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

80 J.M. Elzerman et al.
∆I QPC (nA)
2
1
0
a
t wait
0.2 0.3 0.4
Time (ms)
Injected fraction
1.0
0.5
0.0
b
waiting time ( µ s):
100
129
161
195
273
1500
1.4 1.6 1.8
Injection threshold (nA)
Fig. 33. Setting the injection threshold. (a) Example of QPC-signal for the shortest
waiting time used (0.1 ms). The dotted horizontal line indicates the injection threshold.
Injection is declared successful if the QPC-signal is below the injection threshold
for a part or all of the last 45 µs before the end of the injection stage (twait). Traces
in which injection was not successful, i.e. no electron was injected during twait, are
disregarded. (b) Fraction of traces in which injection was successful, out of a total
of 625 taken for each waiting time. The threshold chosen for analysing all data is
indicated by the vertical line
5.6 Measurement Fidelity
For applications in quantum information processing it is important to know
the accuracy, or fidelity, of the single-shot spin read-out. The measurement
fidelity is characterised by two parameters, α and β (inset to Fig. 34a), which
we now determine for the data taken at 10 T.
The parameter α corresponds to the probability that the QPC-current exceeds
the threshold even though the electron was actually spin-↑, for instance
due to thermally activated tunnelling or electrical noise (similar to “dark
counts” in a photon detector). The combined probability for such processes
is given by the saturation value of the exponential fit in Fig. 31c, α, which
depends on the value of the threshold current. We analyse the data in Fig. 31c
using different thresholds, and plot α in Fig. 34b.
The parameter β corresponds to the probability that the QPC-current
stays below the threshold even though the electron was actually spin-↓ at the
start of the read-out stage. Unlike α, β cannot be extracted directly from the
exponential fit (note that the fit parameter C = p(1 − α − β) contains two
unknowns: p = Γ↓/(Γ↑ +Γ↓) andβ). We therefore estimate β by analysing the
two processes that contribute to it. First, a spin-↓ electron can relax to spin-
↑ before spin-to-charge conversion takes place. This occurs with probability
β1 =1/(1 + T1Γ↓). From a histogram (Fig. 34a) of the actual detection time,
tdetect (see Fig. 31b), we find Γ −1
↓
≈ 0.11 ms, yielding β1 ≈ 0.17. Second, if
the spin-↓ electron does tunnel off the dot but is replaced by a spin-↑ electron
within about 8 µs, the resulting QPC-step is too small to be detected. The