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The period of oscillation T0 in a QR as a function of the transverse and longitudinal effective confinement lengths of the QR lp and lv. ... The period of oscillation T0 in a QR as a function of the electron–phonon coupling strength α and the Coulomb bound potential β. ... Qubit... The period of oscillation T0 in a QR as a function of the ellipsoid aspect ratio e′ and the electron–phonon coupling strength α.
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Microwave spectroscopy of a one-electron double dot. (a) Charge occupancy of the left dot, M, as a function of ε for several microwave frequencies. (b) One-half of the resonance peak splitting as a function of f for several values of VT. Solid lines are best fits to the experimental data using the theory outlined in the text. Inset: Two-level system energy level diagram. (c) Amplitude of the resonance, expressed as Mmax(τ)/Mmax(τ=5ns), as a function of chopped cw period, τ, with f=19GHz. Theory gives a best fit T1=16ns (solid line, see text). Inset: Single photon peak shown in a plot of M as a function of ε for τ=5ns and 1μs. (d) Power dependence of the resonance for f=24GHz. Widths are used to extract the ensemble-averaged charge dephasing time T2*. At higher microwave powers multiple photon processes occur. Curves are offset by 0.3 for clarity. ... Rabi oscillation... Spin qubit... Charge qubit
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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.) ... 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.
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(a) Spin maser oscillation signal observed in a time span of 24 hours. (b) Transient pattern in the initial spin maser oscillation. (c) Steady state oscillation after the transient settled. The signals shown in the ordinates represent the beat between the spin detection signal and a 36.12 Hz fixed frequency reference signal for a lock-in amplifier. ... (a) Fourier spectrum obtained when the newly introduced current source was used for the oscillator operation. The measurement time was 3×104 seconds. (b) Fourier spectrum obtained when the previous current source was used for the oscillator operation. The measurement time was 1×104 seconds. ... Nuclear spin oscillator... Steady state oscillations observed at three low frequencies: (a) ν0=17.7 Hz, (b) ν0=8.9 Hz, (c) ν0=2.5 Hz. The strength of the static field adopted in the individual operations are indicated in the respective panels. ... Frequency precision... Frequency precision of the spin oscillation. The abscissa represents the standard deviation of the frequency ν determined by fitting a function ϕ(t)=2πνt+ϕ0 to the observed precession phases ϕ from t=0 to t=Tm. Solid, dotted and dashed lines are the presentation of three cases with power laws σν∝Tm−3/2, σν∝Tm−1, and σν∝Tm−1/2 respectively.
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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. ... Frequency... Prediction accuracy of simultaneous equations for oscillation frequency. ... Frequencies at different test conditions—300kgm−2s−1.
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Spatial frequencies distributions... Ragged oscillation death... The phase synchronization domains (areas enclosed by the red lines) and the OD regions (black areas) in the parameter space of ε-δω for a ring of coupled Rossler systems with different frequency distributions: (a) G={1,2,3,4,5,6,7,8}, (b) G={1,4,3,6,2,8,5,7}, and (c) G={1,2,3,6,8,4,7,5}. N=8. The ragged OD sates are clear in (b) and (c) within a certain interval of δω indicated by two vertical dashed lines. In all three insets, the values of ωj are plotted for given ω0=0 and δω=N. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... The bifurcation diagram and the largest Lyapunov exponent λ of the coupled Rossler oscillators versus the coupling strength ε with the same spatial arrangement of natural frequencies as in Fig. 1(a)–(c), respectively for δω=0.58. The bifurcation diagram is realized by the soft of XPPAUT [33] where the black dots are fixed points and the red dots are the maximum and minimum values of x1 for the stable periodic solution while the blue dots means the max/min values of x1 for the unstable periodical states. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... The critical curves of OD domain from analysis in N coupled Landau–Stuart oscillators for different N’s: (a) N=2, (b) N=3, and (c)–(e) N=4 for G={1,2,3,4},G={1,2,4,3}, and G={1,3,2,4}, respectively. The ragged OD domain is clear in (d). The numerical results with points within the domains perfectly verify the analytical results. ... The OD regions in the parameter space of ε-δω for a ring of coupled Rossler systems with different frequency distributions: (a) G={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30}, (b) G={26,16,25,18,5,14,10,4,6,7,21,12,23,8,1,15,9,29,28,11,2,20,27,30,3,13,17,22,24,19}, and (c) G={19,22,18,13,10,28,7,15,17,8,30,12,26,11,20,9,27,21,25,6,29,1,23,5,3,24,16,14,4,2}. N=30. In all three insets, the values of ωj are plotted for given ω0=0 and δω=N. ... Coupled nonidentical oscillators
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A phase-locking model for entrainment of peripheral oscillators to the cyclin–CDK oscillator. (a) Molecular mechanism of the Cdc14 release oscillator. The mitotic phosphatase Cdc14 is activated upon release from sequestration in the nucleolus. This release is controlled by a negative feedback loop in which Cdc14 release, promoted by the polo kinase Cdc5, activates APC-Cdh1, which then promotes Cdc5 degradation, allowing Cdc14 resequestration. This negative-feedback oscillator is entrained to the cyclin–CDK cycle at multiple points: by cyclin–CDK promotion of CDC5 transcription and Cdc5 kinase activation, and by cyclin–CDK inhibition of Cdh1 activity. (b) Schematic of multiple peripheral oscillators coupled to the CDK oscillator in budding yeast. As described above, coupling entrains such peripheral oscillators to cell cycle progression; peripheral oscillators also feed back on the cyclin–CDK oscillator itself. For example, major genes in the periodic transcription program include most cyclins, CDC20, and CDC5; Cdc14 directly promotes establishment of the low-cyclin–CDK positive feedback loop by activating Cdh1 and Sic1 as well as more indirectly antagonizing cyclin–CDK activity by dephosphorylating cyclin–CDK targets; the centrosome and budding cycles could communicate with the cyclin–CDK cycle via the spindle integrity and morphogenesis checkpoints. (c) Oscillator coupling ensures once-per-cell-cycle occurrence of events. Three hypothetical oscillators are shown: a master cycle in black, a faster peripheral cycle in blue, and a slower peripheral cycle in red. In the absence of phase-locking (top), the oscillators trigger events (colored circles) without a coherent phase relationship. In the presence of oscillator coupling (bottom), the peripheral oscillators are slowed or accelerated within their critical periods to produce a locked phase relationship, with events occurring once and only once within each master cycle. ... Positive and negative feedback loops in the cyclin–CDK oscillator. (a) Inset: a negative feedback loop which can give rise to oscillations. Such an oscillator is thought to form the core of eukaryotic cell cycles, with cyclin–Cyclin Dependent Kinase (cyclin–CDK) acting as activator, Anaphase Promoting Complex-Cdc20 (APC-Cdc20) acting as repressor, and non-linearity in APC-Cdc20 activation preventing the system from settling into a steady state. Below is shown the cyclin–CDK machinery in eukaryotic cell cycles. CDKs, present throughout the cell cycle, require the binding of a cyclin subunit for activity. These cyclin partners can also determine the localization of the complex and its specificity for targets. At the beginning of the cell cycle, cyclin–CDK activity is low, and ramps up over most of the cycle. Early cyclins trigger production of later cyclins and these later cyclins then turn off the earlier cyclins, so that control is passed from one set of cyclin–CDKs to the next. The last set of cyclins to be activated, the G2/M-phase cyclins, initiate mitosis, and also initiate their own destruction by activating the APC-Cdc20 negative feedback loop. APC-Cdc20 targets the G2/M-phase cyclins for destruction, resetting the cell to a low-CDK activity state, ready for the next cycle. (b) Positive feedback is added to the oscillator in multiple ways. Left: a highly conserved but non-essential mechanism consists of ‘handoff’ of cyclin proteolysis from APC-Cdc20 to APC-Cdh1. Cdh1 is a relative of Cdc20 which activates the APC late in mitosis and into the ensuing G1. Cdh1 is inhibited by cyclin–CDK activity, resulting in mutual inhibition (which is logically equivalent to positive feedback). Middle: antagonism between cyclin–CDK and stoichiometric CDK inhibitors (CKIs) results in positive feedback. These loops stabilize high- and low-CDK activity states. Right: a double positive feedback loop comprising CDK-mediated inhibition of the Wee1 kinase (which inhibits CDK) and activation of the Cdc25 phosphatase (which activates CDK by removing the phosphorylation added by Wee1) is proposed to stabilize intermediate CDK activity found in mid-cycle, and an alternative stable state of high mitotic CDK activity.
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High Frequency Oscillations
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Examples of a spike without HFOs (left) and a spike with HFOs (right), as defined with the Analytic Morse wavelet in the time–frequency domain. ... High Frequency Oscillations... Parameter selection for the Analytic Morse Wavelet; top: time–frequency presentation for different values of n (m=40), bottom: raw signal and filtered signal (80–250Hz). Blue lines represent HFO interval marked visually. ... Examples of detection errors. Left: HFO without isolated blob but having oscillation in the raw signal. Right: HFO without visible oscillation in the raw signal but representing an isolated peak. Blue lines show the HFO interval marked by reviewers. ... Time–frequency
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Qubit... (Color online.) Contour plots of the normalized decay rate γ(τ)/γ0 of the qubit only in the cavity bath, versus the time interval τ between successive measurements, and the central frequency ωcav of the cavity mode. (a) The width of the cavity frequency is λ=10−4Δ, and accordingly the cavity quality factor Q=104. (b) The width of the cavity frequency λ=5×10−3Δ, corresponding to the cavity quality factor Q=2×103. The region 1⩽γ(τ)/γ0⩽1.05 is shown as light magenta. The QZE region corresponds to γ(τ)/γ01. Evidently, a transition from the QZE to the AZE is observed by varying the central frequency of the cavity mode at finite τ (τ>0.6Δ−1 when Q=104, and τ>2.6Δ−1 when Q=2×103). ... (Color online.) Time dependence of the probability for the qubit at its excited state. In the resonant case, the parameters are ωcav=Δ=100g and τ=0.1g−1. In the detuning case, the cavity mode frequency is varied to ωcav=80g. Note that the successive measurements slow down the decay rate of excited state in the resonant case, which is the QZE. While in the detuning case, the measurements speed up the qubit decay rate, which is the AZE. ... The normalized effective decay rate γ(τ)/γ0 of the qubit for two quality factors Q when τ=5Δ−1, in the presence of both the cavity bath and the low-frequency qubitʼs intrinsic bath. ... (Color online.) (a) Sketch of a qubit with the spontaneous dissipation rate γ coupled to a cavity with the loss rate κ via a coupling strength g. (b) and (c) schematically show the bath density spectrum of the qubit environment: (b) the Ohmic qubitʼs intrinsic bath (green dashed) and the Lorentzian cavity bath (red solid), (c) the low-frequency qubitʼs intrinsic bath (green dashed) and the Lorentzian cavity bath (red solid). ... (Color online.) (a) Superconducting circuit model of a frequency-tunable transmission line resonator, which is archived by changing the boundary condition, coupled with a qubit. (b) Superconducting circuit model (1) of the effective tunable inductors, which are consisted of a series array of SQUIDs (2).
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