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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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