Physics Letters A 311 (2003) 292–296
Negative result measurements in mesoscopic systems
Department of Particle Physics, Weizmann Institute of Science, Rehovot 76100, Israel
Received 25 November 2002; accepted 25 March 2003
Communicated by J.P. Vigier
We investigate measurement of electron transport in quantum dot systems by using single-electron transistor as a non-invasive
detector. It is demonstrated that such a detector can operate in the “negative-result measurement” regime. In this case the
measured current is not distorted, providing that it is a non-coherent one. For a coherent transport, however, the possibility of
observing a particular state out of coherent superposition leads to distortion of a measured current even in the “negative-result
measurement” regime. The corresponding decoherence rate is obtained in the framework of quantum rate equations.
2003 Elsevier Science B.V. All rights reserved.
PACS: 03.65.Bz; 73.20.Dx; 73.23.Hk
Rapid progress in nanoscale devices made it possi-
ble to produce new type of detectors like the quantum
point-contact and the single-electron transistor (SET),
which have been already used in different quantum
measurements [1–4]. These devices have been consid-
ered also as possible detectors for a single two level
system (q-bit) [5–7]. It is of a great advantage that
these detectors can be treated entirely quantum me-
chanically, so that the related measurement process
can be investigated in great details. In particular, one
can study quantum mechanical mechanism of deco-
herence and its inﬂuence on a measured system.
In this Letter we consider a measurement of elec-
tron current in quantum dots by using SET in close
proximity of a measured system, so it monitors the
movement of single electrons inside the system [2,4].
E-mail address: firstname.lastname@example.org
We demonstrate that varying parameters of SET one
can put it in the “negative result measurement” regime
. In this case the detector becomes a non-distractive
if a measured current is incoherent one. However, in
the case of coherent measured current, the negative
result measurement distorts it via the decoherence.
We evaluate the decoherence rate for this process and
demonstrate that it is directly related to a possibility of
observation of a particular quantum state of the mea-
sured system out of the linear superposition. Other-
wise the negative result measurement would not affect
the measured current, even if the latter is a coherent
one. This phenomenon produces a peculiar effect in
the current which can be observed experimentally.
We start with a description of measurement of
resonant tunneling currents in quantum dots by using
SET. The system is shown schematically in Fig. 1 .
The SET, represented by the upper dot, is in close
proximity to the lower dot (the measured system).
Both dots are coupled to two separate reservoirs at
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