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  • Silicon Qubits
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  • The current variety of treatment options for epilepsy leaves 30% of those who suffer from this chronic neurological disease without a cure. Therefore, this senior thesis project aims to uncover new insights about the brain structure that underlies susceptibility to epilepsy in hopes that a greater understanding of this underlying structure will catalyze the discovery of novel therapeutic methods which target these underlying differences in brain structure. To drive the discovery of new insights about underlying structure, this project addresses the following tension found in the literature: high frequency oscillations occur in both the brains of those with epilepsy and in the brains of those without epilepsy. Only when high frequency oscillations occur in the brains of those with epilepsy does the brain enter a state of unstable dynamics and seizure activity. This suggests that there is a difference in underlying structure between epileptic and non-epileptic brains, and this study uses computational modeling of neuronal firing to characterize these differences. First, based on a firing rate model, we find that within the phase space of the weight values, there is a band of stability from which one might predict the stability of a set of weights. Then, in the next two versions of the model, we add Hebbian plasticity and homeostatic plasticity. Only through the addition of Hebbian plasticity and homeostatic plasticity does high frequency oscillation, the manipulation described in our driving question, have a lasting effect on the weights. With the addition of a rate based Hebbian plasticity model to the base firing rate model, we find that weights can be perturbed from this band of stability through Hebbian plasticity. Adding a weight based homeostatic plasticity model to the base firing rate and Hebbian plasticity model then gives insight into the fact that having a target weight within a certain location with respect to the band of stability can rescue stability of a set of original weights from the destabilizing effects of Hebbian plasticity. Finally, we explore the effect of high frequency oscillation on various weight combinations within the phase space, and we find that certain weight combinations are projected to an unstable state through high frequency oscillation while other weight combinations remain at a stable state even in the face of high frequency oscillation. The unifying characteristic of those weights which remain stable in the face of high frequency oscillation remains an open question. However, in the process of investigating high frequency oscillations, it was found that weights on the edge of the band of stability are more robust to instability through Hebbian plasticity than weights on the band of stability that are further from the edge. These results suggest that the differential response to high frequency oscillation between epileptic and non-epileptic brains can be attributed at least in part to the location of weights with respect to the band of stability.
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  • Superconducting Qubits
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  • This thesis presents the results of experimental work aimed at realizing the multimodal Rabi Hamiltonian of quantum optics in a circuit QED device. We have fabricated and tested three coplanar waveguide resonators of fundamental frequency ¿0/(2¿) = 92 MHz, two of which contained superconducting transmon qubits. Both qubit devices failed to exhibit signs of light-matter coupling, as deduced through two different measurement techniques. The experimental progress was supplemented with numerical simulations of the multimodal Jaynes-Cummings and Rabi Hamiltonians, which attempted to study cavity-qubit dynamics in the multimodal regime for various light-matter coupling strengths. For a 2-mode Rabi model, we report the observation of a novel localization-delocalization transition in photon occupation between the two modes, which displays signatures that should be readily measured in experiment. Future work should continue attempts to realize strong, multimodal light-matter coupling in circuit QED so as to verify the existence of this transition.
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  • Oscillations are present both in natural speech and in the brain. This may be more than a mere coincidence. Re-instating information in the theta-frequency band has been shown to remarkably improve intelligibility. Moreover, a recent theory has proposed the existence of an internal tracking mechanism that parses and decodes incoming speech at a theta rhythm. This study sought to clarify the importance of theta-frequency band oscillations for speech comprehension as well as to establish their significance as a speech processing mechanism in the human auditory cortex. Here, it is shown that exposure to information in the theta-frequency range can restore intelligibility to a degraded, previously unintelligible stimulus, producing an auditory pop-out effect. This effect was observed regardless of whether participants were exposed to the intact sentence in the auditory or the visual domain. Compressing or extending the presentation speed of the intact sentence reduced the size of the effect, except for an extension rate of 1.5 times the original speed. At a neural level, it was previously unknown whether theta oscillations in auditory regions are internally generated or merely reflect stimulus driven evoked responses. Electrocorticographical recordings from one clinical patient provide evidence for the existence of theta-frequency oscillations in auditory regions, specifically the superior temporal gyrus, which are internally generated and effectively track incoming speech.
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  • Army ants (Eciton burchellii) have been studied for nearly a century, but observable patterns in their traffic organization have not yet been explored, despite the fact that this organization contributes greatly to their optimal foraging. Using pheromones and tactile cues to transmit information from ant to ant, they coordinate their movements in order to optimize traffic and create a collective behavior that increases the overall efficiency of the colony. Garnier et al. (2013) discovered that E. burchellii traffic possesses regular, periodic oscillations that allow it to gain maximum stability. In this paper, we explored these traffic oscillations at trail junctions to determine how army ants optimize their network of foraging trails. After conducting research at La Selva Biological Station in Costa Rica, we found that the mean oscillation frequencies and periods of army ant traffic are uniform and unrelated to traffic direction. Despite this overarching uniformity, each zone of a trail junction possesses a different oscillation frequency compared to the other two zones of the same junction. Lastly, oscillation frequency increases as traffic becomes more unidirectional. By displaying differential oscillatory behavior at trail junctions, army ants spontaneously adapt to their constantly changing environment in order to optimize traffic dynamics. Finally, we propose ideas for future research that have the potential to delve deeper into the study of trail junctions.
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  • The advent of superconducting quantum circuits as a robust scientific platform and contender for quantum computing applications is the result of decades of research in light-matter interaction, low-temperature physics, and microwave engineering. There is growing interest to use this advancing technology to study domains of light-matter interaction that were previously thought to be beyond experimental reach. Our work is part of an initiative to explore non-equilibrium condensed matter physics using photons instead of atoms. Open questions in this area currently pose significant challenges theoretically due to analytical complexity and system sizes which prohibit complete numerical simulations, thus experiment-based research has the potential to lead to significant advancements in this field. Here we examine phenomena that arise when moving beyond standard single-mode strong coupling towards the realm of many-body physics with light in two distinct directions. First we study multimode strong coupling, where a single artificial atom or qubit is simultaneously strongly coupled to a large, but discrete number of non-degenerate photonic modes of a cavity with coupling strengths comparable to the free spectral range. This domain, which falls in between small, discrete and continuum Hilbert spaces, is experimentally realized by coupling a qubit to a low fundamental frequency coplanar waveguide cavity. In this system we report on resonance fluorescence and narrow linewidth emission directly resulting from complex qubit mediated mode-mode interactions. In the second part we explore qubits strongly coupled to photonic crystals, which give rise to exotic physical scenarios, beginning with single and multi-excitation qubit-photon dressed bound states comprising induced, spatially localized photonic modes, centered around the qubits, and the qubits themselves. The localization of these states changes with qubit detuning from the band-edge, offering an avenue of in situ control of bound state interaction. Due to their localization-dependent interaction, these states offer the ability to create one-dimensional chains of bound states with tunable interactions that preserve the qubits' spatial organization, a key criterion for realization of certain quantum many-body models. The unique domains of light-matter interaction discussed here are a subset of exciting research initiatives growing our general understanding of complex, strongly coupled quantum systems.
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  • Circuit quantum electrodynamics (cQED) uses superconducting circuit elements as its building blocks for controllable quantum systems and has become a promising experimental platform for quantum computation and quantum simulation. The ability to tune the coupling rate between circuit elements extends the controllability and flexibility of cQED devices and can be utilized to improve device performance. This thesis presents the study, implementation and application of tunable coupling devices in cQED. The tunability originates from the basic principles of quantum superposition and interference, and unwanted interactions can be suppressed by destructive interference. Following this principle, we design and conduct two experiments that demonstrate the utility of tunable coupling for better device performances in quantum information processing. The first experiment aims to improve the coherence of qubits against noise. We implement a qubit whose frequency and dispersive coupling to a readout resonator can be tuned independently. When the coupling rate is tuned to near zero, the qubit becomes immune to photon number fluctuations in the resonator and exhibits robust coherence time in the presence of noise. The second experiment extends to a multi-qubit system where crosstalk between qubits causes error in quantum gates. We develop a two-qubit device and suppress crosstalk by tuning the ZZ coupling rate between the qubits. The tunable dispersive coupling can also be parametrically modulated to implement a two-qubit entangling gate in the low crosstalk regime. Those devices provide flexible and promising building blocks for cQED systems.
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  • We present a design for a heterojunction bipolar transistor based Colpitts oscillator for cryogenic capacitance measurement. We also present the design of an interdigitated capacitor to detect changes in dielectric constant of a fluid on the surface of a printed circuit board, along with frequency measurements of this system in air and liquid nitrogen. Designs and frequency measurements are also presented for a tunnel diode based oscillator.
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  • Superconducting circuits are an ideal platform for simulating many body physics with photons. Such simulations are greatly enhanced by the ability to engineer photon-photon interactions. Single photon-photon interactions are difficult to design because of the massive nonlinearities required to achieve a strong interaction between individual photons. Nonlinearities arising from single photons are present in the dispersive limit of Jaynes-Cummings Hamiltonian. In this limit, the interaction of two photons is mediated by a virtual qubit excitation. This system can exhibit behavior known as photon blockade, where the presence of a single photon in an optical cavity prevents other photons from entering the cavity. The light exiting the cavity is then antibunched, which serves both as evidence of the quantization of the electromagnetic field and as a signature of photon blockade. Experimentally, we explore the strong qubit-field coupling regime of the Jaynes-Cummings Hamiltonian with circuit quantum electrodynamics. Using conventional microfabrication techniques, we build a superconducting microwave resonator coupled to a transmon qubit based on the Josephson junction. We observe photon number splitting of the qubit energy, demonstrating that we are in the strong coupling qubit-field coupling regime, allowing us to perform quantum non-demolition measurements of the cavity photon number, and providing conclusive evidence of the quantization of the electromagnetic field into photons. Further, we observe nonlinear effects arising from a small photon number consistent with the nonlinear Kerr Hamiltonian approximation of the Jaynes-Cummings Hamiltonian. Because the cavity dissipation ¿ is larger than the single photon cavity frequency shift ¿, we are unable to observe photon blockade or measure photon antibunching. By moving the qubit to a region of the transmission line with a higher electric field and using a tunable SQUID (superconducting quantum interference device) as a qubit, we will be able to realize strong photon-photon interactions for use in quantum simulators.
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