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

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70 J.M. Elzerman et al. ∆I (nA) 3 2 1 0 a 0 1 2 3 4 Time (ms) 2 1 0 b 0 1 2 3 4 Time (ms) Fig. 26. Measured changes in the QPC current, ∆I, with the electrochemical potential in the dot and in the reservoir nearly equal. ∆I is “high” and “low” for 0 and 1 electrons on the dot respectively (Vi =1mV;thestepsin∆I are ≈ 300 pA). Traces are offset for clarity. (a) The dot potential is lowered from top to bottom. (b) The tunnel barrier is lowered from top to bottom a ∆I (nA) 1.2 0.8 0.4 0.0 -0.4 pulse 0 0.5 1.0 Time (ms) electron 1.5 b (nA) 1.0 0.5 0.0 1.0 0.5 0.0 Γ -1= 230 µ s -1 Γ =60µ s 0 0.5 1.0 1.5 Time (ms) Fig. 27. QPC pulse response. (a) Measured changes in the QPC current, ∆I, when a pulse is applied to gate P , near the degeneracy point between 0 and 1 electrons on the dot (Vi = 1 mV). (b) Averageof286tracesasin(a). The top and bottom panel are taken with a different setting of gate M. The damped oscillation following the pulse edges is due to the 8th-order 40 kHz filter the time before tunnelling takes place is randomly distributed, and obtain a histogram of this time simply by averaging over many single-shot traces (Fig. 27b). The measured distribution decays exponentially with the tunnel time, characteristic of a Poisson process. The average time before tunnelling corresponds to Γ −1 , and can be tuned by adjusting the tunnel barrier.
4.5 QPC Versus SET Semiconductor Few-Electron Quantum Dots as Spin Qubits 71 Our measurements clearly demonstrate that a QPC can serve as a fast and sensitive charge detector. Compared to an SET, a QPC offers several practical advantages. First, a QPC requires fabrication and tuning of just a single additional gate when integrated with a quantum dot defined by metal gates, whereas an SET requires two tunnel barriers, and a gate to set the island potential. Second, QPCs are more robust and easy to use in the sense that spurious, low-frequency fluctuations of the electrostatic potential hardly change the QPC sensitivity to charges on the dot (the transition between quantized conductance plateaus has an almost constant slope over a wide range of electrostatic potential), but can easily spoil the SET sensitivity. With an RF-SET, a sensitivity to charges on a quantum dot of ≈2 × 10 −4 e/ √ Hz has been reached [58], and theoretically even a ten times better sensitivity is possible [57]. Could a QPC reach similar sensitivities? The noise level in the present measurement could be reduced by a factor of two or three using a JFET input-stage which better balances input voltage noise and input current noise. Further improvements can be obtained by lowering the capacitance of the filters in the line, or the line capacitance itself, by placing the IV-convertor close to the sample, inside the refrigerator. Much more significant reductions in the instrumentation noise could be realized by embedding the QPC in a resonant electrical circuit and measuring the damping of the resonator. We estimate that with an “RF-QPC” and a low-temperature HEMT amplifier, a sensitivity of 2 × 10 −4 e/ √ Hz could be achieved with the present sample. The noise from the amplifier circuitry is then only 2.5 times larger than the shot noise level. To what extent the signal can be increased is unclear, as we do not yet understand the mechanism through which the dot occupancy is disturbed for Vi > 1mV 4 . Certainly, the capacitive coupling of the dot to the QPC channel can easily be five times larger than it is now by optimizing the gate design [60]. Keeping Vi = 1 mV , the sensitivity would then be 4×10 −5 e/ √ Hz, and a single electron charge on the dot could be measured within a few ns. Finally, we point out that a QPC can reach the quantum limit of detection [63, 64], where the measurement induced decoherence takes the minimum value permitted by quantum mechanics. Qualitatively, this is because (1) information on the charge state of the dot is transferred only to the QPC current and not to degrees of freedom which are not observed, and (2) an external perturbation in the QPC current does not couple back to the charge state of the dot. 4 The statistics of the RTS were altered for Vi > 1 mV, irrespective of (1) whether Vi was applied to the QPC source or drain, (2) the potential difference between the reservoir and the QPC source/drain, and (3) the QPC transmission T .
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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
Page 29 and 30: � p � dθp = g 2π RG for Inter
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Page 33 and 34: References RG for Interacting Fermi
Page 35 and 36: Semiconductor Few-Electron Quantum
Page 39 and 40: 1.2 Implementations Semiconductor F
Page 43 and 44: GaAs n-AlGaAs AlGaAs GaAs Semicondu
Page 49 and 50: ε1 ε0 e Semiconductor Few-Electro
Page 53 and 54: 250 Ω twisted pair 20 MΩ powder
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Page 63 and 64: G ( e / h) 2 2 1 0 Semiconductor Fe
Page 67 and 68: V R (V) V R (V) Semiconductor Few-E
Page 69 and 70: V L (V) -1.084 -1.082 -1.080 -1.078
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Page 77 and 78: a RESERVOIR 200 nm Semiconductor Fe
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Page 85 and 86: a b c V P (mV) 10 5 0 ∆I QPC E F
Page 91 and 92: Spin-down counts 200 100 a Semicond
Page 101 and 102: 6.7 Unresolved Issues Semiconductor
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124 M. Pustilnik and L.I. Glazman G
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126 M. Pustilnik and L.I. Glazman d
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128 M. Pustilnik and L.I. Glazman 1
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130 M. Pustilnik and L.I. Glazman 7
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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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