Contributors:Sun Jia-kui, Li Hong-juan, Jing-lin Xiao
Qubit... The relational curves of the oscillation period T of the qubit to the electron-LO-phonon coupling constant α and the polar angle θ.
... The oscillation period T changes with the confinement length l0 and the electron-LO-phonon coupling constant α.
... The relational curves of the oscillation period T to the confinement length l0 and the polar angle θ.
Contributors:D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, M.H. Devoret, C. Urbina, D. Esteve
Top: Rabi oscillations of the switching probability p (5×104 events) measured just after a resonant microwave pulse of duration τ. Solid line is a fit used to determine the Rabi frequency. Bottom: test of the linear dependence of the Rabi frequency with Uμw.
... (A) Calculated transition frequency ν01 as a function of φ and Ng. (B) Measured center transition frequency (symbols) as a function of reduced gate charge Ng for reduced flux φ=0 (right panel) and as a function of φ for Ng=0.5 (left panel), at 15mK. Spectroscopy is performed by measuring the switching probability p (105 events) when a continuous microwave irradiation of variable frequency is applied to the gate before readout. Continuous line: best fits used to determine circuit parameters. Inset: Narrowest line shape, obtained at the saddle point (Lorentzian fit with a FWHM Δν01=0.8MHz).
Contributors:M. Machida, T. Koyama
The schematic figure for the projected quantum levels in IJJ composed of two junctions, the switching dynamics, and the transition between two quantum states caused by the irradiation of the microwave whose frequency is Ω2.
... Rabi-oscillation... The schematic figure for the quantum levels for IJJ, which are projected onto the potential barrier of the single Josephson junction without the coupling. The energy levels of the out-of-phase and the in-phase oscillations have the highest and the lowest eigen-energies, respectively.
Contributors:Jonas Buchli, Ludovic Righetti, Auke Jan Ijspeert
Typical convergence of an adaptive frequencyoscillator (Eqs. (1)–(3)) driven by a harmonic signal (I(t)=sin(2πt)) and different coupling constants K. The coupling constant determines the convergence speed and the amplitude of oscillations around the frequency of the driving signal in steady state — the higher K the faster the convergence and the larger the oscillations.
... (a) Typical convergence of an adaptive frequencyoscillator (Eqs. (1)–(3)) driven by a harmonic signal (I(t)=sin(2πt)). The frequencies converge in an oscillatory fashion towards the frequency of the input (indicated by the dashed line). After convergence it oscillates with a small amplitude around the frequency of the input. The coupling constant determines the convergence speed and the amplitude of oscillations around the frequency of the driving signal in steady state. In all figures, the top right panel shows the driving signals (note the different scales). (b)–(f) Non-harmonic driving signals. We depict representative results on the evolution of ωdωF=ω−ωFωF vs. time. The dashed line indicates the zero error between the intrinsic frequency ω and the base frequency ωF of the driving signals. (b) Square pulse I(t)=rect(ωFt), (c) Sawtooth I(t)=st(ωFt) (d) Chirp I(t)=cos(ωct) ωc=ωF(1+12(t1000)2). (Note that the graph of the input signal is illustrative only since the change in frequency takes much longer than illustrated.) (e) Signal with two non-commensurate frequencies I(t)=12[cos(ωFt)+cos(22ωFt)], i.e. a representative example how the system can evolve to different frequency components of the driving signal depending on the initial condition ωd(0)=ω(0)−ωF. (f) I(t) is the non-periodic output of the Rössler system. The Rössler signal has a 1/f broad-band spectrum, yet it has a clear maximum in the frequency spectrum. In order to assess the convergence we use ωF=2πfmax, where fmax is found numerically by FFT. The oscillator convergences to this frequency.
... (N=10000, K=0.1) — (a) The FFT (black line) of the Rössler signal (for t=[99800,100000]) in comparison with the distribution of the frequencies of the oscillators (grey bars, normalized to the number of oscillators) at time 105 s. The spectrum of the FFT has been discretized into the same bins as the statistics of the oscillators in order to allow for a good comparison with the results from the full-scale simulation. (b) Time-series of the output signal O(t) (bold line) vs the teaching signal T(t) (dashed line).
... Adaptive frequencyoscillator... The structure of the dynamical system that is capable to reproduce a given teaching signal T(t). The system is made up of a pool of adaptive frequencyoscillators. The mean field produced by the oscillators is fed back negatively on the oscillators. Due to the feedback structure and the adaptive frequency property of the oscillators it reconstructs the frequency spectrum of T(t) by the distribution of the intrinsic frequencies.
... Coupled oscillators... Frequency analysis... (a) (N=1000, K=200) — T(t) is a non-stationary input signal (cf. text), in contrast to Figs. 4 and 5 the histogram of the distribution of the frequency ωi is shown for every 5 s, the grey level corresponds to the number of oscillators in the bins (note the logarithmic scale). The thin white line indicates the theoretical instantaneous frequency. Thus, it can be seen that the distribution tracks very well the non-stationary spectrum, however about 4% of the oscillators diverge after the cross-over of the frequencies. (b) This plots outlines the maximum tracking performance of the system for non-stationary signal. The input signal has a sinusoidal varying frequency. The frequency response of the adaptation is plotted (see text for details). As comparison we plot the first-order transfer function HK∞ and the vertical line indicates ωs=1. (c) The grey area shows the region where the frequency response of the adaptation is H>22. While for slower non-stationary signals the upper bound is a function of K, the bound becomes independent of K for ωs>1 (red dashed line).
Contributors:A Yahalom, R Englman
Two-electron state amplitude in a dimer, with both molecules subject to a periodic force. After a full revolution the two electronic states each change their sign, leaving the total state invariant. Frequencies: ω1=1, ω2=1, G1=−100, G2=−200, G=40 (near adiabatic limit). Thick line: first, initially excited component. Medium thick line: second and third components. Thin line: fourth component.
... Two-electron state amplitudes in a dimer. The thick line shows the time dependent amplitude of the first (initially excited component), the thin line that of the second component in Eq. (5). Frequencies: ω1=1, ω2=4, G1=−40, G2=−80, G=16 (near adiabatic limit)
... Non-adiabaticity effects in the real part of the initially excited component, as a function of time. The frequencies on the two dimers are ω1=1 and ω2=2. The values of the coupling parameters are as follows. Thick line: G1=−80, G2=−160, G=40 (near adiabatic limit). Thin line: G1=−8, G2=−16, G=4 (non-adiabatic case)
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.
Contributors:A.R. Bosco de Magalhães, Adélcio C. Oliveira
Nonlinear oscillator... Visibility dynamics in different timescales for initial state |Ψ2〉 and Γ=0. The timescale τp is associated to the decay of the envelope of the oscillations with characteristic time τr1. A very subtle increase in the amplitudes of the oscillations can be observed around t=τr2. The timescale of the fastest oscillations of the dynamics is τo.
... Visibility dynamics for initial state |Ψ2〉 and Γ varying from 0 to 0.1. For each value of Γ, the unit of time is chosen as the corresponding τp in (a), τr1 in (b), τr2 in (c), and τo in (d). For the majority of values of Γ investigated, the initial dynamics is flattened around t=2τp. Except for very small values of Γ, τr1 and τr2 are associated to partial revivals. When Γ increases, the number of fast initial oscillations decreases, but their characteristic durations are given by τo, which does not vary with Γ.
... Predictability dynamics in different timescales for initial state |Ψ2〉. The timescale τp is associated to the decay of the envelope of the oscillations with characteristic time τo. Revivals can be observed around the first multiples of τr.
... Predictability dynamics in different timescales for initial state |Ψ1〉. The timescale τp is associated to the rise and decay of the oscillations with characteristic time τo. Revivals occur in the region around τr and its first multiples.
... Visibility dynamics in different timescales for initial state |Ψ2〉 and Γ=0.1. The timescale τp is associated to the rise and decay of the initial dynamics. Both τr1 and τr2 are related to partial revivals. There are no oscillations besides the revivals and the initial rise and decay; the timescale of their duration is given by τo.
Contributors:R. Taranko, T. Kwapiński
Current-composed quantity Q(t) (solid lines) and the far-removed qubit QD occupancy, n3 (dashed lines), as a function of time for the horizontal qubit-detector connection, U13=U24=0, 2 or 4, respectively. μL=−μR=20, ΓL=5, ΓR=10, U12=U34=5 and the other parameters are the same as in Fig. 2. The lines for U13=U24=2 (4) are shifted by −1 (−2) for better visualisation.
... The sketch of the qubit-detector systems discussed in the text. Double quantum dot (1 and 4) between the left and right electron reservoirs stands for the qubit charge detector. Qubit is represented by two coupled quantum dots (2 and 3) occupied by a single electron. Straight black (zig-zag red) lines correspond to the tunnel matrix elements V14, V23 (Coulomb interactions, e.g. U14, U24) between the appropriate states. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)
... The asymptotic pulse-induced current I(τ) against the time interval (pulse length) τ – for details see the text – and the charge occupation of the far-removed qubit QD, n3, (dashed lines) for the qubit-detector system schematically shown in Fig. 1b. The upper (bottom) panel corresponds to ΓL=5, ΓR=10 (ΓL=5, ΓR=1). μL=−μR=20 and the other parameters are the same as in Fig. 2. The current lines are multiplied by −2 for better visualisation.
... Current-composed quantity Q(t) (solid lines) and the charge occupation of the far-removed qubit QD, n3, (dashed lines) as a function of time for the qubit-detector system schematically shown in Fig. 1b. The upper (bottom) panel corresponds to (ΓL,ΓR)=(5,1) ((ΓL,ΓR)=(5,10)). The other parameters are: μL=−μR=2 or μL=−μR=20, ε1,2,3,4=0, U24=5, U14=50, n2(t<10)=0, n3(t<10)=1. The lines for μL=−μR=20 are shifted by −1 for better visualisation.
... Upper panel: Current-composed quantity Q(t) (solid lines) and the far-removed qubit QD occupancy, n3, (dashed lines) as a function of time for different qubit-detector connections shown in Fig. 1d (U12=5), Fig. 1c (U12=U24=5) and Fig. 1b (U24=5)—the upper, middle and lower curves, respectively. The bottom panel depicts the corresponding left (solid lines) and right (dashed lines) currents, IL(t), IR(t), flowing in the system for the above three qubit-wire connections. μL=−μR=2, ΓL=5, ΓR=10 and the other parameters are the same as in Fig. 2. The lines in the upper panel for U12=U24=5 and for U24=5 are shifted by −1 and −2, respectively, and by −0.15 and −0.3 in the bottom panel. Note different scales in the vertical axis of both panels.
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
Contributors:T.P. Orlando, Lin Tian, D.S. Crankshaw, S. Lloyd, C.H. van der Wal, J.E. Mooij, F. Wilhelm
Equivalent circuit of the linearized qubit–SQUID system. ϕm and ϕp are the two independent variables of a DC SQUID. ϕm correpsonds to the circulating current of the SQUID, and ϕp couples with the ramping current of the SQUID. The capacitances of the inner oscillator loop and the external oscillator loop are Cm=2CJ and Cp, the shunt capacitance outside the SQUID. Flux of the three loops, q=q0σz, ϕm, and ϕp, are chosen as independent variables in the calculation. Each of the inductances in the three loops interacts by mutual inductances as are indicated by the paired dots near the inductances.
... The measuring circuit of the DC SQUID which surrounds the qubit. CJ and I0 are the capacitance and critical current of each of the junctions, and ϕi are the gauge-invariant phases of the junctions. The qubit is represented symbolically by a loop with an arrow indicating the magnetic moment of the |0〉 state. The SQUID is shunted by a capacitor Csh and the environmental impedance Z0(ω).