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  • 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
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  • FEMTO-ST Institute, Frequency and Time Department, 26, Chemin de l’Epitaphe, Besançon 25000, France... Measured phase noise of a 5MHz high quality quartz crystal resonator. fL denotes the so-called Leeson frequency, i.e. a half of a resonator bandwidth. The dashed line is needed to identify the PSD value at f=1Hz from the carrier which is used to calculate the corresponding Allan deviation [2].
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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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  • 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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  • 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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  • 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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  • 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.
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  • Diagrammatic representation of time-resolved CARS. Both time-circuit and Feynman diagram are illustrated for a non- overlapping sequence of P, S, P′ pulses, with central frequency of the S-pulse chosen to be outside the absorption spectrum of the B←X transition, to ensure that only the P(0,3) component of the third-order polarization is interrogated. In this dominant contribution, all three pulses act on bra (ket) state while the ket (bra) state evolves field free. Note, for the Feynman diagrams, we use the convention of Ref. [6], which is different than that of Ref. [5]. ... The wavepacket picture associated with the evolution of the ket-state in the diagram of Fig. 1, for resonant CARS in iodine. The required energy matching condition for the AS radiation, Eq. (10b) of text, can only be met when the packet reaches the inner turning point of the B-surface. Once prepared, ϕ(3)(t) will oscillate, radiating periodically every time it reaches the inner turning point.
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