Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

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88 J.M. Elzerman et al. (ESR) effect. A microwave magnetic field Bac oscillating in the plane perpendicular to B, at a frequency f = gµBB/h (in resonance with the spin precession about B) causes the spin to make transitions between |↑〉 and |↓〉. The choice of B strength is a trade-off between reliable initialization and read-out (strong B is better) and experimental convenience (low f is easier). We expect that a perpendicular field of 4 Tesla should be sufficient to provide high-fidelity read-out and initialization, with f ≈ 25 GHz (for g = −0.44). Alternatively, in a parallel field we may have to go up to 8 Tesla, corresponding to f ≈ 45 GHz [54], for high-fidelity spin measurement. However, since single-shot read-out is not strictly required, a somewhat lower field could also be enough. Properly timed bursts of microwave power tip the spin state over a controlled angle, e.g. 90 ◦ or 180 ◦ . In order to observe Rabi oscillations, the Rabi period must be at most of the order of the single-spin decoherence time T2. For a Rabi period of 150 ns, we need a microwave field strength Bac of ∼1 mT. If T2 is much longer, there is more time to coherently rotate the spin, so a smaller oscillating field is sufficient. We intend to generate the oscillating magnetic field by sending an alternating current through an on-chip wire running close by the dot (Fig. 38a). If the wire is placed well within one wavelength (which is a few mm at 30 GHz near the surface of a GaAs substrate) from the quantum dot, the dot is in the near-field region and the electric and magnetic field distribution produced by the AC current should be the same as for a DC current [91]. With a wire 200 nm from the dot, a current of ∼1 mA should generate a magnetic field of about 1 mT and no electric field at the position of the dot. To minimize a b I ac 500 nm B ac B 20 µ m Fig. 38. On-chip wire to apply microwaves to a nearby quantum dot. The device was made by Laurens Willems van Beveren and Jort Wever. (a) Scanning electron microscope image of a device consisting of a double quantum dot in close proximity to a gold wire. An AC current through the wire, Iac, generates an oscillating magnetic field, Bac, perpendicular to the plane. If the AC frequency is resonant with the Zeeman splitting due to a large static in-plane magnetic field, B, a spin on the dot will rotate. (b) Large-scale view of the wire, designed to be a 50 Ω coplanar stripline
Semiconductor Few-Electron Quantum Dots as Spin Qubits 89 reflection and radiation losses, the wire is designed to be a shorted coplanar stripline (Fig. 38b) with a 50 Ω impedance. To detect the electron spin resonance (ESR) and obtain a lower bound on T2 from the linewidth of the resonance signal, various methods have been proposed, either using transport measurements [92] or relying on charge detection [93]. In both cases, the required spin-to-charge conversion is achieved by positioning the dot levels around the Fermi energy of the reservoir (Fig. 39a–b). The ESR-field induces spin flips, exciting |↑〉electrons to |↓〉, which can then tunnel out of the dot. This leads to an average current (Fig. 39a) or to a change in the average occupation of the dot (Fig. 39b). However, in this configuration the dot is particularly sensitive to spurious effects induced by the microwaves, such as |↑〉electrons being excited out of the dot via thermal excitation or photon-assisted tunnelling. These processes can completely obscure the spin resonance. ~k T B a b c ↑ ↓ ↑ ↓ Fig. 39. Detecting ESR. (a) To detect ESR in a transport measurement [92], the dot is placed in Coulomb blockade, so that electron spins that are flipped by the ESR field can contribute to a current. (b) A similar configuration is used to detect ESR via changes in the occupation of the dot [90], measured using a charge detector. (c) If the dot is deep in Coulomb blockade during the spin-flip stage, the electron is not easily excited to the reservoir via thermal excitation or photon-assisted tunnelling. (d) The microwaves are off during the spin read-out stage to enhance the measurement fidelity Such problems can be avoided by combining (pulsed) electron spin resonance with single-shot spin measurement. This allows us to separate the spin manipulation stage (during which the microwaves are on) from the spin read-out stage (without microwaves). In this way, excitation out of the dot is prevented by Coulomb blockade (Fig. 39c), until spin read-out is initiated (Fig. 39d). In contrast to the techniques described above – which require a large spin flip rate to generate a measurable current or disturbance of the dot occupation – this approach only requires the spin flip rate to be faster than the decoherence rate. Therefore, a longer T2 allows us to use a smaller Bac, corresponding to (quadratically) smaller microwave power. This should help to suppress heating and photon-assisted tunnelling. In principle, an ESR experiment can be performed in a parallel or a perpendicular magnetic field. The read-out in a perpendicular field is particularly ↑ ↓ d ↓ ↑
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Lecture Notes in Physics Editorial
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W. Dieter Heiss (Ed.) Quantum Dots:
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Preface Nanoscale physics, nowadays
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Contents A Guide for the Reader ...
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A Guide for the Reader Quantum dots
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The Renormalization Group Approach
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RG for Interacting Fermions 5 where
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where � is a shorthand: � ≡ 3
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RG for Interacting Fermions 9 These
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RG for Interacting Fermions 11 is i
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RG for Interacting Fermions 13 the
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RG for Interacting Fermions 15 this
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RG for Interacting Fermions 17 equa
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� p � dθp = g 2π RG for Inter
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RG for Interacting Fermions 21 the
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References RG for Interacting Fermi
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Semiconductor Few-Electron Quantum
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1.2 Implementations Semiconductor F
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GaAs n-AlGaAs AlGaAs GaAs Semicondu
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140 C.W.J. Beenakker A stroboscopic
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142 C.W.J. Beenakker largely indepe
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144 C.W.J. Beenakker The effective
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146 C.W.J. Beenakker Fig. 6. Ensemb
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148 C.W.J. Beenakker 1.4 1.2 1.0 0.
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150 C.W.J. Beenakker 〈ρ(E)〉 =
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152 C.W.J. Beenakker P 0.5 0.4 0.3
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154 C.W.J. Beenakker P(x) 0.4 0.3 0
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156 C.W.J. Beenakker tunnel/ Egap 4
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158 C.W.J. Beenakker its momentum).
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160 C.W.J. Beenakker E00 = π� =
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162 C.W.J. Beenakker 〈ρ(E)〉 δ
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164 C.W.J. Beenakker As described i
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166 C.W.J. Beenakker 0.30 � Egap
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168 C.W.J. Beenakker The τE-depend
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170 C.W.J. Beenakker that a fully m
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172 C.W.J. Beenakker (τ−,τ+), w
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174 C.W.J. Beenakker 61. P. G. Silv
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Heiss W.D. (ed.) Quantum dots.. a doorway to - tiera.ru

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