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© 2014 by Wiley-VCH Verlag GmbH & Co. KGaA. Synchronization of two dissipatively coupled Van der Pol **oscillators** in the quantum regime is studied. Due to quantum noise strict **frequency** locking is absent and is replaced by a crossover from weak to strong **frequency** entrainment. The differences to the behavior of one quantum Van der Pol **oscillator** subject to an external drive are discussed. Moreover, a possible experimental realization of two coupled quantum Van der Pol **oscillators** in an optomechanical setting is described.

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cutoff **frequency**... spin **qubit**

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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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Sources of entangled pairs of photons can be used for encoding signals in quantum-encrypted communications, allowing a sender, Alice, and a receiver, Bob, to exchange keys without the possibility of eavesdropping. In fact, any quantum information system would require single and entangled photons to serve as **qubits**. For this purpose, semiconductor quantum dots (QD) have been extensively studied for their ability to produce entangled light and function as single photon sources.
The quality of such sources is evaluated based on three criteria: high efficiency, small multi-photon probability, and quantum indistinguishability. In this work, a simple quantum dot-based LED (E-LED) was used as a quantum light source for on-demand emission, indicating the potential for use as quantum information devices. Limitations of the device include the fine-structure splitting of the quantum dot excitons, their coherence lengths and charge carrier interactions in the structure.
The quantum dot-based light emitting diode was initially shown to operate in pulsed mode under AC bias **frequencies** of up to several hundreds of MHz, without compromising the quality of emission. In a Hong-ou-Mandel interference type experiment, the quantum dot photons were shown to interfere with dissimilar photons from a laser, achieving high two-photon interference (TPI) visibilities. Quantum entanglement from a QD photon pair was also measured in pulsed mode, where the QD-based entangled-LED (E-LED) was electrically injected at a **frequency** of 203 MHz.
After verifying indistinguishability and good entanglement properties from the QD photons under the above conditions, a quantum relay over 1km of fibre was demonstrated, using input **qubits** from a laser source. The average relay fidelity was high enough to allow for error correction for this BB84-type scheme. To improve the properties of the QD emission, an E-LED was developed based on droplet epitaxy (D-E) QDs, using a different QD growth technique. The relevant chapter outlines the process of QD growth and finally demonstration of quantum entanglement from an electrically injected diode, yielding improvements compared to previous E-LED devices.
For the same reason, an alternative method of E-LED operation based on resonant two-photon excitation of the QD was explored. Analysis of Rabi **oscillations** in a quantum dot with a bound exciton state demonstrated coupling of the ground state and the biexciton state by the external **oscillating** field of a laser, therefore allowing the transition between the two states. The results include a considerable improvement in the coherence length of the QD emission, which is crucial for future quantum network applications. We believe that extending this research can find application in quantum cryptography and in realising the interface of a quantum network, based on semiconductor nanotechnology.

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Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical self-sustained **oscillator** coupled to an external harmonic drive. Using the power spectrum we analyze synchronization in terms of **frequency** entrainment and **frequency** locking in close analogy to the classical case. We show that there is a steplike crossover to a synchronized state as a function of the driving strength. In contrast to the classical case, there is a finite threshold value in driving. Quantum noise reduces the synchronized region and leads to a deviation from strict **frequency** locking.

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main **frequencies**

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The pursuit of novel functional building blocks for the emerging field of quantum computing is one of the most appealing topics in the context of quantum technologies. Herein we showcase the urgency of introducing peptides as versatile platforms for quantum computing. In particular, we focus on lanthanide-binding tags, originally developed for the study of protein structure. We use pulsed electronic paramagnetic resonance to demonstrate quantum coherent **oscillations** in both neodymium and gadolinium peptidic **qubits**. Calculations based on density functional theory followed by a ligand field analysis indicate the possibility of influencing the nature of the spin **qubit** states by means of controlled changes in the peptidic sequence. We conclude with an overview of the challenges and opportunities opened by this interdisciplinary field.

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The quantum statistics of a laser result in noise when measurements of the beam are made. This noise sets a classical limit beyond which a laser cannot be used with increasing sensitivity. This quantum noise limit is imposed on many of the uses of lasers currently, especially in power limited devices such as optical communications. The statistics of the laser photon field can be modified to produce a non-classical state resulting in lower noise than the quantum noise limit when detected appropriately. This state, called a squeezed state, has been measured previously from a cavity enhanced optical parametric **oscillator** (OPO) only at **frequency** sidebands within the linewidth of the cavity. ¶ This thesis reports measurements of squeezing at microwave **frequency** sidebands on an optical beam produced by an optical parametric **oscillator**. This is the first reported measurement of squeezing at **frequency** sidebands at higher longitudinal modes of the cavity from an OPO. Noise reduction below the quantum noise limit is measured at sideband **frequencies** of 5 MHz, 1.7 GHz, 3.4 GHz and 5.1 GHz, corresponding to the zeroth, first, second and third longitudinal modes from the squeezed beam. These results are the highest **frequency** sideband measurements of squeezing to date. In addition to measuring squeezing at different longitudinal modes for the fundamental Gaussian spatial mode, non-classical noise reduction is measured at the same **frequencies** for a squeezed higher order spatial mode, TEM10. ¶ A single mode theoretical model of the OPO is presented, based on the work of ref. [1]. Computer simulations of the squeezing predicted by this model are developed and compared to the experimental results, showing excellent agreement between the different longitudinal modes for each of the two spatial modes measured.

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Cross-**frequency** coupling... **Oscillations**

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