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

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86 J.M. Elzerman et al. effective g-factor geff, which can be larger than the bare g-factor (Fig. 36b). In this case, |↓〉electrons experience a thicker tunnel barrier than |↑〉electrons, resulting in a difference in tunnel rates [43]. In a magnetic field parallel to the 2DEG, the effect only leads to a modest spin-selectivity that does not allow a single-shot measurement. However, a much larger spin-selectivity is possible in a perpendicular magnetic field [88], i.e. in the Quantum Hall regime. Magnetotransport measurements in 2DEGs with odd filling factor have shown that the g-factor can be enhanced by as much as a factor of ten, depending on the field strength. We anticipate that a convenient perpendicular field of ∼4 T could already give enough spinselectivity to allow high-fidelity spin read-out. Therefore, spin read-out should be feasible not only in a large parallel magnetic field, but also in a somewhat smaller perpendicular field. 6.3 Initialization Initialization of the spin to the pure state |↑〉– the desired initial state for most quantum algorithms [1] – has been demonstrated in Sect. 5. Thereitwas shown that by waiting long enough, energy relaxation will cause the the spin on the dot to relax to the |↑〉ground state (Fig. 37a). This is a very simple and robust initialization approach, which can be used for any magnetic field orientation (provided that gµBB >5kBT ). However, as it takes about 5T1 to reach equilibrium, it is also a very slow procedure (≥10 ms), especially at lower magnetic fields, where the spin relaxation time T1 might be very long. A faster initialization method has been used in the “reverse pulse” technique in Sect. 5. By placing the dot in the read-out configuration (Fig. 37b), a spin-up electron will stay on the dot, whereas a spin-down electron will be replaced by a spin-up. After waiting a few times the sum of the typical tunnel times for spin-up and spin-down (∼1/Γ↑ +1/Γ↓), the spin will be with large probability in the |↑〉state. This initialization procedure can therefore be quite fast (
Semiconductor Few-Electron Quantum Dots as Spin Qubits 87 We also have the possibility to initialize the dot to a mixed state, where the spin is probabilistically in |↑〉or |↓〉. In Sect. 5, mixed-state initialization was demonstrated in a parallel field by first emptying the dot, followed by placing both spin levels below EF during the “injection stage” (Fig. 37c). The dot is then randomly filled with either a spin-up or a spin-down electron. This is very useful, e.g. to test two-spin operations (see paragraph 6.6). In a large perpendicular field providing a strong spin-selectivity, initialization to the |↑〉 state is possible via spin relaxation (Fig. 37a) or via direct injection (Fig. 37d). Initialization to a mixed state (or in fact to any state other than |↑〉) is very difficult due to the spin-selectivity. It probably requires the ability to coherently rotate the spin from |↑〉to |↓〉(see paragraph 6.5). 6.4 Coherence Times The long-term potential of GaAs quantum dots as electron spin qubits clearly depends crucially on the spin coherence times T1 and T2. In Sect. 5, wehave shown that the single-spin relaxation time, T1, can be very long – on the order of 1 ms at 8 T. This implies that the spin is only very weakly disturbed by the environment. The dominant relaxation mechanism at large magnetic field is believed to be the coupling of the spin to phonons, mediated by the spin-orbit interaction [22]. The fundamental quantity of interest for spin qubits is the decoherence time of a single electron spin in a quantum dot, T2, which has never been measured. Experiments with electrons in 2DEGs have established an ensembleaveraged decoherence time, T ∗ 2 , of ∼100 ns [89]. Recently, a similar lower bound on T2 has been claimed for a single trapped electron spin, based on the linewidth of the observed electron spin resonance [90]. Theoretically, it has been suggested that the real value of T2 can be much longer [22], and under certain circumstances could even be given by T2 =2T1, limited by the same spin-orbit interactions that limit T1. To build a scalable quantum computer, a sufficiently long T2 (corresponding to more than 10 4 times the gate operation time) is essential in order to reach the “accuracy threshold”. However, for experiments in the near future, we only need to perform a few spin rotations within T2, which might already be possible for much shorter T2, on the order of a µs. This should also be long enough to perform two-spin operations, which are likely to be much faster. To find the actual value of T2, the ability to perform coherent spin operations is required. This is discussed in the next paragraphs. 6.5 Coherent Single-Spin Manipulation: ESR We have not yet satisfied the key requirement for an actual spin qubit: coherent manipulation of one- and two-spin states. To controllably create superpositions of |↑〉and |↓〉, we can use the well-known electron spin resonance
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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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GaAs n-AlGaAs AlGaAs GaAs Semicondu
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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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