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

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74 J.M. Elzerman et al. changes in IQP C thus permits us to measure on a timescale of about 8 µs whether an electron resides on the dot or not (L.M.K.V. et al., see Sect. 4). In this way the QPC is used as a charge detector with a resolution much better than a single electron charge and a measurement timescale almost ten times shorter than 1/Γ . The device is placed inside a dilution refrigerator, and is subject to a magnetic field of 10 T (unless noted otherwise) in the plane of the 2DEG. The measured Zeeman splitting in the dot [54], ∆EZ ≈ 200 µeV, is larger than the thermal energy (25 µeV) but smaller than the orbital energy level spacing (1.1 meV) and the charging energy (2.5 meV). 5.3 Two-Level Pulse Technique To test our single-spin measurement technique, we use an experimental procedure based on three stages: (1) empty the dot, (2) inject one electron with unknown spin, and (3) measure its spin state. The different stages are controlled by voltage pulses on gate P (Fig. 29a), which shift the dot’s energy levels (Fig. 29c). Before the pulse the dot is empty, as both the spin-↑ and spin-↓ levels are above the Fermi energy of the reservoir, EF . Then a voltage pulse pulls both levels below EF . It is now energetically allowed for an electron to tunnel onto the dot, which will happen after a typical time ∼Γ −1 . The particular electron can have spin-↑ (shown in the lower diagram) or spin-↓ (upper diagram). (The tunnel rate for spin-↑ electrons is expected to be larger than that for spin-↓ electrons [82], i.e. Γ↑ >Γ↓, but we do not assume this a priori.) During this stage of the pulse, lasting twait, the electron is trapped on the dot and Coulomb blockade prevents a second electron to be added. After twait the pulse is reduced, in order to position the energy levels in the read-out configuration. If the electron spin is ↑, its energy level is below EF , so the electron remains on the dot. If the spin is ↓, its energy level is above EF , so the electron tunnels to the reservoir after a typical time ∼Γ −1 ↓ .Now Coulomb blockade is lifted and an electron with spin-↑ can tunnel onto the dot. This occurs on a timescale ∼Γ −1 (with Γ = Γ↑ + Γ↓). After tread, the ↑ pulse ends and the dot is emptied again. The expected QPC-response, ∆IQP C, to such a two-level pulse is the sum of two contributions (Fig. 29b). First, due to a capacitive coupling between pulse-gate and QPC, ∆IQP C will change proportionally to the pulse amplitude. Thus, ∆IQP C versus time resembles a two-level pulse. Second, ∆IQP C tracks the charge on the dot, i.e. it goes up whenever an electron tunnels off the dot, and it goes down by the same amount when an electron tunnels on the dot. Therefore, if the dot contains a spin-↓ electron at the start of the read-out stage, ∆IQP C should go up and then down again. We thus expect a characteristic step in ∆IQP C during tread for spin-↓ (dotted trace inside gray circle). In contrast, ∆IQP C should be flat during tread for a spin-↑ electron. Measuring whether a step is present or absent during the read-out stage constitutes our spin measurement.
a b c V P (mV) 10 5 0 ∆I QPC E F Semiconductor Few-Electron Quantum Dots as Spin Qubits 75 empty Q dot =0 E E in t wait inject & wait Q dot =-e t read read-out empty out in out time Q dot=0 time Fig. 29. Two-level pulse technique used to inject a single electron and measure its spin orientation. (a) Shape of the voltage pulse applied to gate P . The pulse level is 10 mV during twait and 5 mV during tread (which is 0.5 ms for all measurements). (b) Schematic QPC pulse-response if the injected electron has spin-↑ (solid line) or spin-↓ (dotted line; the difference with the solid line is only seen during the read-out stage). Arrows indicate the moment an electron tunnels into or out of the quantum dot. (c) Schematic energy diagrams for spin-↑ (E↑) and spin-↓ (E↓) during the different stages of the pulse. Black vertical lines indicate the tunnel barriers. The tunnel rate between the dot and the QPC-drain on the right is set to zero. The rate between the dot and the reservoir on the left is tuned to a specific value, Γ .Ifthe spin is ↑ at the start of the read-out stage, no change in the charge on the dot occurs during tread. In contrast, if the spin is ↓, the electron can escape and be replaced by a spin-↑ electron. This charge transition is detected in the QPC-current (dotted line inside gray circle in (b)) 5.4 Tuning the Quantum Dot into the Read-Out Configuration To perform spin read-out, VM has to be fine-tuned so that the position of the energy levels with respect to EF is as shown in Fig. 29c. To find the correct settings, we apply a two-level voltage pulse and measure the QPC-response
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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
Page 33 and 34: References RG for Interacting Fermi
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132 C.W.J. Beenakker e e N I N S Fi
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134 C.W.J. Beenakker 2 Andreev Refl
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136 C.W.J. Beenakker F E x 8d/hv ga
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138 C.W.J. Beenakker and we have de
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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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