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.
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.
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.
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.
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.
Contributors:Jacky Desbiolles, Gholamhossein Shahgoli, John Fielke, 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
Contributors:Chang-Pu Sun, Qing Ai, Franco Nori, Xiufeng Cao
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).