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arXiv:cond-mat/0406479

Dynamics of the Inductive Single-Electron Transistor

Mika Sillanpää, Leif Roschier, Pertti Juhani Hakonen

Published Jun 21, 2004• 2 citations
arXivHTMLPDF

Abstract

Using a classical equation of motion, dynamics of the phase is analyzed in the Inductive Single-Electron Transistor (L-SET) which is a promising new system suitable for quantum measurement with ultimate sensitivity and low back-action. In a regime of nonlinear dynamics, a shift of the oscillator resonant frequency is discovered which has a direct analogy to the switching of a dc-biased Josephson junction into voltage state. Results are reviewed for the predicted charge sensitivity, and it is shown that a performance challenging the best rf-SETs is foreseeable with the new device.

DOI
10.48550/arxiv.cond-mat/0406479

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Using a classical equation of motion, dynamics of the phase is analyzed in the Inductive Single-Electron Transistor (L-SET) which is a promising new system suitable for quantum measurement with ultimate sensitivity and low back-action. In a regime of nonlinear dynamics, a shift of the oscillator resonant frequency is discovered which has a direct analogy to the switching of a dc-biased Josephson junction into voltage state. Results are reviewed for the predicted charge sensitivity, and it is shown that a performance challenging the best rf-SETs is foreseeable with the new device.
A new type of electrometer is described that uses a single-electron transistor (SET) and that allows large operating speeds and extremely high charge sensitivity. The SET readout was accomplished by measuring the damping of a 1.7-gigahertz resonant circuit in which the device is embedded, and in some ways is the electrostatic "dual" of the well-known radio-frequency superconducting quantum interference device. The device is more than two orders of magnitude faster than previous single-electron devices, with a constant gain from dc to greater than 100 megahertz. For a still-unoptimized device, a charge sensitivity of 1.2 x 10(-5) e/hertz was obtained at a frequency of 1.1 megahertz, which is about an order of magnitude better than a typical, 1/f-noise-limited SET, and corresponds to an energy sensitivity (in joules per hertz) of about 41 Planck's over 2pi.
Here, we report the operation of a superconducting single-electron transistor (S-SET) as a fast and nearly quantum-limited charge-sensitive amplifier. By operating the S-SET such that Cooper pair tunneling is resonant across both of its tunnel junctions, we are able to achieve an excellent charge sensitivity of δq = 1.6 × 10-6e/√(Hz), while also minimizing back action. We find that near its optimal operating point, the S-SET can have both a very low noise temperature Tn≈ 50 mK and a large power gain ASET>;>; 1. These results indicate that our S-SET operates within a factor of 2 of the quantum limit.
The radio-frequency superconducting single electron transistor (RF-SET) is a highly sensitive and fast electrometer operating near the quantum limit. The back-action current noise of the SET induces voltage fluctuations on the system it is coupled to, dephasing its charge states. Here we propose to study the back action of the RF-SET by means of a double quantum dot (DQD) and, an RF-SET electrostatically coupled to one of the two dots. The inelastic current through the DQD is very sensitive to the spectral density of the voltage fluctuations in the nearby environment. By properly choosing the dot size and inter-dot tunnel barrier thickness, one can cause inelastic process to dominate the transport processes. A measurement of the inelastic current through the double dot system can then be used to calculate the spectral density of noise associated with the RF-SET and hence its back action. The design, fabrication and characterization of an RF-SET/DQD system is discussed in this work. Real-time studies of electron dynamics in coupled dots are also addressed.
We study the radio-frequency single-electron transistor (rf-SET) as a readout device for charge qubits. We measure the charge sensitivity of an rf-SET to be 6.3microe/sqrt[Hz] and evaluate the backaction of the rf-SET on a single Cooper-pair box. This allows us to compare the needed measurement time with the mixing time of the qubit imposed by the measurement. We find that the mixing time can be substantially longer than the measurement time, which would allow readout of the state of the qubit in a single shot measurement.
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 present results on a double-island single-electron transistor (DISET) operated at radio frequency (rf) for the fast and highly sensitive detection of charge motion in the solid state. Using an intuitive definition for the charge sensitivity, we compare a DISET to a conventional single-electron transistor (SET). We find that a DISET can be more sensitive than a SET for identical, minimum device resistances in the Coulomb blockade regime. This is of particular importance for rf operation, where ideal impedance matching to 50-Ω transmission lines is only possible for a limited range of device resistances. We report a charge sensitivity of 5.6×10−6e∕Hz for a rf-DISET, together with a demonstration of the single-shot detection of small (⩽0.1e) charge signals on microsecond time scales.