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  • Plot of the linear entropy ζ (as a function of t) of qubit1 initially in state |e〉, the oscillator initially in the number state |1〉 and qubit2 initially in a maximally mixed state, p=0.5 for a longer time-scale, with λ1=1.0 and λ2=0.1. ... Plot of the linear entropy ζ (as a function of t) of qubit1 initially in state |e〉 and the oscillator initially in a binomial state with M=7 and q=0.85. In this case qubit2 is decoupled, λ2=0.0 and λ1=1.0. ... Plot of the linear entropy ζ (as a function of t) of a qubit initially in state |e〉 and the oscillator initially in the mixed state ρosc(0)=f|0〉〈0|+(1−f)|1〉〈1| with λ=1.0 and f=0.5. ... Plot of the linear entropy ζ (as a function of t) of qubit1 initially in state |e〉 and the oscillator initially in a binomial state with M=11 and q=0.95. In this case qubit2 is coupled to the oscillator, with λ2=0.1, λ1=1.0, and p=0.5. ... Plot of the linear entropy ζ (as a function of t) of qubit1 initially in state |e〉 and the oscillator initially in a binomial state with M=100 and q=0.1. In this case qubit2 is decoupled, λ2=0.0 and λ1=1.0.
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  • a) Ground state energy E0 and (b) first excited state energy E1 as a function of the cyclotron frequency ωC for α = 7.0; F = 105.5; l0 = 0.45. ... (a) ground state energy E0 and (b) first excited state energy E1 as a function of the cyclotron frequency ωC for F = 105.0; l0 = 0.45; β = 0.8;. ... Transition frequency ω as a function of the cyclotron frequency ωc for (a) F = 105.0; l0 = 0.45; β = 0.8; ϑ = π/2; φ = 2π, (b) α = 7.0; l0 = 0.45; β = 0.8; ϑ = π/2; φ = 2π, (c) α = 7.0; F = 105.5; β = 0.8; ϑ = π/2; φ = 2π, (d) α = 7.0; F = 105.5; l0 = 0.45; ϑ = π/2; φ = 2π. ... a) ground state energy E0 and (b) first excited state energy E1 as a function of the cyclotron frequency ωC for α = 7.0; l0 = 0.45; β = 0.8. ... Period of oscillation τ as a function of the cyclotron frequency ωC for (a) F = 105.0; l0 = 0.45; β = 0.8; ϑ = π/2; φ = 2π, (b) α = 7.0; l0 = 0.45; β = 0.8; ϑ = π/2; φ = 2π, (c) α = 7.0; F = 105.5; β = 0.8; ϑ = π/2; φ = 2π, (d). α = 7.0; F = 105.5; l0 = 0.45; ϑ = π/2; φ = 2π.
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  • Schematic representation of the systems of a single qubit and two qubits interacting with the single electron transistor. The wavy lines correspond to the Coulomb interaction of electrons localized on the nearest quantum dots. ... The asymptotic current JL(t=∞) tunneling between the left lead and the SET QD against the pulse duration τ which determines the coherent qubit evolution (for details, see the text). The curve A (B, C, D, E) corresponds to the system of one (two) qubit coupled with the SET. The curve B (C) describes the case when the electron tunneling amplitude V inside one (both) qubit has a shape of the rectangular pulse of duration τ. The curve D (E) corresponds to the case when the pulse durations in the first and second qubits are equal τ and 2τ, respectively. εi=0,i=1,2,3,4,5; U1=U2=2, V=1 and μL=-μR=5. ... The probability n4(t) of finding the electron in the nearby qubit QD against the time in the case of two qubits coupled with the SET. The thin, thick and broken curves correspond to the bias voltage Vb=0,2 and 4, respectively. μL=-μR, U1=0.5, U2=1 and the other parameters are as in Fig. 5. ... The probability n3(t) of finding the electron in the nearby qubit QD and the current tunneling between the left lead and the SET QD against the time, the upper and lower panels, respectively. The left (right) panels correspond to one qubit (two qubits) coupled with the SET. The thin solid line describes the qubits with the constant electron energy levels, ε2=-ε3=ε4=-ε5=-1, and the thick, solid and broken lines correspond to harmonically driven energy levels with the amplitude Δ=1 and 2, respectively. ε1=0, μL=2, μR=-2, U1=U2=5, n3(0)=n5(0)=1, n1(0)=n2(0)=n4(0)=0. ... The probabilities n3(t) and n5(t) (the upper panels) of finding electrons in the far-removed qubit QDs against the time for the case of two qubits coupled with the SET. In the lower panel the current JL(t) tunneling between the left lead and the SET QD against the time is displayed. ε1=2, ε2=ε3=ε4=ε5=0, V1=V2=1, U1=U2 and μL=-μR=0.5. ... Charge qubit
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  • 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.
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  • 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.
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  • Silicon beam: (a) instantaneous frequency; (b) instantaneous damping; (c) equivalent modal frequency; (d) equivalent modal damping. _______ primary vacuum; - - - - pressure ∼300 mbar; . . . . . pressure ∼600mbar; – · – · – atmospheric pressure. ... Quartz beam: (a) equivalent modal frequency; (b) equivalent modal damping. _______ primary vacuum; - - - - pressure ∼300mbar; . . . . . pressure ∼600mbar; – · – · – atmospheric pressure. ... (a) Identified modal frequency: quartz structure; (b) identified modal frequency: lithium niobate structure; (c) identified modal damping: quartz structure; (d) identified modal damping: lithium niobate structure; symbols: experimental values; lines: polynomial fitting. and _______ primary vacuum; ● and - - - - pressure ∼300 mbar; ▴ and . . . . . pressure ∼600mbar; ■ and – · – · – atmospheric pressure. ... Department of Physics and Metrology of Oscillator, FEMTO-ST Institute, 32 Avenue de l’Observatoire, 25044 Besançon, France... (a) Instantaneous frequency; (b) instantaneous damping; (c) equivalent modal frequency; (d) equivalent modal damping. _______ 0.2ms−1; - - - - 0.15ms−1; . . . . . 0.10ms−1. ... Lithium niobate beam: (a) equivalent modal frequency; (b) equivalent modal damping. _______ primary vacuum; - - - - pressure ∼300mbar; . . . . . pressure ∼600mbar; – · – · – atmospheric pressure.
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  • Visualization of the ground state |0〉 and the coherent pointer-states |L〉 and |R〉 of the oscillator in the potential V(x).
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  • 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).
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  • 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)
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  • 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 oscillation frequency versus control voltage of (a) chip1 VCO. (b) chip2 VCO.
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