We investigate qubit measurements using a single electron transistor (SET). Applying the Schrödinger equation to the entire system we find that an asymmetric SET is considerably more efficient than a symmetric SET. Yet, its efficiency does not reach that of an ideal detector even in the large asymmetry limit. We also compare the SET detector with a point-contact detector. This comparison allows us to illuminate the relation between information gain in the measurement process and the decoherence generated by these measurement devices. : 73.50.-h, 73.23.-b, 03.65.Yz.
PACSAn obvious candidate for read-out of the two-state system (qubit) is the single electron transistor (SET) [1,2]. In many respects it is better than the point-contact (PC) detector [1], which has already been used for quantum measurements [3]. It has been shown, however, that the symmetric SET has a rather low sensitivity in its normal working regime [4,5]. Therefore it becomes very important to investigate how to improve the effectiveness of the SET by a proper selection of its parameters.In this Letter we examine qubit measurements using the SET by applying the Schrödinger equation to the entire system of the qubit and detector. In this case, we can unambiguously determine the backaction of the charge fluctuations in the SET on the qubit and the sensitivity of the measurement as a function of the detector parameters. We find that by varying the tunneling barriers of the SET, one can force the latter to operate in a regime where the "active measurement" time is very short. Then the SET behaves as a linear quantum detector even if it is strongly coupled to the measured system. We also demonstrate that in this regime the effectiveness of the SET considerably increases, although it does not reach the ultimate value corresponding to an ideal detector. By varying the set-up parameters of the SET one can investigate decoherence generated by this detector in the operation mode in which the signal decreases to zero. This illuminates the relationship between decoherence and distinguishability in different types of measurements.Consider an electrostatic qubit, represented by an electron in a coupled dot. The qubit is placed in close proximity to the SET, Fig. 1. The latter is shown as a potential well, coupled to two reservoirs at different chemical potentials, µ L,R . We assume that the bias voltage V = µ L − µ R is smaller than the energy spacing of the single particle states of the well. This condition is usually realized in semiconductor quantum dots [6]. Then transport takes place through an individual single particle level, E 0 , in contrast to a metallic SET, in which many conducting levels contribute to transport [7]. One finds that if the electron occupies the upper dot (Figs. 1a,1b) the current flows through the level E 0 of the SET. However, if the electron occupies the lower dot (Figs. 1c,1d), the SET is blocked due to the electronelectron repulsion U . Here we assume that U is large enough so that, where Γ L,R are the partial widths of the leve...