, but provides evidence against the phenomelogical Griffith picture of rare, strongly disordered insulating regions. We generalize the latter to long-ranged interactions and show that it predicts to diffusion, in contrast to the local case where it results in subdiffusive behaviour.

Proteins are made of vast chains of amino acids that twist and fold into intricate designs. These structures are held in place by networks of noncovalent interactions. One of these, the hydrogen bond, forms bridges between adjacent pieces of the protein chain and is one of the most important contributors to the shape and stability of proteins. Hydrogen bonds come in all shapes and sizes and a full understanding of these not only aids in our understanding of proteins in general but can bridge the gap to finding cures to many protein-related diseases, such as sickle-cell anemia. The primary aim of this thesis is to discover if a specific type of hydrogen bond, the N-H···N bond, occurs within proteins and if so, if it contributes to the structure and stability of proteins.