Reproduction of the Lorenz signal with an oscillator trained by cross-validation.
... Reconstructed voiced part of the voiced fricative /zh/ by combining linear prediction and the oscillator model.
... Reconstruction of the Lorenz system by the oscillator model with Bayesian training using embedding dimension N=5.
... Nonlinear predictor (a) and oscillator model (b).
... Phase space embeddings of the output of the original Lorenz system (top), the training signals (middle row), and the output of the oscillator model (bottom row). The embedding dimension used for the oscillator is N=3, the RBF network comprises 64 centers.
... Oscillator model... Institute of Communications and Radio-Frequency Engineering, Vienna University of Technology, Vienna 1040, Austria
(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.
Contributors:Meng-Ting Hsu, Tsung-Han Han, Yao-Yen Lee
Voltage controlled oscillator... Microwave Communication and Radio Frequency Integrated Circuit Lab, Department and Institute of Electronic Engineering, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou 64002, Yunlin, Taiwan, ROC... Output oscillationfrequency versus control voltage of (a) chip1 VCO. (b) chip2 VCO.
Contributors:Gholamhossein Shahgoli, John Fielke, Jacky Desbiolles, Chris Saunders
Average PTO power as a function of oscillatingfrequency 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 oscillatingfrequencies.
... Dominant frequency of draft signal over the oscillatingfrequency range.
... Proportion of cycle time for cutting and compaction phases versus oscillatingfrequency (oscillation angle β=+27°).
... Dominant frequency of torque signal over the oscillatingfrequency range.
... Frequency... Oscillating tine
Qubits in solids... Schematic diagram of qubits addressed in a frequency domain. The ions whose 3H4(1)±
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.
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.
Stepped-frequency continuous-wave radar... For the unshifted LPT the first raw frequency-domain sample obtained means of the VNA is aligned with the DFT frequency bin representing frequency Δf. Thus, raw frequency-domain samples do not coincide with the appropriate DFT frequency bins. The negative frequency components are obtained by means of mirroring a conjugated version of the positive ones around DC. Throughout the paper, the positive and negative spectra are depicted by the same individual diagonal patterns.
... The extended array structure with non-zero values only for positive frequencies. Raw data samples are starting at DFT frequency Δf.
... The extended array structure with non-zero values only for negative frequencies. Mirrored conjugated raw data samples are starting at DFT frequency −Δf.
... SNR of the frequency-domain outcome of the FFT for different numbers n of time-domain samples of a sine tone of frequency 2GHz with additive Gaussian noise of standard deviation σ=0.8 sampled with constant sampling frequency, fs=10GHz.
... Department for High-Frequency Technology, Technische Universität Braunschweig, Schleinitzstraße 22, 38106 Braunschweig, Germany... Frequency-domain signal processing... High oscillations for the shifted LPT occurs when fmin is large compared to Δf.
Contributors:Dong-Qi Liu, Gang-Qin Liu, Yan-Chun Chang, Xin-Yu Pan
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 oscillationfrequency 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.