Diagrammatic sketch of a qubit coupled with structured environments. The environment in the 1st case consists of a two level system coupled to a bath. The environment in 2nd case is a damped harmonic oscillator.
... (1st case) P(t) as a function of time for the on-resonance case (ΔA=ΔB), where the decoherence is enhanced with T. Inset (a): Fourier analysis of P(t). One can see that two frequencies are dominating the dynamics and the peaks locate at ΔA±g0. Inset (b): The effective spectral density Jeff(ω). Here, it is not πJeff(ΔA) but πJeff(ΔA±g0) indicates the damping rate γA.
... (2nd case) P(t) as a function of time, where the decoherence is enhanced with T. Inset (a): Fourier analysis of the main plot. One sees that two frequencies are dominating the dynamics and the splitting of the peaks increases with temperature. Inset (b): The effective spectral density Jeff(ω). The square, triangle and circle points correspond to the dominant frequencies of P(t) in different temperatures, respectively. One can see that smaller Jeff’s, which characterize long time dynamics, are almost the same for three different temperatures. This is the reason why the damping rate of P(t) is almost not changing with different temperatures.
Contributors:Jürgen Audretsch, Felix E. Klee, Thomas Konrad
Comparison between simulated evolution of a qubit's Rabi oscillations and processed measurement signal for p¯=0.5, Δp=0.1 and τ=TR/16. Dashed curve: |c1|2 over time (in units of the Rabi period TR) in the presence of weak measurements. Dotted curve: |c1|2 over time in the absence of measurements. The solid curve corresponds to the evolution of the estimate g based on the measurement results.
... Power spectrum of |c1|2 in the presence of measurements. It assumes its maximum at the frequency ΩR of the undisturbed Rabi oscillations.
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.
Flux qubit... Example of the dynamics for the symmetric case ε=0, where the oscillatorfrequency is in resonance with the TSS frequency, i.e., Ω=Δ0. Parameters are: g=0.18Δ0, κ=0.014 (→α=0.004), kBT=0.1ℏΔ0. QUAPI parameters are M=12, K=1, Δt=0.06/Δ0.
... Sz(ω) for two values of the oscillatorfrequency Ω. Parameters are: ε=0, g=0.07Δ0, κ=0.014, kBT=0.1ℏΔ0.
... Main: Dephasing rates corresponding to peak 1 and peak 2 in the Figs. 1 and 3 as a function of the HO frequency Ω. The parameters are: ε=0, g=0.07Δ0, κ=0.014, kBT=0.1ℏΔ0. Inset: Same for stronger damping κ=0.02 with α=0.01=const. (like in ). This implies that with varying Ω also g is changed.
Contributors:J.G Hartnett, P Bilski, E.N Ivanov, M.E Tobar
The Allan deviation of fractional temperature fluctuations of a liquid nitrogen bath (curve 1) and a solid nitrogen bath (curve 2) measured with the ac-bridge. Curve 3 are the measured room temperature fractional fluctuations. Curve 4 are the measured fractional temperature fluctuations in the cavity determined by measuring the oscillatorfrequency fluctuations cooled by a liquid nitrogen bath (77 K). Curve 5 are the measured fractional temperature fluctuations in the cavity determined by measuring the oscillatorfrequency fluctuations cooled to 58 K by a solid nitrogen bath and a foil heater and temperature controller. Curve 6 are the inferred fractional temperature fluctuations in the cavity passively cooled by a solid nitrogen bath (52 K).
... Frequency Standards and Metrology Research Group, Department of Physics, University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia... Schematic of loop oscillator used.
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.
(Color online.) Schematic diagram of the displaced oscillator basis. The horizontal axis x′=x2mω0ℏ. All three wells maintain the same harmonic character, and usual eigenstates as well. The equilibrium position of the left (or the right) well is shifted by a specific constant. The shift direction is to the left (or right) when the qubits are in |+〉=|e1,e2〉 (or |−〉=|g1,g2〉). The middle potential well which is double degenerate corresponds to non-displaced case in which the states of the two qubits are opposite, i.e., |0〉 (|g1,e2〉 or |e1,g2〉), and the equilibrium position is higher than the others. The eigenstates which have the same value of n in the left well are degenerate with that in the right well.
... (Color online.) (a) Schematic diagram of the structure. The two light blue squares are improved three-junction flux qubits fabricated to the center conductor. (b) Schematic graph of the system. Two identical qubits (i.e. parameters Δ, ϵ, energy-level splitting Eq and coupling strength g for both qubits are of the same value) viewed as a two-level system with ground state |g〉 and excited state |e〉, are coupled to a harmonic oscillator whose characteristic frequency is ω0.
... (Color online.) Comparison between the displaced oscillator adiabatic approximation method and the numerical solution for the lowest two levels. ℏω0/Eq=10. The black solid lines stand for the lowest two energy levels calculated by adiabatic approximation. The green dashed line and the red dashed line correspond to the lowest two energy levels obtained by the numerical solution. (a) θ=0. (b) θ=π/6. (c) θ=π/4. (d) θ=π/3.
The sketch of the qubit–detector systems considered in the paper. The qubit (two coupled quantum dots: x and y) is coupled electrostatically via U parameter with one of the detector QDs. Panels A, B and C correspond to the single-QD, double-QD and triple-QD detectors, respectively.
... Qubit QD occupations, nx(t), versus time for the DQD (TQD) detector – curves a–c (d, e) and for different initial conditions. Curves a and d: qubit is ‘frozen’ in the state nx=0,ny=1 until t=40 when the occupancies of all detector QDs achieve their steady state values. Curves b and e: qubit is ‘frozen’ in the state nx=0,ny=1 and also n2=n3=0 until t=40 when the occupancy of the first detector QD, n1, achieves its steady state value. Curve c: all couplings in the qubit–detector system are switched on at t=40 (i.e. nx=0,ny=1, n1=n2=0 for t<40). The other parameters: Vxy=4, U=4, Vij=0.5, Γ=1, εi=0 and μL=−μR=20.
... Charge qubit... The nearby qubit QD occupation, nx(t), as a function of time for the triple-QDs detector shown in Fig. 1C for different values of the qubit tunneling amplitude Vxy=1,2 and 4, respectively. The upper (bottom) panel corresponds to μL=−μR=1 (μL=−μR=10). The other parameters are εi=0, V12=V23=1, Vxy=4, U=4 and the initial conditions as in Fig. 2.
... Nearby qubit QD occupation, nx(t), as a function of time for the triple-QD detector (see Fig. 1C) for different values of U parameter: U=0,2,3,4 and 6, respectively. The bias voltage μL=−μR=10, other parameters and initial conditions as in Fig. 6.
... Nearby qubit QD occupation, nx(t), as a function of time for different forms of the detector depicted in Fig. 1. The upper (bottom) panel corresponds to the ΓL=ΓR=Γ=1 (Γ=0.2). The tunneling coupling between QDs is V=1 for the detector and Vxy=4 for the qubit, energy levels of all QDs are equal to εi=0, μL=−μR=10 and U=4. The qubit was ‘frozen’ in the configuration nx=0, ny=1 for t<15, i.e. until the detector QD occupancies and currents jL and j12 achieved their stationary values. The curves B and C are shifted down by 1 and 2 for clarity.
... Qubit dynamics