Dynamics of the Disk-Pendulum Coupled System With Vertical Excitation

This paper investigates the static and dynamic characteristics of the semi-elliptical rocking disk on which a pendulum pinned. This coupled system’s response is also analyzed analytically and numerically when a vertical harmonic excitation is applied to the bottom of the rocking disk. Lagrange’s Equation is used to derive the motion equations of the disk-pendulum coupled system. The second derivative test for the system’s potential energy shows how the location of the pendulum’s pivotal point affects the number and stability of equilibria, and the change of location presents different bifurcation diagrams for different geometries of the rocking disk. For both vertically excited and unforced cases, the coupled system shows chaos easily, but the proper chosen parameters can still help the system reach and keep the steady state. For the steady state of the vertically excited rocking disk without a pendulum, the variation of the excitation’s amplitude and frequency result in the hysteresis for the amplitude of the response. When a pendulum is pinned on the rocking disk, three major categories of steady states are presently in the numerical way.

Integrated System Technologies for Modular Trapped Ion Quantum Information Processing

Although trapped ion technology is well-suited for quantum information science, scalability of the system remains one of the main challenges. One of the challenges associated with scaling the ion trap quantum computer is the ability to individually manipulate the increasing number of qubits. Using micro-mirrors fabricated with micro-electromechanical systems (MEMS) technology, laser beams are focused on individual ions in a linear chain and steer the focal point in two dimensions. Multiple single qubit gates are demonstrated on trapped 171Yb+ qubits and the gate performance is characterized using quantum state tomography. The system features negligible crosstalk to neighboring ions (< 3e-4), and switching speeds comparable to typical single qubit gate times (< 2 us). In a separate experiment, photons scattered from the 171Yb+ ion are coupled into an optical fiber with 63% efficiency using a high numerical aperture lens (0.6 NA). The coupled photons are directed to superconducting nanowire single photon detectors (SNSPD), which provide a higher detector efficiency (69%) compared to traditional photomultiplier tubes (35%). The total system photon collection efficiency is increased from 2.2% to 3.4%, which allows for fast state detection of the qubit. For a detection beam intensity of 11 mW/cm2, the average detection time is 23.7 us with 99.885(7)% detection fidelity. The technologies demonstrated in this thesis can be integrated to form a single quantum register with all of the necessary resources to perform local gates as well as high fidelity readout and provide a photon link to other systems.

Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators.

We study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast time scale of our oscillators (on the order of 100ns) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.