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

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48 J.M. Elzerman et al. by two quantum point contacts, serving as charge detectors. These enable determination of the precise number of conduction electrons on each dot. This number can be reduced to zero while still allowing transport measurements through the double dot. Even in the few-electron case, the tunnel coupling between the two dots can be controlled over a wide range, from the weakcoupling to the strong-coupling regime. In addition, we use microwave radiation to pump an electron from one dot to the other by absorption of a single photon. The experiments demonstrate that this quantum dot circuit can serve as a good starting point for a scalable spin-qubit system. 2.1 Few-Electron Quantum Dots The experimental development of a quantum computer is presently at the stage of realizing few-qubit circuits. In the solid state, particular success has been achieved with superconducting devices, in which two macroscopic quantum states are used as a qubit two-level system (see [38] and references therein). The opposite alternative would be the use of two-level systems defined by microscopic variables, for instance the spin (or charge) state of single electrons confined in semiconductor quantum dots [27]. For the control of one-electron quantum states by electrical voltages, the first requirement is to realize an appropriate quantum dot circuit containing just a single conduction electron. Single-electron quantum dots have been created in self-assembled structures [39] and also in small vertical pillars defined by etching [40]. (Recently, also semiconductor nanowires and carbon nanotubes have been used for this purpose.) The disadvantage of these types of quantum dots is that they are hard to integrate into circuits with a controllable coupling between the elements, although integration of vertical quantum dot structures is currently being pursued [41, 42]. Alternatively, we can use a system of lateral quantum dots defined in a two-dimensional electron gas (2DEG) by surface gates on top of a semiconductor heterostructure [27]. Here, integration of multiple dots is straightforward, by simply increasing the number of gate electrodes. In addition, the tunnel coupling between the dots can be tuned in situ, since it is controlled by the gate voltages. The challenge is to reduce the number of electrons to one per quantum dot. This has long been impossible, since reducing the electron number tends to be accompanied by a decrease in the tunnel coupling, resulting in a current too small to be measured [43]. In this section, we demonstrate double quantum dot devices containing a voltage-controllable number of electrons, down to a single electron. We have integrated these devices with charge detectors that can read out the charge state of the double quantum dot with a sensitivity better than a single electron charge. The importance of the present circuit is that it can serve as a fully tunable two-qubit system, following the proposal by Loss and DiVincenzo [2], which describes an optimal combination of the single-electron charge degree of freedom (for convenient manipulation using electrical voltages) and the
Semiconductor Few-Electron Quantum Dots as Spin Qubits 49 spin degree of freedom (which promises a long coherence time, essential for encoding quantum information). 2.2 Samples We have fabricated and measured several few-electron double quantum dots, of three different designs (Fig. 14). The first two types have only been used once as few-electron single dots. In both cases, one of the gate electrodes was not functioning, which prevented us from testing if these devices also function as few-electron double dots. The third type of device (Fig. 14c) did function as a double dot, and was used for all subsequent few-electron experiments. To verify that the first device (Fig. 14a) can operate as a few-electron single quantum dot, we performed a large-bias measurement of the differential conductance through the dot. Going towards more negative gate voltage, a series of “Coulomb diamonds” is revealed (Fig. 15a), in which the number of electrons on the dot, N, is constant. This is followed by a region in which the “diamond” does not close, even up to a source-drain voltage of 10 mV, i.e. several times larger than the typical charging energy for a small dot (∼2meV). Therefore, in this region N =0. The tunnel coupling between the dot and the source and drain reservoirs could be changed by simply readjusting the gate voltages. For strong coupling, a zero-bias peak – hallmark of the Kondo effect – became visible throughout the one-electron diamond (Fig. 15b). From the width of the zero-bias peak (Fig. 15c) we found a Kondo temperature of about 0.4 K. The appearance of a one-electron Kondo effect (unpublished) implies that this quantum dot design allows the tunnel coupling to be tuned over a wide range, even in the few-electron regime. In addition, it is striking evidence that we can confine a single spin in a lateral quantum dot. In the second quantum dot design (Fig. 14b), the narrow “plunger” gates approach the dot more from the sides, rather than from below. In this way, they are further away from the central tunnel barrier, reducing the effect they have on the tunnel rate. Also, the gate coming from the top of the picture was made thinner, in order to make the tunnel barriers more easily controllable [43]. Thirdly, the characteristic gates ending in circles (see Fig. 14a) were left out. This device was quite easily tunable. In the rest of this section, we use the third design (Fig. 14c). Two nominally identical devices are studied, both as shown in Fig. 16a. They consist of a double quantum dot flanked by two quantum point contacts (QPCs), defined in a 2DEG that is present below the surface of a GaAs/AlGaAs heterostructure. The layout of the double quantum dot is an extension of previously reported single dot devices [43]. The double dot is defined by applying negative voltages to the 6 central gates. Gate T in combination with the left (right) gate, L (R), controls the tunnel barrier from the left (right) dot to drain 1 (source 2). Gate T in combination with the middle gate, M, controls the tunnel barrier between the two dots. The narrow “plunger” gates, PL and
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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
Page 9 and 10: Contents A Guide for the Reader ...
Page 11 and 12: A Guide for the Reader Quantum dots
Page 13 and 14: The Renormalization Group Approach
Page 15 and 16: RG for Interacting Fermions 5 where
Page 17 and 18: where � is a shorthand: � ≡ 3
Page 19 and 20: RG for Interacting Fermions 9 These
Page 21 and 22: RG for Interacting Fermions 11 is i
Page 23 and 24: RG for Interacting Fermions 13 the
Page 25 and 26: RG for Interacting Fermions 15 this
Page 27 and 28: RG for Interacting Fermions 17 equa
Page 29 and 30: � p � dθp = g 2π RG for Inter
Page 31 and 32: RG for Interacting Fermions 21 the
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
Page 57: Semiconductor Few-Electron Quantum
Page 61 and 62: 10 5 0 -5 Semiconductor Few-Electro
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
Page 71 and 72: B // Semiconductor Few-Electron Qua
Page 77 and 78: a RESERVOIR 200 nm Semiconductor Fe
Page 81 and 82: 4.5 QPC Versus SET Semiconductor Fe
Page 83 and 84: a reservoir dot Semiconductor Few-E
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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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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