### 25677 results for qubit oscillator frequency

Contributors: Michael G. Tanner, David G. Hasko, David A. Williams

Date: 2006-04-01

Resonance response of the SET current to applied microwave **frequencies**, (a) over a large **frequency** range due to coupling with all device elements. (b) A resonance of interest believed to be associated with the IDQD. Central resonance peak is periodically split or suppressed with varying gate potential Vg2. The inset figure shows the response at Vg2=−9.5V (dashed line) and at Vg2=−8V plotted without offset for comparison. The feature repeats periodically as gate potential is increased further.
...**Qubit**...Resonance response of the SET current to applied microwave frequencies, (a) over a large frequency range due to coupling with all device elements. (b) A resonance of interest believed to be associated with the IDQD. Central resonance peak is periodically split or suppressed with varying gate potential Vg2. The inset figure shows the response at Vg2=−9.5V (dashed line) and at Vg2=−8V plotted without offset for comparison. The feature repeats periodically as gate potential is increased further.
...Differentiated SET current measured at 4.2K and zero source–drain bias as Vg1 is swept and Vg2 is incremented. Inset shows the main features: one main Coulomb **oscillation** indicated by the dashed line and subsidiary **oscillations** shown by the dotted lines.
... The fabrication methods and low-temperature electron transport measurements are presented for circuits consisting of a single-island single-electron transistor coupled to an isolated double quantum-dot. Capacitively coupled ‘trench isolated’ circuit elements are fabricated in highly doped silicon-on-insulator using electron beam lithography and reactive ion etching. Polarisation of the isolated double quantum-dot is observed as a function of the side gate potentials through changes in the conductance characteristics of the single-electron transistor. Microwave signals are coupled into the device for excitation of the polarisation states of the isolated double quantum-dot. Resonances attributed to an energy level splitting of the polarisation states are observed with an energy separation appropriate for quantum computation.

Files:

Contributors: A.R. Bosco de Magalhães, Adélcio C. Oliveira

Date: 2016-02-05

Nonlinear **oscillator**...Characteristic entanglement timescales of a **qubit** coupled to a quartic **oscillator**...Visibility dynamics in different timescales for initial state |Ψ2〉 and Γ=0. The timescale τp is associated to the decay of the envelope of the **oscillations** with characteristic time τr1. A very subtle increase in the amplitudes of the **oscillations** can be observed around t=τr2. The timescale of the fastest **oscillations** of the dynamics is τo.
...Visibility dynamics for initial state |Ψ2〉 and Γ varying from 0 to 0.1. For each value of Γ, the unit of time is chosen as the corresponding τp in (a), τr1 in (b), τr2 in (c), and τo in (d). For the majority of values of Γ investigated, the initial dynamics is flattened around t=2τp. Except for very small values of Γ, τr1 and τr2 are associated to partial revivals. When Γ increases, the number of fast initial **oscillations** decreases, but their characteristic durations are given by τo, which does not vary with Γ.
...Predictability dynamics in different timescales for initial state |Ψ2〉. The timescale τp is associated to the decay of the envelope of the **oscillations** with characteristic time τo. Revivals can be observed around the first multiples of τr.
...The structure of the entanglement dynamics of a **qubit** coupled to a quartic **oscillator** is investigated through the calculation of timescales of visibility and predictability, and their relation with the concurrence dynamics. This model can describe a Rydberg atom in a Kerr medium. A method based on the analysis of the different interference processes of the terms that compose the physical quantities studied is proposed, and timescales related to decay, revivals and fast **oscillations** under the decay envelope are computed. The method showed to be effective for the vast majority of cases studied, even when the timescales vary several orders of magnitude. The conditions for expansions in power series to give correct decay timescales are analyzed....Predictability dynamics in different timescales for initial state |Ψ1〉. The timescale τp is associated to the rise and decay of the **oscillations** with characteristic time τo. Revivals occur in the region around τr and its first multiples.
...Visibility dynamics in different timescales for initial state |Ψ2〉 and Γ=0.1. The timescale τp is associated to the rise and decay of the initial dynamics. Both τr1 and τr2 are related to partial revivals. There are no **oscillations** besides the revivals and the initial rise and decay; the timescale of their duration is given by τo.
...The structure of the entanglement dynamics of a **qubit** coupled to a quartic **oscillator** is investigated through the calculation of timescales of visibility and predictability, and their relation with the concurrence dynamics. This model can describe a Rydberg atom in a Kerr medium. A method based on the analysis of the different interference processes of the terms that compose the physical quantities studied is proposed, and timescales related to decay, revivals and fast oscillations under the decay envelope are computed. The method showed to be effective for the vast majority of cases studied, even when the timescales vary several orders of magnitude. The conditions for expansions in power series to give correct decay timescales are analyzed. ... The structure of the entanglement dynamics of a **qubit** coupled to a quartic **oscillator** is investigated through the calculation of timescales of visibility and predictability, and their relation with the concurrence dynamics. This model can describe a Rydberg atom in a Kerr medium. A method based on the analysis of the different interference processes of the terms that compose the physical quantities studied is proposed, and timescales related to decay, revivals and fast **oscillations** under the decay envelope are computed. The method showed to be effective for the vast majority of cases studied, even when the timescales vary several orders of magnitude. The conditions for expansions in power series to give correct decay timescales are analyzed.

Files:

Contributors: S. Filippov, V. Vyurkov, L. Fedichkin

Date: 2011-11-01

**Qubit** dynamics in Bloch ball picture. North pole corresponds to the excited (antisymmetric) energy eigenstate |1〉 and south pole corresponds to the ground (symmetric) state |0〉. Initially the electron is localized in one of the dots. Quality of Rabi **oscillations** Q=40. The effect of image charge potential: (a) K=0 and (b) K=0.4.
...**Qubit** dynamics in Bloch ball picture. North pole corresponds to the excited (antisymmetric) energy eigenstate |1〉 and south pole corresponds to the ground (symmetric) state |0〉. Initially the electron is localized in one of the dots. Quality of Rabi oscillations Q=40. The effect of image charge potential: (a) K=0 and (b) K=0.4.
...Quality of **qubit** Rabi **oscillations** vs. distance to a metal surface. Centers of quantum dots are located 100nm apart. Lines and points correspond to analytical and numerical solutions, respectively.
...A charge-based **qubit** is subject to image forces originating in nearby metal gates. Displacement of charge in an **oscillating** **qubit** indispensably results in moving charges in metal. Therefore, Joule loss is one more source of **qubit** decoherence. We have estimated the quality of Rabi **oscillations** for a realistic double-quantum-dot as Q∼100. This kind of decoherence cannot be suppressed by lowering temperature as it is evoked by surface roughness scattering of electrons which is almost insensitive to temperature. Possibilities to avoid such a decoherence are briefly discussed. The effect of energy dissipation and image charge potential on **qubit** dynamics is studied by means of a specific local-in-time non-Markovian master equation....A charge-based **qubit** is subject to image forces originating in nearby metal gates. Displacement of charge in an oscillating **qubit** indispensably results in moving charges in metal. Therefore, Joule loss is one more source of **qubit** decoherence. We have estimated the quality of Rabi oscillations for a realistic double-quantum-dot as Q∼100. This kind of decoherence cannot be suppressed by lowering temperature as it is evoked by surface roughness scattering of electrons which is almost insensitive to temperature. Possibilities to avoid such a decoherence are briefly discussed. The effect of energy dissipation and image charge potential on **qubit** dynamics is studied by means of a specific local-in-time non-Markovian master equation....Quality of **qubit** Rabi **oscillations** vs. the distance between quantum dots. **Qubit** is located 50nm far from the metal surface. Lines and points correspond to analytical and numerical solutions, respectively.
...The moving charge in the qubit drags charges in metal that indispensably entails Joule loss: d is a double dot separation and D is a distance to the metal surface.
...Quality of qubit Rabi oscillations vs. the distance between quantum dots. **Qubit** is located 50nm far from the metal surface. Lines and points correspond to analytical and numerical solutions, respectively.
...The moving charge in the **qubit** drags charges in metal that indispensably entails Joule loss: d is a double dot separation and D is a distance to the metal surface.
...Quality of qubit Rabi oscillations vs. distance to a metal surface. Centers of quantum dots are located 100nm apart. Lines and points correspond to analytical and numerical solutions, respectively.
... A charge-based **qubit** is subject to image forces originating in nearby metal gates. Displacement of charge in an **oscillating** **qubit** indispensably results in moving charges in metal. Therefore, Joule loss is one more source of **qubit** decoherence. We have estimated the quality of Rabi **oscillations** for a realistic double-quantum-dot as Q∼100. This kind of decoherence cannot be suppressed by lowering temperature as it is evoked by surface roughness scattering of electrons which is almost insensitive to temperature. Possibilities to avoid such a decoherence are briefly discussed. The effect of energy dissipation and image charge potential on **qubit** dynamics is studied by means of a specific local-in-time non-Markovian master equation.

Files:

Contributors: S.K. Ryu, Y.K. Kim, M.K. Kim, S.H. Won, S.H. Chung

Date: 2010-01-01

Behavior of periodically **oscillating** flame with large-scale **oscillation** for Vac=5kV, fac=20Hz, and U0=11m/s.
...Observation of multi-scale oscillation of laminar lifted flames with low-**frequency** AC electric fields...Average amplitude of large-scale oscillation with AC **frequency** for U0=11.0m/s and Vac=5kV.
...**Oscillation** **frequency** in terms of AC **frequency** for U0=11.0m/s and Vac=5kV.
...Edge height of lifted flame together with oscillation amplitude with AC **frequency** for Vac=5kV and U0=11.0m/s.
...Low **frequency**...**Oscillation**...Phase diagrams of HL and dHL/dt for various **oscillation** modes.
...Oscillation **frequency** in terms of AC **frequency** for U0=11.0m/s and Vac=5kV.
...Edge height of lifted flame together with **oscillation** amplitude with AC **frequency** for Vac=5kV and U0=11.0m/s.
...O...Behavior of periodically oscillating flame with large-scale oscillation for Vac=5kV, fac=20Hz, and U0=11m/s.
...Average amplitude of large-scale **oscillation** with AC **frequency** for U0=11.0m/s and Vac=5kV.
...The **oscillation** behavior of laminar lifted flames under the influence of low-**frequency** AC has been investigated experimentally in coflow jets. Various **oscillation** modes were existed depending on jet velocity and the voltage and **frequency** of AC, especially when the AC **frequency** was typically smaller than 30Hz. Three different **oscillation** modes were observed: (1) large-scale **oscillation** with the **oscillation** **frequency** of about 0.1Hz, which was independent of the applied AC **frequency**, (2) small-scale **oscillation** synchronized to the applied AC **frequency**, and (3) doubly-periodic **oscillation** with small-scale **oscillation** embedded in large-scale **oscillation**. As the AC **frequency** decreased from 30Hz, the **oscillation** modes were in the order of the large-scale **oscillation**, doubly-periodic **oscillation**, and small-scale **oscillation**. The onset of the **oscillation** for the AC **frequency** smaller than 30Hz was in close agreement with the delay time scale for the ionic wind effect to occur, that is, the collision response time. **Frequency**-doubling behavior for the small-scale **oscillation** has also been observed. Possible mechanisms for the large-scale **oscillation** and the **frequency**-doubling behavior have been discussed, although the detailed understanding of the underlying mechanisms will be a future study....The oscillation behavior of laminar lifted flames under the influence of low-**frequency** AC has been investigated experimentally in coflow jets. Various oscillation modes were existed depending on jet velocity and the voltage and **frequency** of AC, especially when the AC **frequency** was typically smaller than 30Hz. Three different oscillation modes were observed: (1) large-scale oscillation with the oscillation **frequency** of about 0.1Hz, which was independent of the applied AC **frequency**, (2) small-scale oscillation synchronized to the applied AC **frequency**, and (3) doubly-periodic oscillation with small-scale oscillation embedded in large-scale oscillation. As the AC **frequency** decreased from 30Hz, the oscillation modes were in the order of the large-scale oscillation, doubly-periodic oscillation, and small-scale oscillation. The onset of the oscillation for the AC **frequency** smaller than 30Hz was in close agreement with the delay time scale for the ionic wind effect to occur, that is, the collision response time. **Frequency**-doubling behavior for the small-scale oscillation has also been observed. Possible mechanisms for the large-scale oscillation and the **frequency**-doubling behavior have been discussed, although the detailed understanding of the underlying mechanisms will be a future study. ... The **oscillation** behavior of laminar lifted flames under the influence of low-**frequency** AC has been investigated experimentally in coflow jets. Various **oscillation** modes were existed depending on jet velocity and the voltage and **frequency** of AC, especially when the AC **frequency** was typically smaller than 30Hz. Three different **oscillation** modes were observed: (1) large-scale **oscillation** with the **oscillation** **frequency** of about 0.1Hz, which was independent of the applied AC **frequency**, (2) small-scale **oscillation** synchronized to the applied AC **frequency**, and (3) doubly-periodic **oscillation** with small-scale **oscillation** embedded in large-scale **oscillation**. As the AC **frequency** decreased from 30Hz, the **oscillation** modes were in the order of the large-scale **oscillation**, doubly-periodic **oscillation**, and small-scale **oscillation**. The onset of the **oscillation** for the AC **frequency** smaller than 30Hz was in close agreement with the delay time scale for the ionic wind effect to occur, that is, the collision response time. **Frequency**-doubling behavior for the small-scale **oscillation** has also been observed. Possible mechanisms for the large-scale **oscillation** and the **frequency**-doubling behavior have been discussed, although the detailed understanding of the underlying mechanisms will be a future study.

Files:

Contributors: R. Zadoyan, D. Kohen, D.A. Lidar, V.A. Apkarian

Date: 2001-05-15

Molecular ro-vibronic coherences, joint energy-time distributions of quantum amplitudes, are selectively prepared, manipulated, and imaged in time–**frequency**-resolved coherent anti-Stokes Raman scattering (TFRCARS) measurements using femtosecond laser pulses. The studies are implemented in iodine vapor, with its thermally occupied statistical ro-vibrational density serving as initial state. The evolution of the massive ro-vibronic superpositions, consisting of 103 eigenstates, is followed through two-dimensional images. The first- and second-order coherences are captured using time-integrated **frequency**-resolved CARS, while the third-order coherence is captured using time-gated **frequency**-resolved CARS. The Fourier filtering provided by time-integrated detection projects out single ro-vibronic transitions, while time-gated detection allows the projection of arbitrary ro-vibronic superpositions from the coherent third-order polarization. A detailed analysis of the data is provided to highlight the salient features of this four-wave mixing process. The richly patterned images of the ro-vibrational coherences can be understood in terms of phase evolution in rotation–vibration–electronic Hilbert space, using time-circuit diagrams. Beside the control and imaging of chemistry, the controlled manipulation of massive quantum coherences suggests the possibility of quantum computing. We argue that the universal logic gates necessary for arbitrary quantum computing – all single **qubit** operations and the two-**qubit** controlled-NOT (CNOT) gate – are available in time-resolved four-wave mixing in a molecule. The molecular rotational manifold is naturally “wired” for carrying out all single **qubit** operations efficiently, and in parallel. We identify vibronic coherences as one example of a naturally available two-**qubit** CNOT gate, wherein the vibrational **qubit** controls the switching of the targeted electronic **qubit**....Diagrammatic representation of time-resolved CARS. Both time-circuit and Feynman diagram are illustrated for a non- overlapping sequence of P, S, P′ pulses, with central frequency of the S-pulse chosen to be outside the absorption spectrum of the B←X transition, to ensure that only the P(0,3) component of the third-order polarization is interrogated. In this dominant contribution, all three pulses act on bra (ket) state while the ket (bra) state evolves field free. Note, for the Feynman diagrams, we use the convention of Ref. [6], which is different than that of Ref. [5].
...The manipulation of massive ro-vibronic superpositions using time–**frequency**-resolved coherent anti-Stokes Raman scattering (TFRCARS): from quantum control to quantum computing...Diagrammatic representation of time-resolved CARS. Both time-circuit and Feynman diagram are illustrated for a non- overlapping sequence of P, S, P′ pulses, with central **frequency** of the S-pulse chosen to be outside the absorption spectrum of the B←X transition, to ensure that only the P(0,3) component of the third-order polarization is interrogated. In this dominant contribution, all three pulses act on bra (ket) state while the ket (bra) state evolves field free. Note, for the Feynman diagrams, we use the convention of Ref. [6], which is different than that of Ref. [5].
...The wavepacket picture associated with the evolution of the ket-state in the diagram of Fig. 1, for resonant CARS in iodine. The required energy matching condition for the AS radiation, Eq. (10b) of text, can only be met when the packet reaches the inner turning point of the B-surface. Once prepared, ϕ(3)(t) will **oscillate**, radiating periodically every time it reaches the inner turning point.
... Molecular ro-vibronic coherences, joint energy-time distributions of quantum amplitudes, are selectively prepared, manipulated, and imaged in time–**frequency**-resolved coherent anti-Stokes Raman scattering (TFRCARS) measurements using femtosecond laser pulses. The studies are implemented in iodine vapor, with its thermally occupied statistical ro-vibrational density serving as initial state. The evolution of the massive ro-vibronic superpositions, consisting of 103 eigenstates, is followed through two-dimensional images. The first- and second-order coherences are captured using time-integrated **frequency**-resolved CARS, while the third-order coherence is captured using time-gated **frequency**-resolved CARS. The Fourier filtering provided by time-integrated detection projects out single ro-vibronic transitions, while time-gated detection allows the projection of arbitrary ro-vibronic superpositions from the coherent third-order polarization. A detailed analysis of the data is provided to highlight the salient features of this four-wave mixing process. The richly patterned images of the ro-vibrational coherences can be understood in terms of phase evolution in rotation–vibration–electronic Hilbert space, using time-circuit diagrams. Beside the control and imaging of chemistry, the controlled manipulation of massive quantum coherences suggests the possibility of quantum computing. We argue that the universal logic gates necessary for arbitrary quantum computing – all single **qubit** operations and the two-**qubit** controlled-NOT (CNOT) gate – are available in time-resolved four-wave mixing in a molecule. The molecular rotational manifold is naturally “wired” for carrying out all single **qubit** operations efficiently, and in parallel. We identify vibronic coherences as one example of a naturally available two-**qubit** CNOT gate, wherein the vibrational **qubit** controls the switching of the targeted electronic **qubit**.

Files:

Contributors: F.K. Wilhelm, S. Kleff, J. von Delft

Date: 2004-01-26

Visualization of the ground state |0〉 and the coherent pointer-states |L〉 and |R〉 of the oscillator in the potential V(x).
...Visualization of the ground state |0〉 and the coherent pointer-states |L〉 and |R〉 of the **oscillator** in the potential V(x).
...In the spin-boson model, the properties of the **oscillator** bath are fully characterized by the spectral density of **oscillators** J(ω). We study the case when this function is of Breit–Wigner shape and has a sharp peak at a **frequency** Ω with width Γ≪Ω. We use a number of approaches such as the weak-coupling Bloch–Redfield equation, the non-interacting blip approximation (NIBA) and the flow-equation renormalization scheme. We show, that if Ω is much larger than the **qubit** energy scales, the dynamics corresponds to an ohmic spin-boson model with a strongly reduced tunnel splitting. We also show that the direction of the scaling of the tunnel splitting changes sign when the bare splitting crosses Ω. We find good agreement between our analytical approximations and numerical results. We illuminate how and why different approaches to the model account for these features and discuss the interpretation of this model in the context of an application to quantum computation and read-out. ... In the spin-boson model, the properties of the **oscillator** bath are fully characterized by the spectral density of **oscillators** J(ω). We study the case when this function is of Breit–Wigner shape and has a sharp peak at a **frequency** Ω with width Γ≪Ω. We use a number of approaches such as the weak-coupling Bloch–Redfield equation, the non-interacting blip approximation (NIBA) and the flow-equation renormalization scheme. We show, that if Ω is much larger than the **qubit** energy scales, the dynamics corresponds to an ohmic spin-boson model with a strongly reduced tunnel splitting. We also show that the direction of the scaling of the tunnel splitting changes sign when the bare splitting crosses Ω. We find good agreement between our analytical approximations and numerical results. We illuminate how and why different approaches to the model account for these features and discuss the interpretation of this model in the context of an application to quantum computation and read-out.

Files:

Contributors: Haiteng Jiang, Ali Bahramisharif, Marcel A.J. van Gerven, Ole Jensen

Date: 2015-09-01

It is well established that neuronal **oscillations** at different **frequencies** interact with each other in terms of cross-**frequency** coupling (CFC). In particular, the phase of slower **oscillations** modulates the power of faster **oscillations**. This is referred to as phase–amplitude coupling (PAC). Examples are alpha phase to gamma power coupling as observed in humans and theta phase to gamma power coupling as observed in the rat hippocampus. We here ask if the interaction between alpha and gamma **oscillations** is in the direction of the phase of slower **oscillations** driving the power of faster **oscillations** or conversely from the power of faster **oscillations** driving the phase of slower **oscillations**. To answer this question, we introduce a new measure to estimate the cross-**frequency** directionality (CFD). This measure is based on the phase-slope index (PSI) between the phase of slower **oscillations** and the power envelope of faster **oscillations**. Further, we propose a randomization framework for statistically evaluating the coupling measures when controlling for multiple comparisons over the investigated **frequency** ranges. The method was firstly validated on simulated data and next applied to resting state electrocorticography (ECoG) data. These results demonstrate that the method works reliably. In particular, we found that the power envelope of gamma **oscillations** drives the phase of slower **oscillations** in the alpha band. This surprising finding is not easily reconcilable with theories suggesting that feedback controlled alpha **oscillations** modulate feedforward processing reflected in the gamma band....It is well established that neuronal oscillations at different **frequencies** interact with each other in terms of cross-**frequency** coupling (CFC). In particular, the phase of slower oscillations modulates the power of faster oscillations. This is referred to as phase–amplitude coupling (PAC). Examples are alpha phase to gamma power coupling as observed in humans and theta phase to gamma power coupling as observed in the rat hippocampus. We here ask if the interaction between alpha and gamma oscillations is in the direction of the phase of slower oscillations driving the power of faster oscillations or conversely from the power of faster oscillations driving the phase of slower oscillations. To answer this question, we introduce a new measure to estimate the cross-**frequency** directionality (CFD). This measure is based on the phase-slope index (PSI) between the phase of slower oscillations and the power envelope of faster oscillations. Further, we propose a randomization framework for statistically evaluating the coupling measures when controlling for multiple comparisons over the investigated **frequency** ranges. The method was firstly validated on simulated data and next applied to resting state electrocorticography (ECoG) data. These results demonstrate that the method works reliably. In particular, we found that the power envelope of gamma oscillations drives the phase of slower oscillations in the alpha band. This surprising finding is not easily reconcilable with theories suggesting that feedback controlled alpha oscillations modulate feedforward processing reflected in the gamma band....Measuring directionality between neuronal oscillations of different **frequencies**...Phase spectra between low frequency signal and high frequency envelope. The red curves represent the envelope of high frequency signals. Fig. 1 is adapted from Schoffelen et al. (2005). Left panel: The low frequency signal is leading the high frequency envelope by 10ms. This constant lead translates into a phase-lead that linearly increases with frequency (e.g., 0.25rad for 4Hz, 0.50rad for 8Hz and 0.75rad for 12Hz). Right panel: The low frequency signal is lagging the high frequency envelope by 10ms. This constant lag translates into a phase-lag that linearly decreases with frequency (e.g., −0.25rad for 4Hz, −0.50rad for 8Hz and −0.75rad for 12Hz).
...Cross-**frequency** coupling...Steps applied to compute both CFC and CFD. (A) High **frequency** power at **frequency** v is estimated from the original signal by applying a sliding Hanning tapered time window followed by a Fourier transformation (red line). After that, both the original signal and the power envelope of the high **frequency** signal are divided into segments. Within each segment, the original signal and the power envelope of the high **frequency** signal are Fourier-transformed and cross-spectra between them are computed. (B) CFC and CFD quantification. CFC is quantified by coherence and CFD is calculated from the PSI between the phase of slow **oscillation** fi and power of fast **oscillation** vj. The red segment indicates the **frequency** range over which the PSI is calculated. The PSI is calculated for the bandwidth β.
...Statistical assessment of the CFC and CFD when controlling for multiple comparisons over **frequencies**. (A) Observed CFC/D and clustering threshold. All observed CFC/D values were pooled together (i.e. all **frequency** by **frequency** bins) and the threshold is set at the 99.5th percentile of the resulting distribution (right panel). Contiguous CFC/D values exceeding the threshold formed a cluster (left panel). The summed CFC/D values from a given cluster were considered the cluster score. (B) Circular shifted CFC/D and the cluster reference distribution. Random number of the Fourier-transferred phase segment sequences was circular shifted with respect to the amplitude envelope segments and the CFC/D values were recomputed 1000 times. For each randomization, the CFC/D contiguous values exceeding the threshold were used to form reference clusters (e.g., cluster1, cluster2, and so on in the left panel) and the respective cluster scores were calculated. The resulting 1000 maximum cluster scores formed the cluster-level reference distribution. For the observed cluster score, the p value was determined by considering the fraction of cluster scores in the reference distribution exceeding the observed cluster score (right panel).
...Steps applied to compute both CFC and CFD. (A) High frequency power at frequency v is estimated from the original signal by applying a sliding Hanning tapered time window followed by a Fourier transformation (red line). After that, both the original signal and the power envelope of the high frequency signal are divided into segments. Within each segment, the original signal and the power envelope of the high frequency signal are Fourier-transformed and cross-spectra between them are computed. (B) CFC and CFD quantification. CFC is quantified by coherence and CFD is calculated from the PSI between the phase of slow oscillation fi and power of fast oscillation vj. The red segment indicates the frequency range over which the PSI is calculated. The PSI is calculated for the bandwidth β.
...Neuronal **oscillations**...Phase spectra between low **frequency** signal and high **frequency** envelope. The red curves represent the envelope of high **frequency** signals. Fig. 1 is adapted from Schoffelen et al. (2005). Left panel: The low **frequency** signal is leading the high **frequency** envelope by 10ms. This constant lead translates into a phase-lead that linearly increases with **frequency** (e.g., 0.25rad for 4Hz, 0.50rad for 8Hz and 0.75rad for 12Hz). Right panel: The low **frequency** signal is lagging the high **frequency** envelope by 10ms. This constant lag translates into a phase-lag that linearly decreases with **frequency** (e.g., −0.25rad for 4Hz, −0.50rad for 8Hz and −0.75rad for 12Hz).
...Statistical assessment of the CFC and CFD when controlling for multiple comparisons over frequencies. (A) Observed CFC/D and clustering threshold. All observed CFC/D values were pooled together (i.e. all frequency by frequency bins) and the threshold is set at the 99.5th percentile of the resulting distribution (right panel). Contiguous CFC/D values exceeding the threshold formed a cluster (left panel). The summed CFC/D values from a given cluster were considered the cluster score. (B) Circular shifted CFC/D and the cluster reference distribution. Random number of the Fourier-transferred phase segment sequences was circular shifted with respect to the amplitude envelope segments and the CFC/D values were recomputed 1000 times. For each randomization, the CFC/D contiguous values exceeding the threshold were used to form reference clusters (e.g., cluster1, cluster2, and so on in the left panel) and the respective cluster scores were calculated. The resulting 1000 maximum cluster scores formed the cluster-level reference distribution. For the observed cluster score, the p value was determined by considering the fraction of cluster scores in the reference distribution exceeding the observed cluster score (right panel).
...Cross-**frequency** directionality ... It is well established that neuronal **oscillations** at different **frequencies** interact with each other in terms of cross-**frequency** coupling (CFC). In particular, the phase of slower **oscillations** modulates the power of faster **oscillations**. This is referred to as phase–amplitude coupling (PAC). Examples are alpha phase to gamma power coupling as observed in humans and theta phase to gamma power coupling as observed in the rat hippocampus. We here ask if the interaction between alpha and gamma **oscillations** is in the direction of the phase of slower **oscillations** driving the power of faster **oscillations** or conversely from the power of faster **oscillations** driving the phase of slower **oscillations**. To answer this question, we introduce a new measure to estimate the cross-**frequency** directionality (CFD). This measure is based on the phase-slope index (PSI) between the phase of slower **oscillations** and the power envelope of faster **oscillations**. Further, we propose a randomization framework for statistically evaluating the coupling measures when controlling for multiple comparisons over the investigated **frequency** ranges. The method was firstly validated on simulated data and next applied to resting state electrocorticography (ECoG) data. These results demonstrate that the method works reliably. In particular, we found that the power envelope of gamma **oscillations** drives the phase of slower **oscillations** in the alpha band. This surprising finding is not easily reconcilable with theories suggesting that feedback controlled alpha **oscillations** modulate feedforward processing reflected in the gamma band.

Files:

Contributors: Fang Yuan, Daotong Chong, Quanbin Zhao, Weixiong Chen, Junjie Yan

Date: 2016-07-01

Bubble diameters at the steam mass flux of 250kgm−2s−1.
...Dominant **frequencies** of 10mm nozzle.
...Condensation regime map by Cho et al. [1] (C–chugging, TC—transitional region from chugging to CO, CO—condensation **oscillation**, SC—stable condensation, BCO—bubble condensation **oscillation**, IOC—interfacial **oscillation** condensation).
...Condensation **oscillation**...**Frequencies** at different test conditions—250kgm−2s−1.
...Test conditions.
...FFT results at pool temperature 35°C and steam mass **flux 300kgm**−2s−1.
...Prediction accuracy of simultaneous equations for **oscillation** **frequency**.
...The condensation **oscillation** of submerged steam was investigated theoretically and experimentally at the condensation **oscillation** regime. It was found that pressure **oscillation** **frequency** was consistent with the bubble **oscillating** **frequency** and there was a quasi-steady stage when bubble diameters remained constant. A thermal-hydraulic model for the condensation **oscillation** regime was proposed based on potential flow theory, taking into account the effects of interface condensation and translatory flow. Theoretical derivations indicated that **oscillation** **frequencies** were mainly determined by bubble diameters and translatory velocity. A force balance model was applied to the calculation of bubble diameters at quasi-steady stage, and the **oscillation** **frequencies** were predicted with the calculated diameters. Theoretical analysis and experimental results turned out that **oscillation** **frequencies** at the condensation **oscillation** regime decreased with the increasing steam mass flux and pool temperature. The predicted **frequencies** corresponded to the experimental data well with the discrepancies of ±21.7%....The condensation oscillation of submerged steam was investigated theoretically and experimentally at the condensation oscillation regime. It was found that pressure oscillation **frequency** was consistent with the bubble oscillating **frequency** and there was a quasi-steady stage when bubble diameters remained constant. A thermal-hydraulic model for the condensation oscillation regime was proposed based on potential flow theory, taking into account the effects of interface condensation and translatory flow. Theoretical derivations indicated that oscillation **frequencies** were mainly determined by bubble diameters and translatory velocity. A force balance model was applied to the calculation of bubble diameters at quasi-steady stage, and the oscillation **frequencies** were predicted with the calculated diameters. Theoretical analysis and experimental results turned out that oscillation **frequencies** at the condensation oscillation regime decreased with the increasing steam mass flux and pool temperature. The predicted **frequencies** corresponded to the experimental data well with the discrepancies of ±21.7%....**Frequency**...**Frequencies** at different test conditions—300kgm−2s−1.
...Prediction accuracy of simultaneous equations for oscillation frequency.
... The condensation **oscillation** of submerged steam was investigated theoretically and experimentally at the condensation **oscillation** regime. It was found that pressure **oscillation** **frequency** was consistent with the bubble **oscillating** **frequency** and there was a quasi-steady stage when bubble diameters remained constant. A thermal-hydraulic model for the condensation **oscillation** regime was proposed based on potential flow theory, taking into account the effects of interface condensation and translatory flow. Theoretical derivations indicated that **oscillation** **frequencies** were mainly determined by bubble diameters and translatory velocity. A force balance model was applied to the calculation of bubble diameters at quasi-steady stage, and the **oscillation** **frequencies** were predicted with the calculated diameters. Theoretical analysis and experimental results turned out that **oscillation** **frequencies** at the condensation **oscillation** regime decreased with the increasing steam mass flux and pool temperature. The predicted **frequencies** corresponded to the experimental data well with the discrepancies of ±21.7%.

Files:

Contributors: Dong-Qi Liu, Gang-Qin Liu, Yan-Chun Chang, Xin-Yu Pan

Date: 2014-01-01

Characterization of lifetime of NV center spins. (a) Ramsey interference of NV S1 (circle) and NV S2 (diamond). The oscillation in Ramsey signal originates from the beating among different transitions corresponding to the host three 14N nuclear spin states. The oscillation frequency of Ramsey signal is equal to microwave detuning from spin resonance. Solid lines ~exp[−(t/T2⁎)m] fit the experimental data points, where m is a free parameter. (b) Comparison of Hahn echo coherence time T2 of NV S1 (circle) and NV S2 (diamond). The solid lines are fits to ~exp[−(t/T2)p], in which p is a fit parameter.
...Detection and manipulation of the **qubit**. (a) Fluorescence image of nanodiamond prepared on the CPW transmission line. NV S1 is circled. The inset is a photo of CPW with 20μm gaps fabricated on a silica glass. (b) CW ODMR spectrum for NV S1. The inset is energy levels of NV center. A 532nm laser is used to excite and initialize the NV center. Fluorescence is collected by a confocal microscope. (c) Rabi **oscillation** of NV S1. Rabi **oscillation** period is about 62ns. (d) Hahn echo and CPMG control pulse sequences. πx (πy) implies the direction of microwave magnetic fields parallel to x (y).
...Spectral density of the spin bath. (a) NV S1, (b) NV S2. All values of spectral density S(ω) of the spin bath are extracted from the CPMG data (blue points). Each blue data point represents a specific probed **frequency** ω=πn/t, in which n is the number of control pulses and t is the specific duration. The red points are the average values at a certain **frequency**. The mean spectral density is fit to the Lorentzian function (Eq. (3)) (green line). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
...Overcoming the spin **qubit** decoherence is a challenge for quantum science and technology. We investigate the decoherence process in nanodiamonds by Carr–Purcell–Meiboom–Gill (CPMG) technique at room temperature. We find that the coherence time T2 scales as nγ. The elongation effect of coherence time can be represented by a constant power of the number of pulses n. Considering the filter function of CPMG decoupling sequence as a δfunction, the spectrum density of noise has been reconstructed directly from the coherence time measurements and a Lorentzian noise power spectrum model agrees well with the experiment. These results are helpful for the application of nanodiamonds to nanoscale magnetic imaging....Characterization of lifetime of NV center spins. (a) Ramsey interference of NV S1 (circle) and NV S2 (diamond). The **oscillation** in Ramsey signal originates from the beating among different transitions corresponding to the host three 14N nuclear spin states. The **oscillation** **frequency** of Ramsey signal is equal to microwave detuning from spin resonance. Solid lines ~exp[−(t/T2⁎)m] fit the experimental data points, where m is a free parameter. (b) Comparison of Hahn echo coherence time T2 of NV S1 (circle) and NV S2 (diamond). The solid lines are fits to ~exp[−(t/T2)p], in which p is a fit parameter.
...Detection and manipulation of the qubit. (a) Fluorescence image of nanodiamond prepared on the CPW transmission line. NV S1 is circled. The inset is a photo of CPW with 20μm gaps fabricated on a silica glass. (b) CW ODMR spectrum for NV S1. The inset is energy levels of NV center. A 532nm laser is used to excite and initialize the NV center. Fluorescence is collected by a confocal microscope. (c) Rabi oscillation of NV S1. Rabi oscillation period is about 62ns. (d) Hahn echo and CPMG control pulse sequences. πx (πy) implies the direction of microwave magnetic fields parallel to x (y).
...Spectral density of the spin bath. (a) NV S1, (b) NV S2. All values of spectral density S(ω) of the spin bath are extracted from the CPMG data (blue points). Each blue data point represents a specific probed frequency ω=πn/t, in which n is the number of control pulses and t is the specific duration. The red points are the average values at a certain frequency. The mean spectral density is fit to the Lorentzian function (Eq. (3)) (green line). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
... Overcoming the spin **qubit** decoherence is a challenge for quantum science and technology. We investigate the decoherence process in nanodiamonds by Carr–Purcell–Meiboom–Gill (CPMG) technique at room temperature. We find that the coherence time T2 scales as nγ. The elongation effect of coherence time can be represented by a constant power of the number of pulses n. Considering the filter function of CPMG decoupling sequence as a δfunction, the spectrum density of noise has been reconstructed directly from the coherence time measurements and a Lorentzian noise power spectrum model agrees well with the experiment. These results are helpful for the application of nanodiamonds to nanoscale magnetic imaging.

Files:

Contributors: A.G. Khachatryan, F.A. van Goor, K.-J. Boller

Date: 2006-12-18

The amplitude of a** harmonic ****oscillator** after the action of a pulsed force with a Gaussian envelope and a linear chirp in dependence on the chirp strength, ΔΩ. In this case Ω0=5 and σ=5, 10, and 20; A=1 in all figures.
...The phase of the **oscillator** after action of a linearly-chirped pulsed force as a function of the chirp strength. In this case Ω0=4, σ=5.
...The amplitude of a harmonic **oscillator** after the action of a pulsed force with a Gaussian envelope and a linear chirp in dependence on the chirp strength, ΔΩ. In this case Ω0=5 and σ=5, 10, and 20; A=1 in all figures.
...The motion of a classical (harmonic) **oscillator** is studied in the case where the **oscillator** is driven by a pulsed **oscillating** force with a **frequency** varying in time (**frequency** chirp). The amplitude and phase of the **oscillations** left after the pulsed force in dependence on the profile and strength of chirp, **frequency** and duration of the force is investigated....The amplitude of the **oscillator** after the action of a force with an asymmetrical Gaussian envelope, σ1=5, Ω0=5, σ2=10 and 20.
...The amplitude of the **oscillator** vs. ΔΩ in the case of a periodical chirp in the force. The parameters of the force are: Ω0=5, σ=20, b=4.
...Classical **oscillator**...Classical **oscillator** driven by an oscillating chirped force...The motion of a classical (harmonic) **oscillator** is studied in the case where the **oscillator** is driven by a pulsed oscillating force with a **frequency** varying in time (**frequency** chirp). The amplitude and phase of the oscillations left after the pulsed force in dependence on the profile and strength of chirp, **frequency** and duration of the force is investigated....**Frequency** chirp ... The motion of a classical (harmonic) **oscillator** is studied in the case where the **oscillator** is driven by a pulsed **oscillating** force with a **frequency** varying in time (**frequency** chirp). The amplitude and phase of the **oscillations** left after the pulsed force in dependence on the profile and strength of chirp, **frequency** and duration of the force is investigated.

Files: