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

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82 J.M. Elzerman et al. We now choose the optimal value of the threshold as the one for which the visibility 1 − α − β is maximal (dotted vertical line in Fig. 34b). For this setting, α ≈ 0.07, β1 ≈ 0.17, β2 ≈ 0.15, so the measurement fidelity for the spin-↑ and the spin-↓ state is ∼0.93 and ∼0.72 respectively. The measurement visibility in a single-shot measurement is thus at present 65%. Significant improvements in the spin measurement visibility can be made by lowering the electron temperature (smaller α) and especially by making the charge measurement faster (smaller β). Already, the demonstration of singleshot spin read-out and the observation of T1 of order 1 ms are encouraging results for the use of electron spins as quantum bits. 6 Semiconductor Few-Electron Quantum Dots as Spin Qubits In the previous sections we have described experiments aimed at creating a quantum dot spin qubit according to the proposal by Loss and DiVincenzo [2] (see also paragraph 1.3). The key ingredients for these experiments – performed over the last two years – are a fully tunable few-electron double quantum dot and a quantum point contact (QPC) charge detector. We have operated the QPC in three different ways: 1. By measuring its DC conductance, changes in the average charge on the double dot are revealed, which can be used to identify the charge configuration of the system. 2. By measuring the conductance in real-time (with a bandwidth of ∼100 kHz), we can detect individual electrons tunnelling on or off the dot (in less than 10 µs). 3. By measuring the QPC response to a gate voltage pulse train (with the proper frequency) using a lock-in amplifier, we can determine the tunnel rate between the dot and a reservoir. In addition, by using a large pulse amplitude and measuring changes in the effective tunnel rate, we can identify excited states of the dot. Using these techniques, we have demonstrated that our GaAs/AlGaAs quantum dot circuit is a promising candidate for a spin qubit. However, we do not have a fully functional qubit yet, as coherent manipulation of a singleor a two-spin system has so far remained elusive. In this section, we evaluate the experimental status of the spin qubit project in terms of the DiVincenzo spin-↑) isgivenby1− β1. The probability that this tunnel event is detected (i.e. is not too fast) is given by 1−β2. Therefore, the probability that a spin-↓ electron tunnels out and is detected, is (1−β1)(1−β2). In addition, there is the possibility that the ↓-electron relaxes, with probability β1, but a step in the QPC signal is nevertheless detected, with probability α, due to the “dark count” mechanism. Therefore, the total probability that a spin-↓ electron is declared “spin-down” is given by (1 − β1)(1 − β2)+(αβ1) approximately.
Semiconductor Few-Electron Quantum Dots as Spin Qubits 83 requirements [17]. Fabrication and characterization of a double quantum dot containing two coupled spins has been achieved, as well as initialization and single-shot read-out of the spin state. The single-spin relaxation time was found to be very long, but the decoherence time is still unknown. We present concrete ideas on how to proceed towards coherent spin operations. Single-spin manipulation relies on a microfabricated wire located close to the quantum dot, and two-spin interactions are controlled via the tunnel barrier connecting the respective quantum dots. To demonstrate superposition and entanglement of spin states, we plan to use a charge detection approach, without relying on transport measurements. 6.1 Qubit The first of the five DiVincenzo requirements is to have a scalable physical system with well-characterized qubits. We have fabricated double quantum dot devices in which a single electron can be confined in each of the two dots (see Sect. 2). The spin states |↑〉and |↓〉of the electron, subject to a large magnetic field B, correspond to the two states of the proposed qubit two-level system. The Zeeman splitting, ∆EZ, between the two states can be tuned with the magnetic field, according to ∆EZ = gµBB, with g ≈−0.44 the electron g-factor in GaAs [54], and µB the Bohr magneton. These one-electron dots can be fully characterized using a QPC as a charge detector, with the techniques developed in Sects. 2 and 3. First of all, we can use the QPC to monitor the charge configuration of the double dot, in order to reach the regime where both dots contain just a single electron. Then we can evaluate and tune the tunnel rate from each dot to the reservoir using the lock-in technique described above. The same technique can be employed to determine the energy spectrum of each of the two dots, i.e. the Zeeman splitting between the two qubit states, as well as the energy of orbital excited states. Furthermore, the QPC can be used to monitor the inter-dot tunnel barrier, both qualitatively (from the curvature of lines in the honeycomb diagram, as shown in Fig. 2.6) and quantitatively (by performing photon-assisted tunnelling spectroscopy to measure the tunnel splitting between the one-electron bonding and anti-bonding state, as in [86]). In principle, it is even possible to use the lock-in technique to measure the exchange splitting J between the delocalized two-electron singlet and triplet spin states. However, in practical situations the splitting might be too small (
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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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Semiconductor Few-Electron Quantum
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1.2 Implementations Semiconductor F
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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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