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

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58 J.M. Elzerman et al. two dots is made more transparent, and the intermediate-coupling regime is reached (Fig. 19b). Most lines are still straight, except in the bottom left corner, where they are slightly curved. This signifies that here the inter-dot tunnel-coupling is comparable to the capacitive coupling. If we make VM even less negative, we reach the strong-coupling regime (Fig. 19c). In this case, all lines are very curved, implying that the tunnel-coupling is dominating over the capacitive coupling. In this regime the double dot behaves like a single dot. 2.6 Photon-Assisted Tunnelling The use of gated quantum dots for quantum state manipulation in time requires the ability to modify the potential at high frequencies. We investigate the high-frequency behavior in the region around the last triple points (Fig. 20a), with a 50 GHz microwave-signal applied to gate PL. At the dotted line the 01 and 10 charge states are degenerate in energy, so one electron can tunnel back and forth between the two dots. Away from this line there is an energy difference and only one charge state is stable. However, if the energy difference matches the photon energy, the transition to the other dot is possible by absorption of a single photon. Such photon-assisted tunnelling events give rise to the two lines indicated by the arrows. At the lower (higher) line electrons are pumped from the the left (right) dot to the other one, giving rise to a negative (positive) photon-assisted current. We find that the distance (in terms of gate voltage) between the two photon-assisted tunnelling lines, ∆VL, scales linearly with frequency (Fig. 20b), as expected in the weak-coupling regime [47]. From the absence of bending of the line in Fig. 20b downtoa frequency of 6 GHz, it follows that the inter-dot tunnel coupling is smaller than about 12 µeV. The realization of a controllable few-electron quantum dot circuit represents a significant step towards controlling the coherent properties of single electron spins in quantum dots [2, 49]. Integration with the QPCs permits charge read-out of closed quantum dots. We note that charge read-out only affects the spin state indirectly, via the spin-orbit interaction. The back-action on the spin should therefore be small (until spin-to-charge conversion is initiated), and can be further suppressed by switching on the charge detector only during the read-out stage. Experiments described in the following sections focus on increasing the speed of the charge measurement, such that single-shot read-out of a single electron spin can be accomplished [49, 50]. 3 Excited-State Spectroscopy on a Nearly Closed Quantum Dot via Charge Detection In this section, we demonstrate a method for measuring the discrete energy spectrum of a quantum dot connected very weakly to a single lead. A train of
V L (V) -1.084 -1.082 -1.080 -1.078 a 11 Semiconductor Few-Electron Quantum Dots as Spin Qubits 59 01 00 10 -0.54 -0.55 -0.56 V PR (V) b ∆V L (mV) 5 4 3 2 1 0 0 10 20 30 40 Frequency (GHz) Fig. 20. Photon-assisted tunnelling in a one-electron double quantum dot. (a) Current through the double dot at the last set of triple points, with zero bias voltage (VDOT = VSD1 = VSD2 = 0). A microwave signal of 50 GHz is applied to PL. The microwaves pump a current, IDOT , by absorption of single photons [47]. This photonassisted current shows up as two lines, indicated by the two arrows. The white line (bottom) corresponds to electrons being pumped from the left to the right reservoir, the dark line (top) corresponds to pumping in the reverse direction. In the middle, around the dotted line separating the 01 from the 10 configuration, a finite current is induced by an unwanted voltage drop over the double dot, due to asymmetric coupling of the ac-signal to the two leads. (b) Separation between the two photonassisted tunnelling lines versus microwave frequency. The dependence is linear down to the lowest frequency of about 6 GHz, from which it follows that the inter-dot tunnel coupling (half the energy difference between bonding and anti-bonding state) is smaller than ∼12 µeV voltage pulses applied to a metal gate induces tunnelling of electrons between the quantum dot and a reservoir. The effective tunnel rate depends on the number and nature of the energy levels in the dot made accessible by the pulse. Measurement of the charge dynamics thus reveals the energy spectrum of the dot, as demonstrated for a dot in the few-electron regime. 3.1 Introduction Few-electron quantum dots are considered as qubits for quantum circuits, where the quantum bit is stored in the spin or orbital state of an electron in a single or double dot. The elements in such a device must have functionalities such as initialization, one- and two-qubit operations and read-out [2]. For all these functions it is necessary to have precise knowledge of the qubit energy levels. Standard spectroscopy experiments involve electron transport through the quantum dot while varying both a gate voltage and the source-drain 50
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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
Page 17 and 18: where � is a shorthand: � ≡ 3
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Page 23 and 24: RG for Interacting Fermions 13 the
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Page 27 and 28: 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
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Page 39 and 40: 1.2 Implementations Semiconductor F
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Page 49 and 50: ε1 ε0 e Semiconductor Few-Electro
Page 53 and 54: 250 Ω twisted pair 20 MΩ powder
Page 61 and 62: 10 5 0 -5 Semiconductor Few-Electro
Page 63 and 64: G ( e / h) 2 2 1 0 Semiconductor Fe
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Page 91 and 92: Spin-down counts 200 100 a Semicond
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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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