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Quantum computing requires a set of universal quantum gates. The standard set includes single quantum bit (qubit) gates and the controlled-NOT (CNOT) which is the analog of the classical XOR gate. It flips the state of the target qubit conditioned on the state of the control qubit. We investigated the possibility of implementing a CNOT logic gate using magnetically coupled impurity spins of diamond, namely the electron spin-1 carried by the nitrogen-vacancy color center and the electron spin-12 carried by a nearby nitrogen atom in substitutional position (P1 center). It is shown that a 96ns gate time with a high-fidelity can be realized by means of pulsed electron spin resonance spectroscopy.... (Color online) |A|2 is the probability of finding the spin system in the state |⇓↓〉. It oscillates at the high frequency D (=2.88GHz). The frequency of the beats is χ/2 (=16.7MHz). The amplitude of oscillations is also modulated by an additional cosine wave signal of frequency χ (see text). |C|2 is the probability of finding the spin system in the state |0↓〉. It oscillates at the low frequency χ. It is almost zero in the time interval 90–100ns. The probability of finding spin system in the state |⇑↓〉, |B|2, has the same oscillations than |A|2 but it is anti-phase (see Fig. 3). ... Ideal truth table and schematic representation of a two-qubit CNOT gate irradiated by a sequence of two microwave π/2-pulses of equal width t and a variable waiting time between pulses τ. In the text, x and y are the states of two impurity spins of diamond, namely the spin-12 carried by the P1 center and the spin-1 carried by the NV−1 color center. The symbol ⊕ is the addition modulo 2, or equivalently the XOR operation. ... (Color online) NV−1 Rabi oscillations. Control qubit down: blue, red and green lines correspond, respectively, to the time evolution of |A|2, |B|2 and |C|2, i.e., the probabilities of finding the spin system in the state |⇓↓〉, |⇑↓〉 and |0↓〉. Control qubit up: red, blue and green lines represent, respectively, |A′|2, |B′|2 and |C′|2, i.e., the probabilities of finding the spin system in the state |⇓↑〉, |⇑↑〉 and |0↑〉, i.e., |A′|2=|B|2, |B′|2=|A|2 and |C′|2=|C|2 (see text). Fig. 4 gives details in the interval 60–120ns. They can also be revealed by a zoom in.
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A quantum computer where quantum bits (qubits) are defined in frequency domain and interaction between qubits is mediated by a single cavity mode is proposed. In this quantum computer, qubits can be individually addressed regardless of their positions. Therefore, randomly distributed systems in space can be directly employed as qubits. An application of nuclear spins in rare-earth ions in a crystal for the quantum computer is quantitatively analyzed.... Qubits in solids... Schematic diagram of qubits addressed in a frequency domain. The ions whose 3H4(1)± 3 2–1D2(1) transitions are resonant with a common cavity mode are employed as qubits. ... Basic scheme of the concept of the frequency-domain quantum computer. The atoms are coupled to a single cavity mode. Lasers with frequencies of νk and νl are directed onto the set of atoms and interact with the kth and lth atoms selectively.
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Average PTO power as a function of oscillating frequency for straight (♦: solid line) and bent leg (□: broken line) tines (oscillation angle β=+27°). ... Subsoiler draft signals with time for the control and the range of oscillating frequencies. ... Dominant frequency of draft signal over the oscillating frequency range. ... Proportion of cycle time for cutting and compaction phases versus oscillating frequency (oscillation angle β=+27°). ... Dominant frequency of torque signal over the oscillating frequency range. ... Frequency... Based on the published benefits of oscillatory tillage, a subsoiler was developed at the University of South Australia, which had two deep working oscillatory tines and could be fitted with four shallow leading tines for increased loosening efficiency. A series of field trials were conducted in a sandy-loam soil to determine the most efficient setting of the tine's oscillatory motion and to compare the effect of using straight or bentleg tines. The tines were oscillated with an amplitude at the tip of ±69mm and an oscillation angle of 27° using a forward speed of 3km/h. The frequency of oscillation was varied from 1.9 to 8.8Hz. Analysis showed that the underside of the oscillating tine pushed rearward on the soil during part of the oscillation cycle, this decreased the draft in comparison to rigid tillage from 25.8 to 9.3kN. Increasing oscillation frequency, increased the PTO power requirement from 2.5kW at 1.9Hz to 26.3kW at 8.8Hz. The peaks and troughs in draft and torque were able to be aligned with the various phases of the oscillating tillage. An optimum oscillation frequency of 3.3Hz (velocity ratio of 1.5) was observed for minimum power to operate the oscillating subsoiler. Whilst at this setting, the combined draft and PTO power was similar to the draft power of rigid tillage, but when considering the higher losses due to tractive efficiency and lower PTO power losses, the oscillating tillage would be expected to require around 27% less engine power than rigid tillage.... Oscillating tine
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Nonlinear oscillators are widely used in biology, physics and engineering for modeling and control. They are interesting because of their synchronization properties when coupled to other dynamical systems. In this paper, we propose a learning rule for oscillators which adapts their frequency to the frequency of any periodic or pseudo-periodic input signal. Learning is done in a dynamic way: it is part of the dynamical system and not an offline process. An interesting property of our model is that it is easily generalizable to a large class of oscillators, from phase oscillators to relaxation oscillators and strange attractors with a generic learning rule. One major feature of our learning rule is that the oscillators constructed can adapt their frequency without any signal processing or the need to specify a time window or similar free parameters. All the processing is embedded in the dynamics of the adaptive oscillator. The convergence of the learning is proved for the Hopf oscillator, then numerical experiments are carried out to explore the learning capabilities of the system. Finally, we generalize the learning rule to non-harmonic oscillators like relaxation oscillators and strange attractors.... Adaptive frequency oscillator... 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.
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Summary of resonance frequencies found in all 10 babies (1 and 2 represents first and second run, respectively) ... A screen from our phase analysis program, showing phase analysis performed at four points of the respiratory cycle: top of breath, mid-inspiration, mid-expiration and bottom of breath. Corresponding points from the driving trace and the mouth pressure trace are matched and the phase difference calculated. In this case, the phase difference at the top of breath is 0° at an oscillating frequency of 20 Hz. ... high-frequency oscillation... In an oscillating system driven by a sine wave pump, the resonance frequency of the respiratory system can be determined using phase analysis. At resonance frequency, when elastance and inertance cancel out, flow becomes in-phase with resistance. In premature infants with respiratory distress syndrome, owing to surfactant deficiency, localized areas of hyperinflation and collapse develop, resulting in complex changes in overall pulmonary mechanics. We investigated the effect of measuring resonance frequency of the respiratory system by phase analysis at different points of the respiratory cycle: end of inspiration, end of expiration, mid-inspiration and mid-expiration. Ten ventilated premature infants with respiratory distress syndrome were studied, gestational age ranged from 24 to 30 weeks (mean 27.6 weeks) and birth weight ranged from 0.7 to 1.505 kg (mean 0.984 kg). Results: The resonance frequency was consistently higher when measured at the end of inspiration compared with the end of expiration. The expected trend of phase variation, that is, negative below the resonance frequency and positive above, was most consistently found when analysis was done at the end of inspiration. Conclusions: These findings were most likely a result of the complexity of pulmonary mechanics in the surfactant-deficient lungs, rendering the single compartment model we based our theory on inadequate. However, phase analysis performed at the end of inspiration seemed to produce the most reliable and consistent results.
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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... To demonstrate and quantify the occurrence of false High Frequency Oscillations (HFOs) generated by the filtering of sharp events. To distinguish real HFOs from spurious ones using analysis of the raw signal.
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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.) ... 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.
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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%.... 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... In this paper, the effect of spatial frequencies distributions on the oscillation death in a ring of coupled nonidentical oscillators is studied. We find that the rearrangement of the spatial frequencies may deform the domain of oscillation death and give rise to a ragged oscillation death in some parameter spaces. The usual critical curves with shape V in the parameter space of frequency-mismatch vs coupling-strength may become the shape W (or even shape WV). This phenomenon has been not only numerically observed in coupled nonidentical nonlinear systems, but also well supported by our theoretical analysis.
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Nonlinear oscillator... He’s frequency formulation is used to obtain the relationship between the frequency and amplitude of a nonlinear oscillator. The general approach is to choose two linear oscillators; in this paper, however, one linear oscillator and the Duffing oscillator are chosen as trial equations. The solution procedure is of utter simplicity, while the result is of high accuracy.... He’s frequency formulation
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