Contributors:R. Zadoyan, D. Kohen, D.A. Lidar, V.A. Apkarian
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. , which is different than that of Ref. .
... 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.
Contributors:S. Filippov, V. Vyurkov, L. Fedichkin
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.
... 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.
Contributors:Yun-Fei Liu, Jing-Lin Xiao
The relational curve of the oscillating period T and the electron–LOP coupling constant α.
... Qubit... The relational curve of the oscillating period T and the confinement length R.
Contributors:Haiteng Jiang, Ali Bahramisharif, Marcel A.J. van Gerven, Ole Jensen
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).
... 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).
... Cross-frequency directionality
Contributors:J.R. Petta, A.C. Johnson, J.M. Taylor, A. Yacoby, M.D. Lukin, C.M. Marcus, M.P. Hanson, A.C. Gossard
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
Contributors:S.K. Ryu, Y.K. Kim, M.K. Kim, S.H. Won, S.H. Chung
Behavior of periodically oscillating flame with large-scale oscillation for Vac=5kV, fac=20Hz, and U0=11m/s.
... Oscillationfrequency in terms of AC frequency for U0=11.0m/s and Vac=5kV.
... Low frequency... Average amplitude of large-scale oscillation with AC frequency for U0=11.0m/s and Vac=5kV.
... Oscillation... Phase diagrams of HL and dHL/dt for various oscillation modes.
... Edge height of lifted flame together with oscillation amplitude with AC frequency for Vac=5kV and U0=11.0m/s.
Contributors:A.G. Khachatryan, F.A. van Goor, K.-J. Boller
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 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... Frequency chirp
Contributors:F.K. Wilhelm, S. Kleff, J. von Delft
Visualization of the ground state |0〉 and the coherent pointer-states |L〉 and |R〉 of the oscillator in the potential V(x).
Contributors:Ludovic Righetti, Jonas Buchli, Auke Jan Ijspeert
Adaptive frequencyoscillator... The left plot of this figure represents the evolution of ω(t) when the adaptive Hopf oscillator is coupled to the z variable of the Lorenz attractor. The right plot represents the z variable of the Lorenz attractor. We clearly see that the adaptive Hopf oscillators can correctly learn the pseudo-frequency of the Lorenz attractor. See the text for more details.
... Plots of the frequency of the oscillations of the Van der Pol oscillator according to ω. Here α=50. There are two plots, for the dotted line the oscillator is not coupled and for the plain line the oscillator is coupled to F=sin30t. The strength of coupling is ϵ=2. We clearly see basins of phase-locking, the main one for frequency of oscillations 30. The other major basins appear each 30n (dotted horizontal lines). We also notice small entrainment basins for some frequencies of the form 30pq. For a more detailed discussion of these results refer to the text.
... We show the adaptation of the Van der Pol oscillator to the frequencies of various input signals: (a) a simple sinusoidal input (F=sin(40t)), (b) a sinusoidal input with uniformly distributed noise (F=sin(40t)+uniform noise in [−0.5,0.5]), (c) a square input (F=square(40t)) and (d) a sawtooth input (F=sawtooth(40t)). For each experiment, we set ϵ=0.7 and α=100 and we show three plots. The right one shows the evolution of ω(t). The upper left graph is a plot of the oscillations, x, of the system, at the beginning of the learning. The lower graph shows the oscillations at the end of learning. In both graphs, we also plotted the input signal (dashed). In each experiment, ω converges to ω≃49.4, which corresponds to oscillations with a frequency of 40 rad s−1 like the input and thus the oscillator correctly adapts its frequency to the frequency of the input.
... Frequency spectra of the Van der Pol oscillator, both plotted with ω=10. The left figure is an oscillator with α=10 and on the right the nonlinearity is higher, α=50. On the y-axis we plotted the square root of the power intensity, in order to be able to see smaller frequency components.
... This figure shows the convergence of ω for several initial frequencies. The Van der Pol oscillator is perturbed by F=sin(30t), with coupling ϵ=0.7, α=50. We clearly see that the convergence directly depends on the initial conditions and as expected the different kinds of convergence correspond to the several entrainment basins of Fig. 7.
Contributors:A. Yoshimi, T. Inoue, T. Furukawa, T. Nanao, K. Suzuki, M. Chikamori, M. Tsuchiya, H. Hayashi, M. Uchida, N. Hatakeyama, S. Kagami, Y. Ichikawa, H. Miyatake, K. Asahi
(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.