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Illustration of a linear ion trap including an axial magnetic field gradient. The static field makes individual ions distinguishable in frequency space by Zeeman-shifting their internal energy levels (solid horizontal lines represent qubit states). In addition, it mediates the coupling between internal and external degrees of freedom when a driving field is applied (dashed horizontal lines stand for vibrational energy levels of the ion string, see text). ... Rabi oscillations on the optical E2 transition S1/2-D5/2 in Ba + . A fit of the data (solid line) yields a Rabi frequency of 71.4 × 2πkHz and a transversal relaxation time of 100 μs (determined by the coherence time of the ir light used to drive the E2 resonance). ... Illustration of the coupled system ‘qubit ⊗ harmonic oscillator’ in a trap with magnetic field gradient. Internal qubit transitions lead to a displacement dz of the ion from its initial equilibrium position and consequently to the excitation of vibrational motion. In the formal description the usual Lamb–Dicke parameter is replaced by a new effective one (see text). ... (a) Relevant energy levels and transitions in 138Ba + . (b) Schematic drawing of major experimental elements. OPO: Optical parametric oscillator; YAG: Nd:YAG laser; LD: laser diode; DSP: Digital signal processing system allows for real time control of experimental parameters; AOM: Acousto-optic modulators used as optical switches and for tuning of laser light; PM: Photo multiplier tube, serves for detection of resonance fluorescence. All lasers are frequency and intensity stabilized (not shown). ... Schematic drawing of the resonances of qubits j and j + 1 with some accompanying sideband resonances. The angular frequency vN corresponds to the Nth axial vibrational mode, and the frequency separation between carrier resonances is denoted by δω.
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Dynamics controlled by f-STIRAP strategy for the preparation of the superposed state |R〉. Panels (a) and (b) show, respectively, the evolution of the localization in the right well for different values of λ and the Rabi frequencies of the different pulses. Rabi frequencies are in atomic units. The solid line of panel (b) corresponds to the Stokes pulse and the dashed one to the pump pulse. The total duration of the process is of the order of 4.5ps. ... Qubit... Half-live time τ1/2 in fs and the time τmax for which C(t) (Eq. (12)) vanishes for the two reference frequencies (Eq. (7)) and temperatures used in the simulations ... Robustness of the f-STIRAP process as a function of the peak Rabi frequency and the delay between the pulses for a total duration of 4.5ps of the overall field. Rabi frequency and delay are in atomic units. The upper and the lower part of the figure correspond, respectively, to λ=5×10−4 and λ=2×10−3.
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Driven qubit
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PES of the qubit system (a) and total dipole surface (b). For both surfaces: −52.8 pm⩽rA1⩽+52.8pm and −37.4pm⩽rE⩽+37.4pm. ... Normal modes included in the quantum dynamical calculation. (a) Coordinates of the qubit modes, (b) coordinates of the non-qubit modes. ... Spectral analysis of the NOT (top) and CNOT (bottom) gate. The solid lines correspond to the spectra of the optimized pulses, the dashed lines to the spectra of the sub pulses. The vertical lines indicate the relevant qubit basis transition frequencies for the quantum gates. ... spectroscopical data of the qubit vibrational modes E and A1 and the non-qubit modes, the δ-deformation mode (E) and the dissociative mode (A1)
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Free oscillation response of pendulum mechanism. ... Free oscillation response... Low frequency
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High-frequency oscillations... An example of the implantation schedule (patient #1) demonstrating areas with conventional frequency ictal patterns, ictal high-frequency oscillations, hyperexcitability, and radiological lesions. ... An example of the implantation schedule (patient #7) demonstrating areas with conventional frequency ictal patterns, ictal high-frequency oscillations, hyperexcitability, and radiological lesions. ... Summary table for statistical analysis. HFO=high frequency oscillations, CFIP=conventional frequency ictal patterns.
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Apparent dilational elasticity modulus as a function of oscillation frequency for drops of water (♦), water/ethanol 86:14 (■), ethanol (▴), amplitude of volume oscillations 8%. ... Surface tension and apparent dilational elasticity modulus E as a function of oscillation frequency for an air bubble in pure water. ... Oscillating drops and bubbles... Surface tension and apparent dilational elasticity modulus E as a function of oscillation frequency for a drop of pure water in air. ... Apparent dilational elasticity modulus as a function of oscillation frequency for drops of silicon oil (●), paraffin oil (■), amplitude of volume oscillations 2%. ... Limiting frequency... Apparent dilational elasticity modulus as a function of oscillation frequency for drops of water (♦), water/ethanol 86:14 (■), ethanol (▴), amplitude of volume oscillations 2%.
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(A) Comparison of the frequency of oscillations during oblique, pure horizontal and pure vertical saccades. Number of observations is plotted on y-axis, while x-axis represents bins of oscillation frequency. Each data point represents the number of observations in a given frequency bin. Black trace suggests oblique saccade, Gray traces with circular symbols are horizontal saccades and triangular symbols represent vertical saccade. Dashed lines depict median oscillation frequency. (B) Comparison of frequency oblique saccade oscillations with the frequency of orthogonal saccadic oscillations during pure horizontal and vertical saccades. Each data point depicts one subject. Black data points are comparison with pure horizontal saccade, gray data points are comparison with vertical saccade. Dashed gray line is an equality line. (C) Comparison of the amplitude of the sinusoidal modulation of oblique, horizontal, and vertical saccade trajectories. Number of samples is plotted on y-axis, while x-axis represents the amplitude bins. Each data point depicts number of observations in a given bin of the histogram. Black trace shows oblique saccade, Gray trace with circuit symbol is a horizontal saccade and the triangular symbol is a vertical saccade. Dashed lines represent median values. ... An example of horizontal, vertical, and oblique saccade from one healthy subject. The left column depicts horizontal saccade; central column vertical, and right column is oblique saccade. Panels A, B and C illustrate eye position vector plotted along y-axis. Panels D, E and F represent eye velocity vector plotted along y-axis while ordinate in panels G, H and I illustrate eye acceleration. In each panel, x-axis represents corresponding time. Arrows in panels C, F, I show oscillations in oblique saccade trajectory.
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Spontaneously occurring fast ‘ripple’ oscillations (400–500Hz) in the neocortex of the rat during high-voltage spindles. (A) Averaged high-voltage spindles and associated unit firing histograms from layers IV–VI. (B) Wide-band (a and a′; 1Hz–5kHz), filtered field (b and b′; 200–800Hz), and filtered unit (c and c′; 0.5–5kHz) traces from layers IV and V, respectively. (C) Averaged fast waves and corresponding unit histograms. The field ripples are filtered (200–800Hz) derivatives of the wide-band signals recorded from 16 sites. Note the sudden phase-reversal of the oscillating waves (arrows) but locking of unit discharges (dashed lines). These phase reversed dipoles likely reflect synchronous discharge of layer 5 neurons in the vicinity of the recording electrode. ... Self-organized burst of activity in the CA3 region of the hippocampus produces a sharp wave sink in the apical dendrites of CA1 pyramidal neurons and also discharge interneurons. The interactions between the discharging pyramidal cells and interneurons give rise to a short-lived fast oscillation (‘ripple’; 140–200Hz), which can be detected as a field potential in the somatic layer. The strong CA1 population burst brings about strongly synchronized activity in the target populations of parahippocampal structures as well. These parahippocampal ripples are slower and less synchronous, compared to CA1 ripples.
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High-frequency oscillations... Time–frequency distributions. On the left side, the full 20–1000 Hz range is displayed for three exemplary subjects. The two graphs per subject show the ERG and VEP activity, respectively. The high-frequency oscillations appear as a distinct area which in most cases is around or above 100 Hz. The flash was given at t=0. Those parts of the time–frequency diagram which would be contaminated by edge effects are displayed in white. Their spread is due to the inevitable frequency-dependent finite time resolution, which also causes the spurious pre-stimulus activity at low frequencies. The white rectangles in the diagrams mark the regions of interest, which are shown enlarged on the right side for all 7 subjects. The arrows link the high-frequency maxima of ERG and VEP. Most subjects produced activity around or above 100 Hz in both VEP and ERG. However, only in one subject (S1) the frequencies matched. Asterisks indicate the significance levels of frequency differences in standard notation, based on a sequential Bonferroni adjustment. No significance value could be obtained for subject S3.
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