Time-resolved charge detection with cross-correlation techniques

Abstract

We present time-resolved charge sensing measurements on a GaAs double quantum dot with two proximal quantum point contact (QPC) detectors. The QPC currents are analyzed with cross-correlation techniques, which enables us to measure dot charging and discharging rates for significantly smaller signal-to-noise ratios than required for charge detection with a single QPC. This allows to reduce the current level in the detector and therefore the invasiveness of the detection process and may help to increase the available measurement bandwidth in noise-limited setups.

Full text

Page 1

arXiv:0810.2406v2 [cond-mat.mes-hall] 27 Feb 2009
Time-resolved charge detection with cross-correlation techniques
B. K¨ ung,∗O. Pf¨ affli, S. Gustavsson, T. Ihn, and K. Ensslin
Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
M. Reinwald and W. Wegscheider
Institut f¨ ur Experimentelle und Angewandte Physik,
Universit¨ at Regensburg, 93040 Regensburg, Germany
(Dated: January 13, 2009)
We present time-resolved charge-sensing measurements on a GaAs double quantum dot with two
proximal quantum point-contact (QPC) detectors. The QPC currents are analyzed with cross-
correlation techniques, which enable us to measure dot charging and discharging rates for signif-
icantly smaller signal-to-noise ratios than required for charge detection with a single QPC. This
allows us to reduce the current level in the detector and therefore the invasiveness of the detection
process and may help to increase the available measurement bandwidth in noise-limited setups.
PACS numbers: 73.23.Hk, 73.40.Gk
The use of quantum point contacts (QPCs) as charge
sensors integrated in semiconductor quantum dot (QD)
structures1has become a well-established experimental
technique in current nanoelectronics research. The time-
resolved operation of such sensors2,3,4allows us to ob-
serve the charge and spin dynamics of single electrons5,6
which has potential applications in metrology7or for
the implementation of qubit readout schemes in quan-
tum information processing.8Another appealing prop-
erty of the QD-QPC system is that it opens the possibil-
ity of studying a well-defined quantum mechanical mea-
surement process and testing the theory of measurement-
induced decoherence.9
The difficulty in achieving quantum-limited charge de-
tection is mainly the limited bandwidth of the readout
circuit compared to charge coherence times.
tion, decoherence mechanisms exist that are due to the
QPC but not directly linked to detection, such as the
excitation of electrons in the QD driven by noise in the
QPC,10an effect which is more pronounced at higher
source-drain voltages. Both problems are related to the
limit in signal-to-noise ratio (SNR) offered by present-
day setups. A common experimental approach to over-
come such a limitation is the use of cross correlation
of independent measurement channels. In the context
of charge sensing, correlation techniques have previously
been used in Al single electron transistor setups to sup-
press background charge noise11and to obtain estimates
for the spatial distribution of sources thereof.12High-
frequency noise measurements usually rely on correla-
tion techniques which eliminates noise contributions of
the wiring and the amplifiers.13
In the present work we present cross-correlated charge
sensing measurements in a double quantum dot (DQD)
sample with two charge readout QPCs. The potential
advantages of such a design for the continuous quan-
tum measurement of charge qubit oscillations have been
put forward by Jordan and B¨ uttiker.14While the cor-
responding time scales are yet beyond our experimen-
tally achievable bandwidth, we demonstrate the bene-
In addi-
fit of cross-correlation techniques in the classical detec-
tion of electron tunneling. By a detailed analysis of the
cross-correlation function of the QPC currents and of
higher-order correlators, we are able to measure tunnel-
ing rates in a manner eliminating uncorrelated amplifier
noise. Compared to a measurement of the same quan-
tities using only one channel, we are able to reduce the
detector current by roughly 1 order of magnitude.
VS (mV)
VD (mV)


395400 405410
−195
−190
−185
1
I
II
10 100 1000
Counts/s
VS (mV)
VD (mV)


395400405 410
−195
−190
−185
(0,0)
(1,0)
(0,1)
(1,1)
−1 −0.50 0.51
C0
S
1I
2I
500 nm
D
C
(a)
(b)
(c)
0.0
0.2
∆I (nA)
0123
Time (s)
Confguration I
PC2
PC1
0.0
0.2
∆I (nA)
0 0.02
Time (s)
0.04
Confguration II
PC1
PC2
FIG. 1: (Color online) (a) Inset: AFM micrograph of the
sample which consists of two QDs in series (QD1 and QD2)
with two charge readout QPCs, denoted PC1 and PC2. The
source, drain, and center barriers can be tuned with in-plane
gates S, D, and C. Main graph: part of the DQD charge sta-
bility diagram obtained by counting the number of switching
events in I2. (b) Detector currents recorded at two different
gate configurations indicated in (a). Dot-lead tunneling pro-
cesses (I) cause identical switching directions in both QPCs
whereas inter-dot processes (II) cause opposite switching.
(c) Current correlator C0 = ?I1I2?/(?I2
from the raw data used in (a), revealing the correlation-
anticorrelation pattern in the VS-VD plane. Numbers (n,m)
indicate the electron occupancy of the dots relative to the
state (0,0).
1??I2
2?)1/2extracted

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2
The inset of Fig. 1(a) shows the structure, fabricated
on a GaAs/AlGaAs heterostructure containing a two-
dimensional electron gas 34nm below the surface (den-
sity: 5 × 1015m−2and mobility: 40m2/Vs at 4.2K).
The electron gas was locally depleted by anodic oxi-
dation with an atomic force microscope (AFM).15The
measurements were performed in a3He/4He dilution re-
frigerator with an electron temperature of about 80mK,
as determined from the width of thermally broadened
Coulomb blockade resonances.16The structure consists
of two QDs in series (denoted QD1 and QD2) with two
charge-readout QPCs (PC1 and PC2). The strength of
the tunneling coupling to source and drain leads is tuned
with the gates denoted S and D; gate C controls the in-
terdot coupling and is kept at a constant voltage for these
measurements.
Both QPCs are voltage biased and tuned to conduc-
tances below 2e2/h. Their currents are measured with
an I/V converter with a bandwidth of 19kHz and sam-
pled at a rate of 50kS/s. The data is stored for further
processing in the form of time traces typically few sec-
onds long. Electrons entering or leaving either dot cause
steps in the currents that can be counted.2Figure 1(a)
shows a color plot of the count rate in PC2 vs S and
D gate voltages close to a pair of triple points of the
DQD system17at zero source-drain voltage. Lines with
negative slope belong to equilibrium tunneling events be-
tween the dots and the leads. The inter-dot charging en-
ergy (0.3meV) is much larger than the thermal energy,
therefore also the line of inter-dot tunneling events with
positive slope is observable. The corresponding tunnel-
ing rate of about 1kHz is the largest in the system. Few
additional counts outside the main resonances are due to
excitation processes driven by the currents in the QPCs
(Ref. 10) (source-drain voltage 300µV).
Due to geometry, the capacitive coupling between the
QPCs and the QDs is asymmetric; charging QD1 will, for
example, cause a larger step in the conductance of PC1
than charging QD2. Accordingly, the steps due to dot-
lead tunneling events have the same sign in both QPCs
whereas inter-dot events cause opposite switching as seen
in the time traces plotted in Fig. 1(b). A simple param-
eter which characterizes the correlation between the two
channels is the correlator
C0=
?I1I2? − ?I1??I2?
1? − ?I1?2??I2
??I2
2? − ?I2?2, (1)
where angular brackets denote time averaging. We ob-
tain this quantity, as well as any other cross-correlation
expression discussed later in this paper, by digital pro-
cessing of the raw time trace data. In Fig. 1(c), we plot
C0 calculated from the same data as used in panel (a).
It clearly displays the expected pattern of positive and
negative correlations along the charging lines of the DQD
stability diagram. Note that in the following, we implic-
itly assume the mean values of I1and I2to be subtracted
by setting ?I1? = ?I2? = 0.
Going beyond this more qualitative information, in the
following we analyze how to extract physical tunneling
rates with the help of cross-correlation techniques and
apply this to the example of tunneling from the lead into
and out of QD2 (rates Γinand Γout) in the present sam-
ple. The underlying problem is to extract these two char-
acteristic parameters of a random telegraph signal (RTS)
I(c)which is, as we assume, a component of both QPC
currents, along with uncorrelated noise. If the noise is
stronger than the signal, the information on the actual
time dependence of I(c)is lost even if there are two mea-
surement channels available. This is however not a prob-
lem since one can determine the rates Γin,outentirely on
the basis of time-averaged quantities derived from I(c).
For the analysis presented here, these are on the one hand
its autocorrelation function from which we can extract a
characteristic time constant τ0= 1/(Γin+ Γout) and on
the other hand its skewness γ which depends on the oc-
cupation probabilities of the high and low current states
of I(c)and allows one to determine the ratio Γin/Γout.
The sought-after Γin,outare then uniquely determined by
τ0 and γ. This concept of exploiting third-order cumu-
lants of a telegraph signal for measurement has also been
discussed in Ref. 18.
To state this more precisely, we split up the QPC cur-
rents according to Ij = αjI(c)+ I(n)
αjare dimensionless factors (α1> 0 by convention) and
I(n)
j
are mutually uncorrelated noise components. The
product of I1 and I2 appearing in the cross-correlation
function C(τ) = ?I1(t)I2(t + τ)? then consists of four
terms among which any one containing a factor I(n)
I(n)
2
is integrated to zero. The only nonvanishing part is
then proportional to the autocorrelation function of the
signal I(c),
j
, j = 1, 2, where
1
or
C(τ) ≈ α1α2?I(c)(t)I(c)(t + τ)?
= α1α2?I(c)2?e−|τ|/τ0,
where the decay time of the exponential is given by
τ0= 1/(Γin+Γout).19Note that form (2) of C(τ) implies a
purely Poissonian tunneling process. On time scales rele-
vant for our measurements, non-Poissonian statistics can
occur when excited dot states are involved20and would
manifest itself in a deviation of C(τ) from the exponential
shape. Figure 2(a) shows a set of C(τ) curves belonging
to the crossover from the (1,0) to the (1,1) state in the
DQD charge stability diagram. For curves in the cen-
ter of this plot, the electrochemical potential of QD2 is
roughly aligned with that of the lead, and the tunnel-
ing in and out rates are similar. The peak amplitude of
C(τ) is largest in this regime. It is proportional to ?I(c)2?
which is maximum in the case of a symmetric RTS, as
we discuss later in more detail. Moving away from this
point, the peak amplitude decays. The behavior of the
peak width outside the resonance is determined by the
behavior of the rates Γin,out: While one of the rates tends
to zero, the other approaches its finite saturation value
which is also the saturation value of 1/τ0.
width therefore remains nonzero.
(2)
The peak

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3
10-9
10-8
10-7
10-6
S (nA2/Hz)
101
102
103
104
f (Hz)
(SPC1SPC2)1/2
SC
SRTS
10
–4
10
–3
σ(〈 I1I2〉) (nA
2)
0.11 10100
T (ms)
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-4-2024
τ (ms)
μQD2−µlead = 33 µeV
µQD2−µlead = −20 µeV
2ln(2)τ0
〈I1I2〉
C(τ) (×10³ nA²)
(b) (a)
(c)
FIG. 2: (Color online) (a) Evolution of the current cross-
correlation function C(τ) = ?I1(t + τ)I2(t)? when crossing
the (1,0) → (1,1) charging line in the DQD stability diagram
[outside the scan range of Fig. 1(b)]. The curves are offset
for clarity; going from the lowest to the uppermost curve cor-
responds to adding one electron to QD2. C(τ) exhibits an
exponential decay ∼ exp(−|τ|/τ0) characteristic for the ran-
dom telegraph signal present in both QPC currents. The cen-
ter curves, which feature the largest amplitude C(0), belong
to QPC signals with rather balanced occupation of the high-
and low-current states. (b) Noise reduction due to cross cor-
relation in time traces measured on a Coulomb peak. Plotted
are the Fourier transform SC of the cross-correlation function
and the geometric mean of the two QPC current spectra SPC1
and SPC2. The dashed line represents the ideal RTS spec-
trum SRTS(f) = 2?I2
?I2
viation σ(?I1I2?) of the average ?I1I2? = T−1RT
as a function of the integration time T. The solid line marks
the expected ∼ T−1/2behavior.
RTS?τ0/[1 + τ2
0(2πf)2] with parameters
RTS? = 0.22 × 10−3nA2and τ0 = 0.8ms. (c) Standard de-
0I1(t)I2(t)dt
The noise reduction due to the cross correlation is
best visualized in the frequency domain. In Fig. 2(b),
we plot the geometric mean of the power spectral densi-
ties of some example time traces I1 and I2 along with
the Fourier transform of their cross-correlation func-
tion. The spectrum of the raw traces consists of the
Lorentzian contribution of the telegraph signal and a
noise background on the order of 10−7nA2/Hz which
is dominated by the (current-independent) noise of the
room-temperature I/V converter and contains an addi-
tional current-dependent part that is most likely related
to charge noise in the sample. In the cross-correlation
spectrum, the signal part is unchanged; the noise on the
other hand is clearly suppressed. This remains, for the
moment, a qualitative statement, and we postpone the
quantitative discussion about the noise reduction to the
end of the paper.
The correlation time τ0gives the sum of the two tun-
neling rates but is insensitive to their relative magnitude.
A second experimental parameter is therefore needed
which depends on Γin/Γoutand is also accessible in high-
noise conditions. It is natural to consider the skewness
γ = ?I(c)3?/?I(c)2?3/2because it parametrizes the degree
of asymmetry in the current distribution function of I(c),
which is in turn fully determined by Γin/Γout. Namely,
the occupation probability of the low-current state of the
RTS (electron on the dot) is plow= Γin/(Γin+Γout); anal-
ogously phigh = Γout/(Γin+ Γout). Assuming a current
difference of ∆I between the two states and ?I(c)? = 0,
then the nth central moment of I(c)is given by
?I(c)n? = plow(−phigh∆I)n+ phigh(plow∆I)n
=
(Γin+ Γout)n+1[Γn−1
ΓinΓout
in
− (−Γout)n−1]∆In. (3)
In calculating the skewness based on Eq. (3) for n = 2
and 3, we see that the current scale ∆I, i.e., the informa-
tion on the strength of the QD-QPC coupling, is elimi-
nated. After some algebra, we obtain the expression
γ =
?I(c)3?
?I(c)2?3/2=
Γin− Γout
(ΓinΓout)1/2.(4)
Using Eq. (4) and the previously determined τ0 =
1/(Γin+ Γout), we can now write down the total event
rate,
Γtot =
ΓinΓout
Γin+ Γout
= (Γin+ Γout)
ΓinΓout
Γ2
in+ 2ΓinΓout+ Γ2
out
=
1
τ0(4 + γ2).(5)
The individual tunneling rates are then given by
Γin/out=
2
τ0(4 + γ2∓ γ?4 + γ2).(6)
The skewness is experimentally accessed through an
appropriate combination of second- and third-order cor-
relators computed from the raw time traces I1 and I2
that have the property to be insensitive to the back-
ground noise.On the one hand, we use again ?I1I2?
which is the cross-correlation function at zero time differ-
ence C(τ = 0) and is equal to αiαj?I(c)2?. On the other
hand, we use the combinations ?I2
tional to the third moment of I(c). In writing the QPC
currents as a sum of signal and noise, Ij= αjI(c)+I(n)
it is readily seen that any term containing the noise I(n)
gives zero contribution to the time average and we have
?I2
pressed as
iIj? which are propor-
j
,
j
iIj? ≈ α2
iαj?I(c)3?.The skewness can then be ex-
γ ≈ sgn??I1I2
2????I2
1I2??I1I2
?I1I2?3
2?
?1/2
.(7)
The asymmetry in this formula is caused by our previous
choice α1> 0; i.e., we fixed the sign of I(c)such that it
is positively correlated with I1. This freedom of choice
is not unique to our correlation analysis. Instead, the

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4
−40−20
μQD2−μlead (μeV)
02040
0
0.1
0.2
0.3
Rate (kHz)


0
1
2
Rate (kHz)


0
0.5
1
Rate (kHz)


Γtot
X
C
Γtot
Γout
X
C
Γout
Γin
C
Γin
X
FIG. 3:
Γtot = ΓinΓout/(Γin+Γout) as determined by electron counting
(marked with the letter “C”) and by current cross-correlation
(“X”). The sweep range is indicated by a line in the top graph
of Fig. 4(a).
(Color online) Plots of the rates Γin, Γout, and
assignment of one detector event type (e.g., “PC1 current
up”) to one system event type (e.g., “electron tunneling
from QD2 into lead”) has to be done in any case.
Before turning to the experimental results, we discuss
the role of the integration time T in the cross-correlation
process. How large do we have to choose T until the
cross-correlation function (2) is reproduced to a good ac-
curacy? In order to estimate the remaining noise contri-
bution to C(τ) after averaging, we treat the integration
as a summation over samples that are separated in time
by the typical autocorrelation time of the noise τn and
are therefore statistically independent. Using the cen-
tral limit theorem, we write the standard deviation of
this sum as (τn/T)1/2(σ(n)
where we have introduced the symbols σ(n)
for the noise in the channels. It should not exceed the
contribution of the telegraph signal α1α2?I(c)2?. For the
data presented here, time traces were recorded for 5s
and digitally low-pass filtered at 3kHz (τn ≈ 0.1ms),
yielding an expected noise reduction of 0.005. As seen
from Eq. (3), the quantity α1α2?I(c)2? contains a factor
ΓinΓoutand is therefore small whenever one of the tun-
neling rates is small. As a result, the situation where
the two rates are similar presents the optimal case for a
correlation measurement.
Even disregarding any uncorrelated noise, the expo-
nential shape of the autocorrelation function of I(c)is the
limit of infinite integration time. It is practically reached
under the condition that T covers a sufficient number of
switching events, T ≫ 1/Γtot. This second condition on
T is therefore linked to the statistical uncertainty of the
measurement.
In Fig. 3, we compare the outcome of the conventional
(counting) method and the correlation procedure for a
constant bias of 222µV across the QPCs. The two data
sets are generally in good agreement, with small system-
1 σ(n)
2 )1/2[cf. Fig. 2(a), inset],
j
= ?I(n)2
j
?1/2
atic deviations on the sides of the Coulomb peak and
a certain scatter due to low statistics in the tails. The
observed asymmetry between tunneling in and out pro-
cesses (i.e., the difference in the maximum values of Γin
and Γout) can be explained by the existence of a second
degenerate quantum state in QD2.
Having checked the consistency of the two methods in
a regime where both are applicable, we test the correla-
tion method in a regime with smaller signal levels. We do
this by reducing the source-drain voltage on the QPCs.
The step height αj∆I(c)of the RTS is approximately pro-
portional to the bias whereas the noise level σ(n)
constant. The ratio of the two is the SNR relevant for the
standard counting analysis. an insufficient SNR will re-
sult in systematic measurement errorsdue to false counts,
namely, an overestimation of the slower rate in case of an
asymmetric RTS, or of both rates in case of a symmetric
RTS. Assuming a certain current distribution of the am-
plifier noise around the discrete current levels of the RTS,
say a Gaussian distribution, the false count rate can be
estimated as the number of statistically independent cur-
rent measurements that lie outside a distance αj∆I(c)/2
from the mean. We can express it with the help of the er-
ror function as 0.5[1−erf(SNR/2√2)]/τn. The lower plot
in Fig. 4(a) shows a measurement of the signal-to-noise
ratio along with the estimated false count rate calculated
in this manner. The value for the SNR considered suffi-
cient depends on the desired accuracy; here we require a
SNR of more than 6 which results in a false count rate on
the order of 10Hz and which is reached for source-drain
voltages larger than 150µV.
j
remains
In comparison, the measurement of Γtotshown in the
upper plot of Fig. 4(a) demonstrates that the cross-
correlation analysis is applicable down to significantly
lower bias voltages, therefore reducing both the power
dissipated by the sensors and the energy scale of the emit-
ted radiation. As discussed, the best results are obtained
close to the maximum of the peak where the rate is mea-
sured reliably, i.e., with fluctuations below the statistical
uncertainty due to the finite number of detected events,
down to bias voltages of 22µV. Only below (and in the
tails of the peak) the errors grow and eventually the anal-
ysis algorithm fails.
We now formulate a more precise criterion for compar-
ing the two methods. In particular, it is first of all neces-
sary to quantify the residual noise. For this purpose, we
define σ(n)
X
as the standard deviation of the fluctuations
in the function C(τ) [cf. Fig. 2(a)] measured in the ab-
sence of a RTS signal. The ratio (σ(n)
be considered as a measure for the success in suppress-
ing the noise by current cross correlation. However, the
quantitative meaning of the noise level in the correlation
case is different compared to the counting case. The ac-
tual parameter of interest is the measurement uncertainty
caused by this noise. Calculating it in the general case is
a nontrivial task, on the one hand, because of the com-
plexity of the analysis algorithm and, on the other hand,
X/σ(n)
1 σ(n)
2 )1/2can

Page 5

5
0.84
0.80
0.76
0.72
I2 (nA)
II: QPC bias 82 μV
0.20
0.24
0.28
I2 (nA)
01020 3040
Time (ms)
III: QPC bias 22 μV
250
P(I) (nA-1)
2.25
2.15
2.05
I2 (nA)
I: QPC bias 222 μV
00100100200 200
10
10
10
10
0
1
2
3
False Counts/sec
0
2
4
6
8
SNR
QPC bias (µV)
VS (mV)


435
436
437
I
II
III
0200 400
ΓX
tot (Hz)
(a) (b)
FIG. 4: (Color online) (a) Top: tunneling rate ΓX
QD2 and lead as a function of QPC bias (applied to both PC1
and PC2) and S gate voltage determined by cross-correlation
analysis.Bottom: SNR for the counting analysis and ex-
pected false count rate as a function of QPC bias.
false count rate was calculated from the SNR data assum-
ing Gaussian amplifier noise with an autocorrelation time of
τn = 0.1ms. A SNR of 6 will result in a false count rate
on the order of 10Hz and can therefore be considered as the
minimum requirement for the counting analysis. It is reached
for bias voltages above approximately 150µV. (b) Examples
of the time dependence (left column) and current distribution
function P(I) (right column) of I2 recorded at three different
QPC bias voltages indicated in the top graph in (a). The RTS
as a component of the current is recognized by the naked eye
in all three cases, but only the trace “I” allows for a determi-
nation of the transition rates without significant error when
analyzed with a counting algorithm.
totbetween
The
because of the many experimental variables that play a
role such as the absolute value of Γtot, RTS asymmetry,
measurement bandwidth, noise spectrum, and differences
between the two channels (i.e., in the parameters αjand
σ(n)
j
). We therefore restrict our discussion to the specific
measurement situation discussed in this paper, in par-
ticular, to the case of nearly identically coupled QPCs
(α1 = α2 = 1). We ask this question: by how much,
starting from the limiting counting SNR of 6, can we
reduce the signal strength ∆I until we expect the corre-
lation procedure to generate the same absolute error of
about 10Hz in Γtot? We write this “figure of merit” as
∆Imin,X
∆Imin,C
=
∆Imin,X
?
σ(n)
X
?
σ(n)
σ(n)
X
?
1 σ(n)
2
?
σ(n)
1 σ(n)
∆Imin,C
2
. (8)
The third factor in Eq. (8) is the original (inverse) SNR
for the counting algorithm. The first factor can be consid-
ered as the analog for the cross-correlation case, relating
the signal strength to the residual noise σ(n)
was determined with a numerical simulation. In apply-
ing the data analysis algorithm to randomly generated
time traces imitating the experimental ones (symmetric
RTS with overlaid Gaussian noise, low-pass filtering with
3kHz, Γtot= 0.3kHz, and T = 5s), the measurement un-
certainty is obtained from the scatter in the output. The
minimum ∆I for an error below 10Hz determined in this
way was given by 11(σ(n)
in Eq. (8) is the noise reduction achieved in experiment;
we measured σ(n)
and σ(n)
2
≈ 16 × 10−12A. Plugging in these numbers we
find
X
in C(τ). It
X)1/2. Finally, the second factor
X≈ 2.2×10−24A2, σ(n)
1
≈ 21×10−12A,
∆Imin,X
∆Imin,C
≈ 11 ·
1
√150·1
6= 0.15.(9)
This means that in the case of the correlation experiment
one can obtain meaningful values for the tunneling rates
for signal-to-noise ratios approaching 1.
To summarize, we have measured charge fluctuations
on a GaAs DQD in a time-resolved manner simulta-
neously with two QPC charge sensors. By evaluating
their cross-correlation function and third-order correla-
tors, we are able to determine the two time constants
of tunneling back and forth between one dot and the
adjacent lead. Obtaining the same information directly
from either of the two QPC signals requires a signifi-
cantly larger RTS amplitude because of the limitation
due to amplifier noise. An interesting prospect is the ap-
plication of the correlation technique to radio-frequency
QPC setups21,22,23where it would allow us to push the
shot-noise limitation to the detection bandwidth toward
the regime of charge qubit coherence times.
The authors thank Yuval Gefen and Lieven Vander-
sypen for fruitful discussion. Financial support from the
Swiss National Science Foundation (Schweizerischer Na-
tionalfonds) is gratefully acknowledged.
∗Electronic address: kuengb@phys.ethz.ch
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