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arXiv:cond-mat/0408051 · Physical Review B

Single qubit measurements with an asymmetric single-electron transistor

S. A. Gurvitz, G. P. Berman

Published Aug 3, 2005• 45 citations
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Abstract

We investigate qubit measurements using a single-electron transistor (SET). Applying the Schr\"odinger 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.

DOI
10.1103/physrevb.72.073303

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We investigate qubit measurements using a single-electron transistor (SET). Applying the Schr"odinger 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.
We consider a system of two solid state charge qubits, coupled to a single readout device, consisting of a single-electron transistor (SET). The conductance of each tunnel junction is influenced by its neighboring qubit, and thus the current through the transistor is determined by the qubits' state. The full counting statistics of the electrons passing the transistor is calculated, and we discuss qubit dephasing, as well as the quantum efficiency of the readout. The current measurement is then compared to readout using real-time detection of the SET island's charge state. For the latter method we show that the quantum efficiency is always unity. Comparing the two methods a simple geometrical interpretation of the quantum efficiency of the current measurement appears. Finally, we note that full quantum efficiency in some cases can be achieved measuring the average charge of the SET island, in addition to the average current.
In this paper we consider the continuous weak measurement of a solid‐state qubit by single electron transistors (SET). For single‐dot SET, we find that in nonlinear response regime the signal‐to‐noise ratio can violate the universal upper bound imposed quantum mechanically on any linear response detectors. We understand the violation by means of the cross‐correlation of the detector currents. For double‐dot SET, we discuss its robustness against wider range of temperatures, quantum efficiency, and the relevant open issues unresolved.
We consider charge qubit monitoring (continuous-in-time weak measurement) by a single-electron transistor (SET) operating in the sequential-tunneling regime. We show that commonly used master equations for this regime are not of the Lindblad form that is necessary and sufficient for guaranteeing valid physical states. In this paper we derive a Lindblad-form master equation and a corresponding quantum trajectory model for continuous measurement of the charge qubit by a SET. Our approach requires that the SET-qubit coupling be strong compared to the SET tunneling rates. We present an analysis of the quality of the qubit measurement in this model (sensitivity versus back action). Typically, the strong coupling when the SET island is occupied causes back action on the qubit beyond the quantum back action necessary for its sensitivity, and hence the conditioned qubit state is mixed. However, in one strongly coupled, asymmetric regime, the SET can approach the limit of an ideal detector with an almost pure conditioned state. We also quantify the quality of the SET using more traditional concepts such as the measurement time and decoherence time, which we have generalized so as to treat the strongly responding regime.
We report an experimental observation of the backaction of a single-electron transistor (SET) measuring the Coulomb staircase of a single-electron box. As current flows through the SET, the charge state of the SET island fluctuates. These fluctuations capacitively couple to the box and cause changes in the position, width, and asymmetry of the Coulomb staircase. A sequential tunneling model accurately recreates these effects, confirming this mechanism of the backaction of a SET. This is a first step toward understanding the effects of quantum measurement on solid-state qubits.