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

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84 J.M. Elzerman et al. 6.2 Read-Out We have achieved single-shot read-out of the spin orientation of an individual electron in a quantum dot (see Sect. 5). Our approach utilizes the Zeeman splitting, induced by a large magnetic field parallel to the 2DEG, to create spin-to-charge conversion (Fig. 35a). This is followed by real-time detection of single-electron tunnelling events using the QPC. The total visibility of the spin measurement is ∼65%, limited mostly by the ∼40 kHz bandwidth of our current measurement setup, and also by thermal excitation of electrons out of the quantum dot, due to the high effective electron temperature of ∼300 mK. a b E F ↓ ↑ ∆E Z Fig. 35. Schematic energy diagrams depicting spin-to-charge conversion based on a difference in energy (a) between |↑〉and |↓〉, or on a difference in tunnel rate (b) We estimate that we can improve the visibility of the spin read-out technique to more than 90% by lowering the electron temperature below 100 mK, and especially by using a faster way to measure the charge on the dot. This could be possible with a “radio-frequency QPC” (RF-QPC), similar to the well-known RF-SET [57]. In this approach, the QPC is embedded in an LC circuit with a resonant frequency of ∼1 GHz. By measuring the reflection or transmission of a resonant carrier wave, we estimate that it should be possible to read out the charge state of the nearby quantum dot in ∼1 µs, an order of magnitude faster than is currently attainable. A disadvantage of the read-out technique based on the Zeeman splitting is that it relies on accurate positioning of the dot-levels with respect to the Fermi energy of the reservoir, EF (see Fig. 35a). This makes the spin read-out very sensitive to charge switches, which can easily push the |↑〉 level above EF , or pull |↓〉below EF , resulting in a measurement error. To counteract this effect, a large enough Zeeman splitting is required (in Sect. 5 a magnetic field of more than 8 Tesla was used, although with a more stable sample a lower field might be sufficient). On the other hand, a smaller Zeeman splitting is desirable because it implies a lower and therefore more convenient resonance frequency for coherent spin manipulation. In addition, the spin relaxation time is expected to be longer at smaller ∆EZ. Therefore, a different spin read-out mechanism that is less sensitive to charge switches and can function at lower fields would be very useful. E F ↓ ↑ ∆E Z
Semiconductor Few-Electron Quantum Dots as Spin Qubits 85 A particularly convenient way to perform spin-to-charge conversion could be provided by utilizing not a difference in energy between spin-up and spindown, but a difference in tunnel rate (Fig. 35b). To read out the spin orientation of an electron on the dot, we simply raise both dot levels above EF ,so that the electron can leave the dot. If the tunnel rate for spin-up electrons, Γ↑, is much larger than that for spin-down electrons, Γ↓, then at a suitably chosen time the dot will have a large probability to be already empty if the spin was up, but a large probability to be still occupied if the spin is down. Measuring the charge on the dot within the spin relaxation time can then reveal the spin state. This scheme is very robust against charge switches, since no precise positioning of the dot levels with respect to the leads is required: both levels simply have to be above EF . Also, switches have a small influence on the tunnel rates themselves, as they tend to shift the whole potential landscape up or down, which does not change the tunnel barrier for electrons in the dot [87]. Of course, the visibility of this spin measurement scheme depends on the difference in tunnel rate we can achieve. A difference in tunnel rate for spin-up and spin-down electrons is provided by the magnetic field. From large-bias transport measurements in a magnetic field parallel to the 2DEG [82], we find that the spin-selectivity (Γ↑/Γ↓) grows roughly linearly from ∼1.5 at5Teslato∼5 at 14 Tesla. This is in good agreement with the spin-selectivity of about 3 that was found at 10 Tesla using the single-shot spin measurement technique of Sect. 5. We believe that this spin-dependence of the tunnel rates is due to exchange interactions in the reservoirs. If ∆EZ is the same in the dot as in the reservoirs, the tunnel barrier will be the same for |↑〉and |↓〉electrons, giving Γ↑ = Γ↓ (Fig. 36a). However, close to the dot there is a region with only |↑〉electrons, where an electron that is excited from |↑〉 to |↓〉 must overcome not only the single-particle Zeeman energy but also the many-body exchange energy between the reservoir electrons [88]. We can describe this situation with an a b E F ∆E Z E CB 0↔↓ 0↔↑ ↓ ↑ E F ∆E +E Z X E CB 0↔↓ 0↔↑ Fig. 36. Exchange interaction in the reservoirs leading to spin-selective tunnel rates. (a) Schematic diagram of the conduction band edge ECB near the dot for electrons with spin-up (solid line) andspin-down(dashed line). If ∆EZ in the reservoirs is the same as in the dot, the tunnel rates do not depend on spin. (b) Theexchange energy EX in the reservoirs close to the dot induces spin-dependent tunnel rates ↓ ↑
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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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1.2 Implementations Semiconductor F
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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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