### 111 results for qubit oscillator frequency

Contributors: Zou, Xudong, Seshia, Ashwin Arunkumar

Date: 2015-04-28

**frequency** stability of non-linear MEMS **oscillators** has not been previously...**frequency** stability of a nonlinear MEMS **oscillator** under variable damping...**oscillator** noise predict an improvement in **frequency** stability with increasing...**Oscillators**...**oscillator**. The random walk **frequency** noise and flicker **frequency** noise...**frequency** but also the phase/**frequency** noise of a nonlinear MEMS square ... Linear models for **oscillator** noise predict an improvement in **frequency** stability with increasing Quality factor. Although it is well known that this result does not apply to non-linear **oscillators**, systematic experimental investigations of the impact of damping on **frequency** stability of non-linear MEMS **oscillators** has not been previously reported. This paper studies the **frequency** stability of a nonlinear MEMS **oscillator** under variable damping conditions. Analytical and experimental investigation of a MEMS square-wave **oscillator** embedding a double-ended tuning fork resonator driven into the non-linear regime is introduced. The experimental results indicate that for a pre-set drive level, the variation of air-damping changes the onset of nonlinear behaviour in the resonator, which not only impacts the output **frequency** but also the phase/**frequency** noise of a nonlinear MEMS square wave **oscillator**. The random walk **frequency** noise and flicker **frequency** noise levels are strongly correlated with the non-linear operating point of the resonator, whereas the white phase and white **frequency** noise levels are impacted both by the output power and by operative nonlinearities.

Contributors: Owen, Edmund Thomas, Barnes, Crispin H. W.

Date: 2013-09-04

**oscillator** is proposed. The robustness of this technique is demonstrated...**qubit** to the electron's momentum. In order to incorporate this e ffect...**qubits** is the spin of an electron. However, in semiconductors, the spin-orbit...**qubits** are initially in the same state, no entanglement is generated as...**qubit**-**qubit**
interaction. Therefore, for an arbitrary initial state, this...two-**qubit** states using a pair of interacting particles in a one-dimensional ... 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.

Contributors: Varnava, Christiana

Date: 2018-02-07

**oscillations** in a quantum dot with a bound exciton state demonstrated ...**qubits**. For this purpose, semiconductor quantum dots (QD) have been extensively...**oscillating** field of a laser, therefore allowing the transition between...**frequencies** of up to several hundreds of MHz, without compromising the...**qubits** from a laser source. The average relay fidelity was high enough ... 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.

Contributors: Martins, BM, Das, Arijit Kumar, Antunes, L, Locke, James Charles

Date: 2017-02-22

**frequency** doubling in modulating growth. We propose that the two-peak ...**frequency** doubling of outputs....**oscillations**. It remains unclear how these different **frequencies** are generated...**oscillation** is dependent on $\textit{sigC}$, without which $\textit{psbAI ... Organisms use circadian clocks to generate 24-h rhythms in gene expression. However, the clock can interact with other pathways to generate shorter period **oscillations**. It remains unclear how these different **frequencies** are generated. Here, we examine this problem by studying the coupling of the clock to the alternative sigma factor $\textit{sigC}$ in the cyanobacterium $\textit{Synechococcus elongatus}$. Using single-cell microscopy, we find that $\textit{psbAI}$, a key photosynthesis gene regulated by both $\textit{sigC}$ and the clock, is activated with two peaks of gene expression every circadian cycle under constant low light. This two-peak **oscillation** is dependent on $\textit{sigC}$, without which $\textit{psbAI}$ rhythms revert to one oscillatory peak per day. We also observe two circadian peaks of elongation rate, which are dependent on $\textit{sigC}$, suggesting a role for the **frequency** doubling in modulating growth. We propose that the two-peak rhythm in $\textit{psbAI}$ expression is generated by an incoherent feedforward loop between the clock, $\textit{sigC}$ and $\textit{psbAI}$. Modelling and experiments suggest that this could be a general network motif to allow **frequency** doubling of outputs.

Contributors: Orchini, A, Illingworth, SJ, Juniper, Matthew Pudan

Date: 2015-05-14

**frequency** and time domains, using the flame position as a control parameter...**frequency** domain technique, which is commonly used in academic and industrial...**frequency** domain and the time domain methods. This reveals deficiencies...**frequency**-dependent boundary conditions. We cast the linear acoustics ...**frequency**-locked, quasiperiodic, and chaotic **oscillations**. We identify ... 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.

Contributors: Juniper, Matthew Pudan, Kashinath, Karthik, Li, Larry

Date: 2018-02-16

**oscillations**....**frequency** and the natural (self-excited) **frequency**, as well as at their...**oscillations**. In some cases, we find that such forcing can reduce the ...**oscillations**: periodic, quasi-periodic and chaotic. When the periodic ...**frequency** to the natural **frequency**; (iv) the response amplitude at lock-in ... 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**.

Contributors: Lörch, N, Nigg, SE, Nunnenkamp, Andreas, Tiwari, RP, Bruder, C

Date: 2017-08-16

self-**oscillators** and predict consequences for small **oscillator** networks...**oscillators** can be mediated via a detuned **oscillator**. We also propose ...**frequencies** of the self-**oscillators** are as close as possible. We show ...**oscillator** does not exactly match the amount the second **oscillator** may...self-**oscillators** cannot synchronize and detuning their **frequencies** can ... 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.

Contributors: Butler, James L, Hay, Audrey, Paulsen, Ole

Date: 2018-03-23

**oscillations** via sinusoidal blue light stimulation at theta **frequency**....**oscillations** than stimulation of either mEC and CA1, whose gamma **oscillations**...**oscillations** with different properties. These three gamma **oscillations**...**frequency** mechanisms in slice, we showed using pharmacology that all three...**frequency**. All three gamma **oscillations** had a current sink-source pair ... The entorhinal-hippocampal system is an important circuit in the brain, essential for certain cognitive tasks such as memory and navigation. Different gamma **oscillations** occur in this circuit, with the medial entorhinal cortex (mEC), CA3, and CA1 all generating gamma **oscillations** with different properties. These three gamma **oscillations** converge within CA1, where much work has gone into trying to isolate them from each other. Here we compared the gamma generators in the mEC, CA3, and CA1 using optogenetically-induced theta-gamma **oscillations**. Expressing channelrhodopsin (ChR2) in principal neurons in each of the three regions allowed for induction of gamma **oscillations** via sinusoidal blue light stimulation at theta **frequency**. Recording the **oscillations** in CA1 in vivo, we found that CA3 stimulation induced slower gamma **oscillations** than CA1 stimulation, matching in vivo reports of spontaneous CA3 and CA1 gamma **oscillations**. In brain slices ex vivo, optogenetic stimulation of CA3 induced slower gamma **oscillations** than stimulation of either mEC and CA1, whose gamma **oscillations** were of similar **frequency**. All three gamma **oscillations** had a current sink-source pair between the perisomatic and dendritic layers of the same region. Taking advantage of this powerful model to analyse gamma **frequency** mechanisms in slice, we showed using pharmacology that all three gamma **oscillations** were dependent on the same types of synaptic receptor, being abolished by blockade of either GABA(A) receptors or AMPA/kainate receptors, and insensitive to blockade of NMDA receptors. These results indicate that a fast excitatory-inhibitory feedback loop underlies the generation of gamma **oscillations** in all three regions.

Contributors: Li, Larry, Juniper, Matthew

Date: 2012-05-07

**oscillations** at discrete natural **frequencies**. The forcing
is applied around...**oscillate** at their own natural **frequencies** and are often assumed
to be...**oscillator**. They include (i) the coexistence of the natural and forcing...**frequencies**, then it should be possible to weaken
thermoacoustic **oscillations**...**oscillating** at one **frequency** is sensitive to
forcing at other **frequencies** ... 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.

Contributors: Kypraiou, Anna-Maria, Allison, PM, Giusti, Andrea, Mastorakos, Epaminondas

Date: 2018-06-05

**frequency**, with increasing broadband contributions in higher modes and...**oscillations** is studied experimentally. The flames were imaged using OH...**frequency** spectra of the coefficients of the POD modes have peaks at the...**frequencies**, f. About 70% of the energy of the total fluctuations in the ... The response of three flames with different degrees of premixedness (fully premixed, non-premixed with radial, and non-premixed with axial fuel injection) to acoustic **oscillations** is studied experimentally. The flames were imaged using OH* chemiluminescence and OH Planar Laser Induced Fluorescence (OH PLIF) at 5 kHz. In addition to a flame kinematics analysis, the amplitude dependence of the transfer function was calculated. The dominant spatial structures of the heat release and their periodicity were examined using the Proper Orthogonal Decomposition (POD) method. The non-premixed system with radial fuel injection showed the highest response to acoustic forcing, followed by the fully premixed and the non-premixed system with axial fuel injection. In addition, the response of the non-premixed system with radial fuel injection was greater than that of the fully premixed system for various bulk velocities U, global φ, forcing amplitudes, A and forcing **frequencies**, f. About 70% of the energy of the total fluctuations in the NPR case is contained in the first four POD modes, a percentage that decreases with overall equivalence ratio, but only this drops to about 40% for the NPA flame. The **frequency** spectra of the coefficients of the POD modes have peaks at the forcing **frequency**, with increasing broadband contributions in higher modes and for the NPA flame.