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Quantum states can contain correlations which are stronger than is possible in classical systems. Quantum information technologies use these correlations, which are known as entanglement, as a resource for implementing novel protocols in a diverse range of fields such as cryptography, teleportation and computing. However, current methods for generating the required entangled states are not necessarily robust against perturbations in the proposed systems. In this thesis, techniques will be developed for robustly generating the entangled states needed for these exciting new technologies. The thesis starts by presenting some basic concepts in quantum information proccessing. In Ch. 2, the numerical methods which will be used to generate solutions for the dynamic systems in this thesis are presented. It is argued that using a GPU-accelerated staggered leapfrog technique provides a very efficient method for propagating the wave function. In Ch. 3, a new method for generating maximally entangled two-qubit states using a pair of interacting particles in a one-dimensional harmonic oscillator is proposed. The robustness of this technique is demonstrated both analytically and numerically for a variety of interaction potentials. When the two qubits are initially in the same state, no entanglement is generated as there is no direct qubit-qubit interaction. Therefore, for an arbitrary initial state, this process implements a root-of-swap entangling quantum gate. Some possible physical implementations of this proposal for low-dimensional semiconductor systems are suggested. One of the most commonly used qubits is the spin of an electron. However, in semiconductors, the spin-orbit interaction can couple this qubit to the electron's momentum. In order to incorporate this e ffect into our numerical simulations, a new discretisation of this interaction is presented in Ch. 4 which is signi ficantly more accurate than traditional methods. This technique is shown to be similar to the standard discretisation for magnetic fields. In Ch. 5, a simple spin-precession model is presented to predict the eff ect of the spin-orbit interaction on the entangling scheme of Ch. 3. It is shown that the root-of-swap quantum gate can be restored by introducing an additional constraint on the system. The robustness of the gate to perturbations in this constraint is demonstrated by presenting numerical solutions using the methods of Ch. 4.
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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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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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Many thermoacoustic systems exhibit rich nonlinear behaviour. Recent studies show that this nonlinear dynamics can be well captured by low-order time domain models that couple a level set kinematic model for a laminar flame, the G-equation, with a state-space realization of the linearized acoustic equations. However, so far the G-equation has been coupled only with straight ducts with uniform mean acoustic properties, which is a simplistic configuration. In this study, we incorporate a wave-based model of the acoustic network, containing area and temperature variations and frequency-dependent boundary conditions. We cast the linear acoustics into state-space form using a different approach from that in the existing literature. We then use this state-space form to investigate the stability of the thermoacoustic system, both in the frequency and time domains, using the flame position as a control parameter. We observe frequency-locked, quasiperiodic, and chaotic oscillations. We identify the location of Neimark–Sacker bifurcations with Floquet theory. We also find the Ruelle–Takens–Newhouse route to chaos with nonlinear time series analysis techniques. We highlight important differences between the nonlinear response predicted by the frequency domain and the time domain methods. This reveals deficiencies with the frequency domain technique, which is commonly used in academic and industrial studies of thermoacoustic systems. We then demonstrate a more accurate approach based on continuation analysis applied to time domain techniques.
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Synchronization is a universal concept in nonlinear science but has received little attention in thermoacoustics. In this numerical study, we take a dynamical systems approach to investigating the influence of harmonic acoustic forcing on three different types of self-excited thermoacoustic oscillations: periodic, quasi-periodic and chaotic. When the periodic system is forced, we find that: (i) at low forcing amplitudes, it responds at both the forcing frequency and the natural (self-excited) frequency, as well as at their linear combinations, indicating quasi-periodicity; (ii) above a critical forcing amplitude, the system locks in to the forcing; (iii) the bifurcations leading up to lock-in and the critical forcing amplitude required for lock-in depend on the proximity of the forcing frequency to the natural frequency; (iv) the response amplitude at lock-in may be larger or smaller than that of the unforced system and the system can exhibit hysteresis and the jump phenomenon owing to a cusp catastrophe; and (v) at forcing amplitudes above lock-in, the oscillations can become unstable and transition to chaos, or switch between different stable attractors depending on the forcing amplitude. When the quasi-periodic system is forced at a frequency equal to one of the two characteristic frequencies of the torus attractor, we find that lock-in occurs via a saddle-node bifurcation with frequency pulling. When the chaotic system is forced at a frequency close to the dominant frequency of its strange attractor, we find that it is possible to destroy chaos and establish stable periodic oscillations. These results show that the open-loop application of harmonic acoustic forcing can be an effective strategy for controlling periodic or aperiodic thermoacoustic oscillations. In some cases, we find that such forcing can reduce the response amplitude by up to 90 %, making it a viable way to weaken thermoacoustic oscillations.
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Classically, the tendency towards spontaneous synchronization is strongest if the natural frequencies of the self-oscillators are as close as possible. We show that this wisdom fails in the deep quantum regime, where the uncertainty of amplitude narrows down to the level of single quanta. Under these circumstances identical self-oscillators cannot synchronize and detuning their frequencies can actually help synchronization. The effect can be understood in a simple picture: Interaction requires an exchange of energy. In the quantum regime, the possible quanta of energy are discrete. If the extractable energy of one oscillator does not exactly match the amount the second oscillator may absorb, interaction, and thereby synchronization, is blocked. We demonstrate this effect, which we coin quantum synchronization blockade, in the minimal example of two Kerr-type self-oscillators and predict consequences for small oscillator networks, where synchronization between blocked oscillators can be mediated via a detuned oscillator. We also propose concrete implementations with superconducting circuits and trapped ions. This paves the way for investigations of new quantum synchronization phenomena in oscillator networks both theoretically and experimentally.
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In the analysis of thermoacoustic systems, a flame is usually characterised by the way its heat release responds to acoustic forcing. This response depends on the hydrodynamic stability of the flame. Some flames, such as a premixed bunsen flame, are hydrodynamically globally stable. They respond only at the forcing frequency. Other flames, such as a jet diffusion flame, are hydrodynamically globally unstable. They oscillate at their own natural frequencies and are often assumed to be insensitive to low-amplitude forcing at other frequencies. If a hydrodynamically globally unstable flame really is insensitive to forcing at other frequencies, then it should be possible to weaken thermoacoustic oscillations by detuning the frequency of the natural hydrodynamic mode from that of the natural acoustic modes. This would be very beneficial for industrial combustors. In this thesis, that assumption of insensitivity to forcing is tested experimentally. This is done by acoustically forcing two different selfexcited flows: a non-reacting jet and a reacting jet. Both jets have regions of absolute instability at their base and this causes them to exhibit varicose oscillations at discrete natural frequencies. The forcing is applied around these frequencies, at varying amplitudes, and the response examined over a range of frequencies (not just at the forcing frequency). The overall system is then modelled as a forced van der Pol oscillator. The results show that, contrary to some expectations, a hydrodynamically self-excited jet oscillating at one frequency is sensitive to forcing at other frequencies. When forced at low amplitudes, the jet responds at both frequencies as well as at several nearby frequencies, and there is beating, indicating quasiperiodicity. When forced at high amplitudes, however, it locks into the forcing. The critical forcing amplitude required for lock-in increases with the deviation of the forcing frequency from the natural frequency. This increase is linear, indicating a Hopf bifurcation to a global mode. The lock-in curve has a characteristic ∨ shape, but with two subtle asymmetries about the natural frequency. The first asymmetry concerns the forcing amplitude required for lock-in. In the non-reacting jet, higher amplitudes are required when the forcing frequency is above the natural frequency. In the reacting jet, lower amplitudes are required when the forcing frequency is above the natural frequency. The second asymmetry concerns the broadband response at lock-in. In the non-reacting jet, this response is always weaker than the unforced response, regardless of whether the forcing frequency is above or below the natural frequency. In the reacting jet, that response is weaker than the unforced response when the forcing frequency is above the natural frequency, but is stronger than it when the forcing frequency is below the natural frequency. In the reacting jet, weakening the global instability – by adding coflow or by diluting the fuel mixture – causes the flame to lock in at lower forcing amplitudes. This finding, however, cannot be detected in the flame describing function. That is because the flame describing function captures the response at only the forcing frequency and ignores all other frequencies, most notably those arising from the natural mode and from its interactions with the forcing. Nevertheless, the flame describing function does show a rise in gain below the natural frequency and a drop above it, consistent with the broadband response. Many of these features can be predicted by the forced van der Pol oscillator. They include (i) the coexistence of the natural and forcing frequencies before lock-in; (ii) the presence of multiple spectral peaks around these competing frequencies, indicating quasiperiodicity; (iii) the occurrence of lock-in above a critical forcing amplitude; (iv) the ∨-shaped lock-in curve; and (v) the reduced broadband response at lock-in. There are, however, some features that cannot be predicted. They include (i) the asymmetry of the forcing amplitude required for lock-in, found in both jets; (ii) the asymmetry of the response at lock-in, found in the reacting jet; and (iii) the interactions between the fundamental and harmonics of both the natural and forcing frequencies, found in both jets.
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Resonant MEMS accelerometers offer the potential for very high resolution and wide bandwidth measurements over a large input dynamic range. The read-out is implemented by constructing an oscillator with the resonator as the primary frequency determining element. The noise of this oscillator front-end typically determines the resolution of the device, and the noise floor is set by the modulation of operative noise processes by the system dynamics. The resonator element is typically operated in the linear regime to prevent the detrimental impact of resonator non-linearities on noise conversion limiting frequency stability. However, by operating at higher drive power levels it is possible to also increase the signal-to-noise ratio for sufficiently large input frequencies. This paper shows that improved device performance over a wide bandwidth is possible by employing appropriate amplitude and phase feedback schemes to optimally bias the resonator thus enabling both short-term and long-term measurements with an electrically tunable resolution.
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