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

Spin-down counts
200
100
a
Semiconductor Few-Electron Quantum Dots as Spin Qubits 81
1-β
α
β
1-α
0
0.0 0.2 0.4
Detection time (ms)
d
u
Probability
1.0
0.8
0.6
0.4
0.2
0.0
b
α
1-β
1-β 2
0.6 0.8 1.0
Threshold (nA)
Fig. 34. Measurement fidelity. (a) Histogram showing the distribution of detection
times, tdetect, in the read-out stage (see Fig. 31b for definition tdetect). The exponential
decay is due to spin-↓ electrons tunnelling out of the dot (rate = Γ↓) and
due to spin flips during the read-out stage (rate = 1/T1). Solid line: exponential fit
with a decay time (Γ↓ +1/T1) −1 of 0.09 ms. Given that T1 = 0.55 ms, this yields
Γ −1
↓
≈ 0.11 ms. Inset: fidelity parameters. A spin-↓ electron is declared “down” (d)
or “up” (u) with probability 1 − β or β, respectively. A spin-↑ electron is declared
“up” or “down” with probability 1−α or α, respectively. (b) Open squares represent
α, obtained from the saturation value of exponential fits as in Fig. 31c for different
values of the read-out threshold. A current of 0.54 nA (0.91 nA) corresponds to
the average value of ∆IQP C when the dot is occupied (empty) during tread. Open
diamonds: measured fraction of “reverse-pulse” traces in which ∆IQP C crosses the
injection threshold (dotted black line in Fig. 31d). This fraction approximates 1−β2,
where β2 is the probability of identifying a spin-↓ electron as “spin-up” due to the
finite bandwidth of the measurement setup. Filled circles: total fidelity for the spin-
↓ state, 1 − β, calculated using β1 =0.17. The vertical dotted line indicates the
threshold for which the visibility 1 − α − β (separation between filled circles and
open squares) is maximal. This threshold value of 0.73 nA is used in the analysis of
Fig. 31
probability that a step is missed, β2, depends on the value of the threshold.
It can be determined by applying a modified (“reversed”) pulse (Fig. 31d).
For such a pulse, we know that in each trace an electron is injected in the
dot, so there should always be a step at the start of the pulse. The fraction
of traces in which this step is nevertheless missed, i.e. ∆IQP C stays below
the threshold (dotted black line in Fig. 31d), gives β2. We plot 1 − β2 in
Fig. 34b (open diamonds). The resulting total fidelity for spin-↓ is given by
1 − β ≈ (1 − β1)(1 − β2)+(αβ1). The last term accounts for the case when a
spin-↓ electron is flipped to spin-↑, but there is nevertheless a step in ∆IQP C
due to the dark-count mechanism 6 . In Fig. 34b we also plot the extracted
value of 1 − β as a function of the threshold.
6 Let us assume there is a spin-↓ electron on the dot at the start of the read-out
stage. The probability that the ↓-electron tunnels out (i.e. that it does not relaxto