### 142 results for qubit oscillator frequency

Contributors: Zou, Xudong, Seshia, Ashwin

Date: 2015-04-28

The Impact of Damping on the **Frequency** Stability of Nonlinear MEMS **Oscillators**...**Oscillators**...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. ... 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

Entanglement and quantum gate processes in the one-dimensional quantum harmonic **oscillator**...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. ... 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: Walter, S, Nunnenkamp, Andreas, Bruder, C

Date: 2018-10-31

Quantum synchronization of two Van der Pol **oscillators**...© 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. ... © 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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Contributors: Butler, James L, Mendonça, Philipe RF, Robinson, Hugh, Paulsen, Ole

Date: 2016-02-23

Intrinsic Cornu Ammonis Area 1 Theta-Nested Gamma Oscillations Induced by Optogenetic Theta **Frequency** Stimulation...Gamma **oscillations** (30–120 Hz) are thought to be important for various cognitive functions, including perception and working memory, and disruption of these **oscillations** has been implicated in brain disorders, such as schizophrenia and Alzheimer's disease. The cornu ammonis area 1 (CA1) of the hippocampus receives gamma **frequency** inputs from upstream regions (cornu ammonis area 3 and medial entorhinal cortex) and generates itself a faster gamma **oscillation**. The exact nature and origin of the intrinsic CA1 gamma **oscillation** is still under debate. Here, we expressed channelrhodopsin-2 under the CaMKIIα promoter in mice and prepared hippocampal slices to produce a model of intrinsic CA1 gamma **oscillations**. Sinusoidal optical stimulation of CA1 at theta **frequency** was found to induce robust theta-nested gamma **oscillations** with a temporal and spatial profile similar to CA1 gamma in vivo. The results suggest the presence of a single gamma rhythm generator with a **frequency** range of 65–75 Hz at 32°C. Pharmacological analysis found that the **oscillations** depended on both AMPA and GABAA receptors. Cell-attached and whole-cell recordings revealed that excitatory neuron firing slightly preceded interneuron firing within each gamma cycle, suggesting that this intrinsic CA1 gamma **oscillation** is generated with a pyramidal–interneuron circuit mechanism.
SIGNIFICANCE STATEMENT This study demonstrates that the cornu ammonis area 1 (CA1) is capable of generating intrinsic gamma **oscillations** in response to theta input. This gamma generator is independent of activity in the upstream regions, highlighting that CA1 can produce its own gamma **oscillation** in addition to inheriting activity from the upstream regions. This supports the theory that gamma **oscillations** predominantly function to achieve local synchrony, and that a local gamma generated in each area conducts the signal to the downstream region....Gamma oscillations (30–120 Hz) are thought to be important for various cognitive functions, including perception and working memory, and disruption of these oscillations has been implicated in brain disorders, such as schizophrenia and Alzheimer's disease. The cornu ammonis area 1 (CA1) of the hippocampus receives gamma **frequency** inputs from upstream regions (cornu ammonis area 3 and medial entorhinal cortex) and generates itself a faster gamma oscillation. The exact nature and origin of the intrinsic CA1 gamma oscillation is still under debate. Here, we expressed channelrhodopsin-2 under the CaMKIIα promoter in mice and prepared hippocampal slices to produce a model of intrinsic CA1 gamma oscillations. Sinusoidal optical stimulation of CA1 at theta **frequency** was found to induce robust theta-nested gamma oscillations with a temporal and spatial profile similar to CA1 gamma in vivo. The results suggest the presence of a single gamma rhythm generator with a **frequency** range of 65–75 Hz at 32°C. Pharmacological analysis found that the oscillations depended on both AMPA and GABAA receptors. Cell-attached and whole-cell recordings revealed that excitatory neuron firing slightly preceded interneuron firing within each gamma cycle, suggesting that this intrinsic CA1 gamma oscillation is generated with a pyramidal–interneuron circuit mechanism.
SIGNIFICANCE STATEMENT This study demonstrates that the cornu ammonis area 1 (CA1) is capable of generating intrinsic gamma oscillations in response to theta input. This gamma generator is independent of activity in the upstream regions, highlighting that CA1 can produce its own gamma oscillation in addition to inheriting activity from the upstream regions. This supports the theory that gamma oscillations predominantly function to achieve local synchrony, and that a local gamma generated in each area conducts the signal to the downstream region. ... Gamma **oscillations** (30–120 Hz) are thought to be important for various cognitive functions, including perception and working memory, and disruption of these **oscillations** has been implicated in brain disorders, such as schizophrenia and Alzheimer's disease. The cornu ammonis area 1 (CA1) of the hippocampus receives gamma **frequency** inputs from upstream regions (cornu ammonis area 3 and medial entorhinal cortex) and generates itself a faster gamma **oscillation**. The exact nature and origin of the intrinsic CA1 gamma **oscillation** is still under debate. Here, we expressed channelrhodopsin-2 under the CaMKIIα promoter in mice and prepared hippocampal slices to produce a model of intrinsic CA1 gamma **oscillations**. Sinusoidal optical stimulation of CA1 at theta **frequency** was found to induce robust theta-nested gamma **oscillations** with a temporal and spatial profile similar to CA1 gamma in vivo. The results suggest the presence of a single gamma rhythm generator with a **frequency** range of 65–75 Hz at 32°C. Pharmacological analysis found that the **oscillations** depended on both AMPA and GABAA receptors. Cell-attached and whole-cell recordings revealed that excitatory neuron firing slightly preceded interneuron firing within each gamma cycle, suggesting that this intrinsic CA1 gamma **oscillation** is generated with a pyramidal–interneuron circuit mechanism.
SIGNIFICANCE STATEMENT This study demonstrates that the cornu ammonis area 1 (CA1) is capable of generating intrinsic gamma **oscillations** in response to theta input. This gamma generator is independent of activity in the upstream regions, highlighting that CA1 can produce its own gamma **oscillation** in addition to inheriting activity from the upstream regions. This supports the theory that gamma **oscillations** predominantly function to achieve local synchrony, and that a local gamma generated in each area conducts the signal to the downstream region.

Contributors: Varnava, Christiana

Date: 2018-02-07

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....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. ... 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: Walter, Stefan, Nunnenkamp, Andreas, Bruder, Christoph

Date: 2018-10-31

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....Quantum synchronization of a driven self-sustained **oscillator**. ... 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.

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

Date: 2015-05-14

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....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....**Frequency** domain and time domain analysis of thermoacoustic oscillations with wave-based acoustics ... 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: Martins, BM, Das, Arijit, Antunes, L, Locke, James

Date: 2017-02-22

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....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....**Frequency** doubling in the cyanobacterial circadian clock ... 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: Butler, James L, Hay, Audrey, Paulsen, Ole

Date: 2018-03-23

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....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. ... 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: Juniper, Matthew, Kashinath, Karthik, Li, Larry

Date: 2018-02-16

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....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**. ... 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**.